ACS Physical Chemistry Thermochemistry Study Guide

What is the third law of thermodynamics?

The entropy of a perfect crystal is zero.

What is the second law of thermodynamics?

As a whole, the universe always tends towards increasing entropy.

What is the relationship between number of microstates and entropy?

More microstates = higher entropy

What is the relationship between temperature and entropy?

Temperature increases, entropy increases (direct)

What is the relationship between atomic weight and entropy?

Heavier = increased entropy (direct)

What happens to entropy when a substance is dissolved in another?

Entropy increases

What is the relationship between moles of gas and entropy?

When moles of gas increase, entropy increases (direct)

What is the relationship between free energy, enthalpy, and entropy?

deltaG(system)=deltaH(system)-TdeltaS(system)

What does change in G measure?

The extent of the spontaneity of a process, and the useful energy available from it

What is the relationship between work and spontaneous processes?

Spontaneous processes produce work

What is the relationship between work and non-spontaneous processes?

Non-spontaneous processes require work

What does -w mean?

Work is being produced - spontaneous

What does a positive sign for w mean?

Work is required - non-spontaneous

Can a change be spontaneous in both directions?

No

What is an extensive property?

Value depends on the amount of substance

What does ΔG > 0 mean?

Non-spontaneous process - requires work

What does ΔG < 0 mean?

Spontaneous process - produces work

What does standard free energy of formation mean? ΔGo

The free energy change that occurs when 1 mole of a compound is made from its elements

What is the standard free energy of formation for an element in its standard state? ΔGf

0

What does reversing a reaction do to the standard free energy of formation? ΔG0

Changes its sign

Why are most exothermic reactions spontaneous?

Because the large negative ΔH/large energy release makes the free energy change negative.

What happens when ΔH and ΔS have opposite signs?

The reaction occurs spontaneously at all temperatures or at none.

What happens when enthalpy (ΔH) is negative and entropy (ΔS) is positive?

Spontaneous at all temperatures, negative free energy

What is the likely sign of ΔH and ΔS for a combustion reaction?

Negative ΔH, positive ΔS

What happens when ΔH is positive and ΔS is negative?

Nonspontaneous at all temperatures

What happens when ΔH and ΔS are both positive?

Reaction becomes spontaneous as temperature increases

What happens when ΔH and ΔS are both negative?

Reaction becomes spontaneous as temperature decreases

Why can the maximum work of a system never obtained from a real process?

Because such an irreversible process will always involve some free energy being converted to heat

How do you find where a reaction becomes spontaneous?

Set ΔG equal to zero and solve -- use T=deltaH/deltaS to find the temperature value.

Is a chemical reaction proceeding to equilibrium a spontaneous or non-spontaneous change?

Spontaneous

How to determine reaction direction from ΔG?

ΔG<0 reaction proceeds to the right ΔG>0 reaction proceeds to the left

Which direction does the reaction proceed if ΔG is positive?

To the left / to reactants

Which direction does the reaction proceed if ΔG is negative?

To the right/ to products

How to predict ΔS(system)? (change in entropy of a system)

Positive ΔS(system) means available microstates increases/disorder increases

How to calculate the ΔSo (aka standard entropy change) of the formation of one mole of gas from its elements?

1. Write the balanced chemical equation with the proper coefficients that make the product ONE MOLE. 2. Find the value of the one mole of product in Appendix B. This is the deltaS(standard) for the product. 3. Find the value of the reactants in Appendix B for deltaS(standard) and multiply them by the coefficients you got in step 1. 4. Use total = products-reactants for your final value.

How to calculate ΔG (free energy) using enthalpy ΔH and entropy ΔS values?

ΔG=ΔH-TΔS

What is the equation that relates ΔG to K?

ΔG=-RT ln K

What is the Boltzmann constant?

ln(# of microstates)

What does a big W mean?

More microstates

What does more microstates mean?

Big ΔS - more entropy

What does fewer microstates mean?

Smaller ΔS - less entropy

What happens to entropy when volume is increased?

Microstates increase, entropy increases

What is the relationship between ΔS of a system, q, and T?

ΔS(system)=qrev/T

What happens to entropy ΔS when temperature increases?

It increases

What is the relationship between mass and entropy ΔS?

As mass increases, entropy increases

What is the relationship between molecular complexity and entropy ΔS?

As molecular complexity increases, entropy increases

What is the relationship between ΔG and Q?

ΔG=RTlnQ

What happens to K as ΔG becomes more positive?

It gets smaller

What happens to K as ΔG becomes more negative?

It gets bigger

What direction does a reaction proceed if ln Q/K is positive?

Reaction proceeds to the left/reactants

What direction does a reaction proceed if ln Q/K is negative?

Reaction proceeds to the right/products

Extensive Property

property which is directly proportional to the size of the system (i.e.. V, m, E )

Intensive Property

property which does not depend on the size of the system (i.e. P, T, density, molar volume)

van der Waals constants

a reflects how strong the molecules attract each other (IM forces); b reflects the size of the molecule --- van der Waals equation extends beyond the ideal gas law to take into account attractive and repulsive forces

Isotherm

plot of P as a function of molar volume at constant temperature

Law of Corresponding States

Law which states "all gases have the same properties of they are compared at corresponding conditions"

Boyle Temperature

temperature at which repulsive and attractive interactions cancel and the gas appears to behave ideally

Heat (q)

the manner of energy transfer that results from temperature difference between system and surroundings ("unorganized motion")

Work (w)

the transfer of energy between system and surroundings as a result of existence of unbalanced forces between the two ("organized motion")

State Function

property that depends on the state of the system, and not upon the history of the system (i.e. energy, entropy)

Reversible Process

when pressure the pressure exerted on the system and the pressure of the system differ only infinitesimally so slight changes are able to be made

Path Function

property that depends on the path taken to reach the state of the system

Adiabatic Process

process which no energy as heat is transferred (dq = 0 ; therefore, dU=dw )

Enthalpy (H)

total heat content of a system; it is equivalent to the internal energy plus the products of pressure and volume

Heat of Combustion

the heat involved in a combustion reaction --chemical reactions that absorb heat ( dH > 0) are called endothermic --chemical reactions that release heat (dH <0) are called exothermic

Entropy (S)

unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system ---dS=0 for cyclic processes or reversible processes in isolated system ---dS > 0 for spontaneous processes in isolated systems

Helmoltz Energy (A)

= U - TS ---will decrease during any spontaneous process that occur at constant T and V and will achieve its minimum value at equilibrium

Gibbs Energy (G)

= H - TS = A + PV ---will decrease as a result of any spontaneous process until the system reaches equilibrium

Fugacity

thermodynamic property which described the deviations of ideality; the ratio f/p is the coefficient

Gibbs Phase Rule

F = C - P + 2 ---Phase (P): numer of phases ( P=1 is for within a region, P=2 is for on the coexistence curve, P=3 is for at the critical point) ---Component (C): chemically independent variable describing how many components are in the system ---Degrees of Freedom (F): number of intensive variables we can change yet still be in the same phase

Azeotrope

a mixture for which there is no change in composition upon boiling (not possible to achieve separation)

Colligative Property

property which depends only on the number of solute particles present, not on their identity (i.e. vapor pressure, boiling point, freezing point, osmotic pressure)

Reaction Quotient (Q) vs. Equilibrium Constant (K)

--- at equilibrium dG=0 ; Qp=Kp --- If Qp < P: dG <0 so reaction is moving L to R --- If Qp > P: dG >0 so reaction is moving R to L

Colloids

Contains some particles that are intermediate in size between the small particles in a solution and the larger particles in a suspension

Bose-Einstein Condensate

Fifth state of matter that exists at extremely low temperatures and atoms behave as a single particle

Pressure

Result of force distributed over an area

Charles's Law

The volume of a gas is directly proportional to its temperature in kelvins if the pressure and the # of particles of the gas are constant

Boyle's Law

The volume of a gas is inversely proportional to its pressure if the temperature and the # of particles are constant

Endothermic

The system absorbs energy from its surroundings

Heat of Fushion

The energy a substance must absorb in order to change from a solid to liquid

Exothermic

The system releases energy to its surroundings

Deposition

When a gas changes directly to a solid

Sublimation

When a solid changes directly to a gas

Alkaline Earth Metals

The elements in group 2A; differences shown by reactivity to water

Halogens

The elements in group 7A; highly reactive nonmetals

Noble Gases

The elements in group 8A; colorless odorless and extremely unreactive

Anion

An ion with a negative charge

Cation

An ion with a positive charge

Polar Covalent Bond

A covalent bond in which electrons are not shared equally

2. An equation of state interrelates

pressure, volume, temperature, and amount of substance: p = f(T,V,n).

6. A diathermic boundary is a boundary that

permits the passage of energy as heat.

7. An adiabatic boundary is a boundary that

prevents the passage of energy as heat.

7. Thermal equilibrium is a condition in which

no change of state occurs when two objects A and B are in contact through a diathermic boundary.

8. The Zeroth Law of thermodynamics states that

if A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A.

9. The Celsius and thermodynamic temperature scales are related by

T/K = θ/°C + 273.15.

10. A perfect gas obeys the perfect gas equation

pV = nRT, exactly under all conditions.

11. Dalton's law states that the

pressure exerted by a mixture of gases is the sum of the partial pressures of the gases.

12. The partial pressure of any gas is defined as

p_J = x_J p, where x_J = n_J/n is its mole fraction in a mixture and p is the total pressure.

13. In real gases, molecular interactions affect the equation of state; the true equation of state is expressed in terms of virial coefficients

B, C, . . . : pV_m = RT(1 + B/V_m + C/V^2_m + · · · ).

14. The vapour pressure is the

pressure of a vapour in equilibrium with its condensed phase.

15. The critical point is the point at which the

volumes at each end of the horizontal part of the isotherm have merged to a single point. The critical constants p_c, V_c, and T_c are the pressure, molar volume, and temperature, respectively, at the critical point.

16. A supercritical fluid is a

dense fluid phase above its critical temperature and pressure.

17. The van der Waals equation of state is an

approximation to the true equation of state in which attractions are represented by a parameter a and repulsions are represented by a parameter b: p = nRT/(V− nb) − a(n/V)^2.

18. A reduced variable is

the actual variable divided by the corresponding critical constant.

19. According to the principle of corresponding states, real gases at the same reduced volume and reduced temperature exert

the same reduced pressure.

2. The system is the part of the world in which we have a special interest. The surroundings is the region

outside the system where we make our measurements.

3. An open system has a boundary through which matter can be

transferred.

3. A closed system has a boundary through which matter

cannot be transferred.

3. An isolated system has a boundary through which

neither matter nor energy can be transferred.

4. Energy is the capacity to

do work. The internal energy is the total energy of a system.

5. Work is the transfer of energy by motion against an opposing force,

dw = −Fdz . Heat is the transfer of energy as a result of a temperature difference between the system and the surroundings.

6. An exothermic process

releases energy as heat to the surroundings.

6. An endothermic process

absorbs energy as heat from the surroundings.

7. A state function is a property that depends only on

the current state of the system and is independent of how that state has been prepared.

8. The First Law of thermodynamics states that

the internal energy of an isolated system is constant, ΔU = q + w.

9. Expansion work is the work of expansion (or compression) of a system,

dw = −p_exdV. The work of free expansion is w = 0.

9. The work of expansion against a constant external pressure is

w = −p_exΔV.

9. The work of isothermal reversible expansion of a perfect gas is

w = −nRT ln(V_f /V_i).

10. A reversible change is a change that

can be reversed by an infinitesimal modification of a variable.

11. Maximum work is achieved in a

reversible change.

12. Calorimetry is the study of

heat transfers during physical and chemical processes.

13. The heat capacity at constant volume is defined as

C_V = (∂U/∂T) _V.

14. The heat capacity at constant pressure is

C_p = (∂H/∂T) _p.

14. For a perfect gas, the heat capacities are related by

C_p − C_V = nR.

14. The enthalpy is defined as

H = U + pV.

14. The enthalpy change is the

energy transferred as heat at constant pressure, ΔH = q_p.

15. During a reversible adiabatic change, the temperature of a perfect gas varies according to

T_f = T_i(V_i/V_f)^(1/c), c = CV,m/R. The pressure and volume are related by pV^γ = constant, with γ = C_p,m/C_V,m.

16. The standard enthalpy change is the

change in enthalpy for a process in which the initial and final substances are in their standard states. The standard state is the pure substance at 1 bar.

17. Enthalpy changes are additive, as in

Δ_subH® = Δ_fusH® + Δ_vapH® .

18. The enthalpy change for a process and its reverse are related by

ΔforwardH® = −ΔreverseH®.

19. The standard enthalpy of combustion is the

standard reaction enthalpy for the complete oxidation of an organic compound to CO2 gas and liquid H2O if the compound contains C, H, and O, and to N2 gas if N is also present.

20. Hess's law states that the standard enthalpy of an overall reaction is the

sum of the standard enthalpies of the individual reactions into which a reaction may be divided.

21. The standard enthalpy of formation (Δ_fH® ) is the

standard reaction enthalpy for the formation of the compound from its elements in their reference states. The reference state is the most stable state of an element at the specified temperature and 1 bar.

22. The standard reaction enthalpy may be estimated by combining enthalpies of formation

Δ_rH® =ΣProducts νΔfH® −ΣReactants νΔfH® .

23. The temperature dependence of the reaction enthalpy is given by Kirchhoff's law

Δ_rH® (T2) = Δ_rH® (T1) + Integral (T2 to T1) Δ_rC® pdT.

24. An exact differential is an

infinitesimal quantity that, when integrated, gives a result that is independent of the path between the initial and final states. An inexact differential is an infinitesimal quantity that, when integrated, gives a result that depends on the path between the initial and final states.

25. The internal pressure is defined as

π_T = (∂U/∂V) _T . For a perfect gas, π_T = 0.

26. The Joule-Thomson effect is the

cooling of a gas by isenthalpic expansion.

27. The Joule-Thomson coefficient is defined as

μ = (∂T/∂p) _H.

27. The isothermal Joule-Thomson coefficient is defined as

μ_T = (∂H/∂p) _T = −C_pμ.

28. The inversion temperature is the

temperature at which the Joule-Thomson coefficient changes sign.

2. The Second Law in terms of entropy:

The entropy of an isolated system increases in the course of a spontaneous change: ΔS_tot > 0.

3. The thermodynamic definition of entropy is

dS = dq_rev /T.

4. The statistical definition of entropy is given by the Boltzmann formula

S = k lnW.

4. A Carnot cycle is a cycle composed of a

sequence of isothermal and adiabatic reversible expansions and compressions.

5. The efficiency of a heat engine is

ε = |w|/q_h.

5. The Carnot efficiency is

ε_rev = 1 − T_c /T_h.

7. The Clausius inequality is

dS ≥ dq/T.

8. The normal transition temperature, T_trs, is the temperature at which

two phases are in equilibrium at 1 atm.

8. The entropy of transition at the transition temperature is

Δ_trsS = Δ_trsH/T_trs.

9. Trouton's rule states that

many normal liquids have approximately the same standard entropy of vaporization (about 85 J K−1 mol−1).

10. The variation of entropy with temperature is given by

S(T_f) = S(T_i) + Integral (T_f to T_i) (C_p /T)dT.

11. The entropy of a substance is measured from the

area under a graph of C_p /T against T, using the Debye extrapolation at low temperatures, C_p = aT3 as T→0.

12. The Nernst heat theorem states that the entropy change accompanying any physical or chemical transformation

approaches zero as the temperature approaches zero: ΔS→0 as T→0 provided all the substances involved are perfectly ordered.

13. Third Law of thermodynamics:

The entropy of all perfect crystalline substances is zero at T = 0.

14. The standard reaction entropy is calculated from

Δ_rS® =ΣProducts νS® m -Σreactants νS® m .

15. The standard molar entropies of ions in solution are reported on a scale in which

S* (H+, aq) = 0 at all temperatures.

16. The Helmholtz energy is

A = U − TS.

16. The Gibbs energy is

G = H − TS.

17. The criteria of spontaneity may be written as:

(a) dS_U,V ≥ 0 and dU_S,V ≤ 0, or (b) dA_T,V ≤ 0 and dG_T,p ≤ 0.

18. The criterion of equilibrium at constant temperature and volume,

dA_T,V = 0.

18. The criterion of equilibrium at constant temperature and pressure,

dG_T,p = 0.

19. The maximum work and the Helmholtz energy are related by

w_max = ΔA.

19. The maximum additional (non-expansion) work and the Gibbs energy are related by

w_add,max = ΔG.

20. The standard Gibbs energy of reaction is given by

Δ_rG® = Δ_rH® − TΔ_rS® =ΣProducts νG® m -Σreactants νG® m .

21. The standard Gibbs energy of formation (Δ_fG®) is the

standard reaction Gibbs energy for the formation of a compound from its elements in their reference states.

22. The standard Gibbs energy of reaction may be expressed in terms of

Δ_fG®, Δ_rG® =ΣProducts νΔfG® −ΣReactants νΔfG®.

23. The standard Gibbs energies of formation of ions are reported on a scale in which

Δ_fG® (H+, aq) = 0 at all temperatures.

24. The fundamental equation is

dU = TdS − pdV.

25. The Maxwell relations are

.

26. A thermodynamic equation of state is an

expression for pressure in terms of thermodynamic quantities, π_T = T(∂p/∂T) _V − p.

27. The Gibbs energy is best described as a function of pressure and temperature,

dG = Vdp − SdT.

27. The variation of Gibbs energy with pressure and temperature are, respectively,

(∂G/∂p) _T = V and (∂G/∂T) _p = −S.

28. The temperature dependence of the Gibbs energy is given by the Gibbs-Helmholtz equation,

(∂(G/T)/∂T) _p = −H/T2.

29. For a condensed phase, the Gibbs energy varies with pressure as

G(p_f) = G(p_i) + V_mΔp. For a perfect gas, G(p_f) = G(p_i) + nRT ln(p_f/p_i).

1. A phase is a form of matter that is

uniform throughout in chemical composition and physical state.

2. A transition temperature is the temperature at which the two phases are in

equilibrium.

3. A metastable phase is a

thermodynamically unstable phase that persists because the transition is kinetically hindered.

4. A phase diagram is a diagram showing the

regions of pressure and temperature at which its various phases are thermodynamically stable.

5. A phase boundary is a

line separating the regions in a phase diagram showing the values of p and T at which two phases coexist in equilibrium.

6. The vapour pressure is the

pressure of a vapour in equilibrium with the condensed phase.

7. Boiling is the condition of

free vaporization throughout the liquid.

8. The boiling temperature is the temperature at which the

vapour pressure of a liquid is equal to the external pressure.

9. The critical temperature is the temperature at which a liquid surface

disappears and above which a liquid does not exist whatever the pressure. The critical pressure is the vapour pressure at the critical temperature.

10. A supercritical fluid is a

dense fluid phase above the critical temperature.

11. The melting temperature (or freezing temperature) is the temperature at which, under a specified pressure, the liquid and solid phases of a substance

coexist in equilibrium.

12. The triple point is a point on a phase diagram at which

the three phase boundaries meet and all three phases are in mutual equilibrium.

13. The chemical potential μ of a pure substance is the

molar Gibbs energy of the substance.

14. The chemical potential is

uniform throughout a system at equilibrium.

15. The chemical potential varies with temperature as

(∂μ /∂T) _p = −S_m and with pressure as (∂μ /∂p) _T = V_m.

16. The vapour pressure in the presence of applied pressure is given by

p = p*e^(V_mΔP/RT).

17. The temperature dependence of the vapour pressure is given by the Clapeyron equation,

dp/dT = Δ_trsS/Δ_trsV.

18. The temperature dependence of the vapour pressure of a condensed phase is given by the Clausius-Clapeyron equation,

d ln(p/dT) = Δ_vapH/RT^2.

19. The Ehrenfest classification is a classification of

phase transitions based on the behavior of the chemical potential.

1. The partial molar volume is the

change in volume per mole of A added to a large volume of the mixture: V_J = (∂V/∂n_J)_p,T,n′.

1. The total volume of a mixture is

V = n_AV_A + n_BV_B.

2. The chemical potential can be defined in terms of the partial molar Gibbs energy,

μ_ J = (∂G/∂n_J) _p,T,n′.

2. The total Gibbs energy of a mixture is

G = n_Aμ_A + n_Bμ_B.

3. The fundamental equation of chemical thermodynamics relates the change in Gibbs energy to changes in pressure, temperature, and composition:

dG = Vdp − SdT + μ_Adn_A + μ_Bdn_B + · · ·.

4. The Gibbs-Duhem equation is

Σn_Jdμ_J = 0.

5. The chemical potential of a perfect gas is

μ = μ+ RT ln(p/pp*), where μ* is the standard chemical potential, the chemical potential of the pure gas at 1 bar.

6. The Gibbs energy of mixing of two perfect gases is given by

Δ_mixG = nRT(x_A ln x_A + x_B ln x_B).

7. The entropy of mixing of two perfect gases is given by

Δ_mixS = -nR(x_A ln x_A + x_B ln x_B).

8. The enthalpy of mixing for perfect gases is

Δ_mixH = 0 for perfect gases.

9. An ideal solution is a solution in which all components obeys Raoult's law

(p_A = x_Ap_A*) throughout the composition range.

10. The chemical potential of a component of an ideal solution is given by

μ_A = μ_A* + RT ln x_A.

11. An ideal-dilute solution is a solution for which the solute obeys Henry's law

(p_B = x_BK_B*) and the solvent obeys Raoult's law.

12. The Gibbs energy of mixing of two liquids that form an ideal solution is given by

Δ_mixG = nRT(x_A ln x_A + xB ln xB).

13. The entropy of mixing of two liquids that form an ideal solution is given by

Δ_mixS = -nR(xA ln xA + xB ln xB).

14. An excess function (XE) is the

difference between the observed thermodynamic function of mixing and the function for an ideal solution.

16. A colligative property is a property that

depends only on the number of solute particles present, not their identity.

17. The elevation of boiling point is given by

ΔT = K_bb, where Kb is the ebullioscopic constant.

17. The depression of freezing point is given by

ΔT = K_fb, where Kf is the cryoscopic constant.

21. The activity is defined as

a_A = p_A/p_A*.

22. The solvent activity is related to its chemical potential by

μ_A = μ_A* + RT ln a_A. The activity may be written in terms of the activity coefficient γ_A = a_A/x_A.

26. The Debye-Hückel theory of activity coefficients of electrolyte solutions is based on the assumption that

Coulombic interactions between ions are dominant; a key idea of the theory is that of an ionic atmosphere.

5. Thermal analysis is a technique for

detecting phase transitions that takes advantage of the effect of the enthalpy change during a first-order transition.

6. The vapour pressure of an ideal solution is given by

p = p_B + (p_A − p*_B)x_A.

6. The composition of the vapour of an ideal solution,

y_A = x_Ap_A/{p_B + (p_A − pp*_B)x_A}, y_B = 1 − yA.

7. The total vapour pressure of a mixture is given by

p = p_A p_B/{p_A + (p_B − p*_A)y_A}.

8. An isopleth is a line of

constant composition in a phase diagram. A tie line is a line joining two points representing phases in equilibrium.

9. The lever rule allows for the calculation of the relative amounts of two phases in equilibrium:

nαlα = nβlβ.

10. A temperature-composition diagram is a phase diagram in which the boundaries show the

composition of the phases that are in equilibrium at various temperatures.

11. An azeotrope is a mixture that

boils without change of composition.

12. Partially miscible liquids are liquids that

do not mix in all proportions at all temperatures.

13. The upper critical solution temperature is the

highest temperature at which phase separation occurs in a binary liquid mixture.

13. The lower critical solution temperature is the

temperature below which the components of a binary mixture mix in all proportions and above which they form two phases.

14. A eutectic is the mixture with the

lowest melting point; a liquid with the eutectic composition freezes at a single temperature. A eutectic halt is a delay in cooling while the eutectic freezes.

15. Incongruent melting occurs when a compound

melts into its components and does not itself form a liquid phase.

1. The extent of reaction (ξ) is defined such that,

when the extent of reaction changes by a finite amount Δξ, the amount of A present changes from n_A,0 to n_A,0− Δξ.

2. The reaction Gibbs energy is the slope of the graph of the Gibbs energy plotted against the extent of reaction:

Δ_rG = (∂G/∂ξ) _p,T; at equilibrium, Δ_rG = 0.

3. An exergonic reaction is a reaction for which

Δ_rG < 0; such a reaction can be used to drive another process. An endergonic reaction is a reaction for which ΔrG > 0.

4. The general expression for ΔrG at an arbitrary stage of the reaction is

Δ_rG = Δ_rG* + RT ln Q.

5. The equilibrium constant (K) may be written in terms of Δ_rG* as

Δ_rG* = −RT ln K.

6. The standard reaction Gibbs energy may be calculated from standard Gibbs energies of formation,

ΔrG=ΣProducts νΔfG −ΣReactants νΔfG=Σν_JΔ_fGΣν_JΔ_fG* (J).

7. Thermodynamic equilibrium constant is an equilibrium constant K expressed in terms of activities (or fugacities):

K = Πa_J ν_J Equilibrium .

8. A catalyst does not affect the

equilibrium constant.

9. Changes in pressure do not affect the equilibrium constant:

(∂K/∂p) _T = 0. However, partial pressures and concentrations can change in response to a change in pressure.

10. Le Chatelier's principle states that a system at equilibrium, when subjected to a disturbance,

responds in a way that tends to minimize the effect of the disturbance.

11. Increased temperature favors the ____ in exothermic reactions and the _____ in endothermic reactions.

Reactants and Products.

12. The temperature dependence of the equilibrium constant is given by the van 't Hoff equation:

d(ln K/dT) = Δ_rH/RT^2. To calculate K at one temperature in terms of its value at another temperature, and provided ΔrHH* is independent of temperature, we use ln K2 − ln K1 = −(Δ_rH*/R)(1/T_2 − 1/T_1).

13. A galvanic cell is an electrochemical cell that

produces electricity as a result of the spontaneous reaction occurring inside it.

13. An electrolytic cell is an electrochemical cell in which a

non-spontaneous reaction is driven by an external source of current.

14. Oxidation is the

removal of electrons from a species.

14. Reduction is the

addition of electrons to a species

14. A redox reaction is a reaction in which there is a transfer of

electrons from one species to another.

15. The anode is the electrode at which

oxidation occurs.

15. The cathode is the electrode at which

reduction occurs.

16. The electromotive force (emf) is the cell potential when

it is balanced by an exactly opposing source of potential so that the cell reaction occurs reversibly, the composition is constant, and no current flows.

17. The cell potential and the reaction Gibbs energy are related by

−νFE = Δ_rG.

18. The standard emf is the standard reaction Gibbs energy expressed as a potential:

E® = Δ_rG® /νF.

19. The Nernst equation is the equation for the emf of a cell in terms of the composition:

E = E® − (RT/νF) ln Q.

20. The equilibrium constant for a cell reaction is related to the standard emf by

ln K = νFE® /RT.

21. The standard potential of a couple (E®) is the standard emf of a cell in which a couple forms the ______ and the standard hydrogen electrode is the _____.

Right-hand electrode and Left-hand electrode.

22. To calculate the standard emf, form the difference of electrode potentials:

E® = E® (right) − E® (left).

23. The temperature coefficient of cell potential is given by

dE® /dT = Δ_rS® /νF.

24. The standard reaction entropy and enthalpy are calculated from the temperature dependence of the standard emf by:

Δ_rS ® = νFdE® /dT, Δ_rH® = −ν(FE ® − TdE® /dT).

Calorimetry

Method of determining heat change in a system by measuring heat exchanged in the surroundings

What enthalpy sign do exothermic reactions have?

Negative

What enthalpy sign do endothermic reactions have?

Positive

Le Châtelier's Principle

States that if an equilibrium system is subject to change, the equilibrium shifts in the direction which tends to counter that change

Isobaric

Constant P

Isothermal

Constant T

Isochoric

Constant V

Adiabadic

No heat flows in or out of the system (Q =0; ∆U = W)

Relationship between heat and work

∆U = Q + W

Work Equation

W = -Pext (Vf - Vi)

Enthalpy

H = U + PV

Change in enthalpy at constant presssure

∆H = ∆U + P∆V

Equation for Cv for monoatomic gas

Cv = (3/2)R

Equation for Cp for monoatomic gas

Cp = (5/2)R

Equation for Cv for diatomic gas

Cv = (5/2)R

Equation for Cp for diatomic gas

Cp = (7/2)R

Gibb's phase rule

f = c - p + 2 (f is the number of degrees of freedom of a system; c is the number of components is the system; p is the number of phases present)

Boyle's Law

At constant T and for a given sample of gas, the pressure of a gas is inversely proportional to its volume

Boyle's Law

, P∝1/V

Charles' Law

The volume of a given sample of gas at constant pressure is proportional to its absolute temperature

V∝T

Charles' Law

The Kinetic Model of Gases is based on what assumptions?

1) Gas consists of molecules in ceaseless random motion moving in straight linesbetween collisions , 2) The size of the molecule is negligible , 3) The molecules do not interact with each other or the wall of the vessel

Root-mean-square (r.m.s) speed

c=√(3RT/M), Molar mass must be in kg mol-1, Temperature must be in K, Units = ms-1

What is the van der Waals equation of state?

(p+a(n/v)^2)(V-nb) = RT , a and b are van der Waals parameters, specific for a given gas but independent of temperature

What is the equation for the molar heat capacity and give its units?

q = Cm x n x ∆T , Units: J K-1 mol-1

What is the equation for the specific heat capacity and give its units?

, q = Cs x m x ∆T , Units: J K-1 g-1 , The specific heat capacity of liquid water is 4.18 JK-1 g-1 Calculate the energy required to heat 1 mol of water from 25 °C to 90 °C , q = Cs x n x ∆T = 4.18 x 18 x (90-25) = 4.9kJmol-1

When a gas expands and moves a piston, how do you calculate the work done ?

Work done = external pressure x change in volume, The system is losing energy the external pressure is negative

work done = -p(ex) x ∆V , Calculate the work done when a gas is compressed from 750cm3 to 500cm3 by an external pressure of 100kPa , work done = external pressure x change in volume , = 100x10^3 (Pa) x 250x10^-6 (m3) = 25J , Because the gas is compressed the external pressure is positive

...

What type of property is internal energy?

Both extensive and a state function

What is internal energy, give its symbol and give the equation for a change in internal energy

Internal energy is the total energy of a system, It has the symbol U, ∆U = q + w

What is the relationship between enthalpy change and internal energy?

∆U = ∆H -p∆V p is pressure (constant)

What is the equation for the variation of entropy with temperature?

∆S = q(rev) / T , q(rev) = quantity of heat added reversibly ∆S = Cp ln (Tf/Ti)

What is the difference between K and Q?

K is the thermodynamic equilibrium constant and is calculated at equilibrium whereas Q although calculated in the same way it doesn't have to be at equilibrium

What relationship between Q and K has a tendency to form products?

Q < K

What relationship between Q and K has a tendency to form reactants?

Q > K

What is the relationship between ∆rG and K?

∆rG = -RT lnK

What is the van't Hoff equation for a reaction at a given temperature

lnK = (∆rS/R) - (∆rH/RT)

The equilibrium for the dissociation of one mole of iodine vapour is 3.94 x10-4 at 900K and the standard enthalpy is 154 kJmol-. Calculate the equilibrium constant at 1200K assuming the standard enthalpy remains constant

ln(K2/K1) = - ∆rH/R(1/T2 - 1/T1) , ANS = 6.7 x 10-2 at 1200K

At low vapour pressure, it is easy for a liquid to transition into a gas, true or false?

True

What is a Daniell cell's cell diagram?

Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s)

What is a Galvanic Cell?

An electrochemical cell that produces electricity as a result of a spontaneous reaction

What is an Electrolytic Cell?

A non-spontaneous reaction is forced by an external source of current

What is a Fuel Cell?

Galvanic cells in which the reagents are supplied continuously

During cell notation where is the oxidation half reaction?

Left

During cell notation where is the reduction half reaction?

Right

What side does the anode appear in the cell notation?

Left

What side does the cathode appear in the cell notation?

Right

What is the cell notation for a calomel electrode?

Hg(l) | Hg2Cl2(s) | Cl-(aq)

Standard electrode potentials are given as? (oxidation/reduction)

reduction

What is the relationship between electrical work and standard gibbs energy change for a reaction?

∆rG = we = -VQ, 1J = 1V x 1C

If Ecell is positive what will ∆rG be?

∆rG will be negative therefore the reaction is spontaneous

What is the energy per photon and what is its units?

E = hv = hc/ λ , Units: Joules

What is the equation for transmittance?

T = It/I0 , light intensity emmitted / light intensity added

What is the equation for absorbance?

A = - log T

If a sample absorbs 20% of light what is T and A?

T = 0.8 , A= - log (0.8) = 0.1

What is Beer-Lambert Law? Give units

A = εcl , A has no units so the units must cancel out , ε usually in dm3 mol-1 cm-1 , c has to be in mol dm-3 , l has to be in cm

Repulsive

Force exist between the molecules of gasses when Z>1

Clapeyron equation

Governs the temperature dependence of pressure in a two-phase, one component system

Clausius-Clapeyron equation

Gives the relationship between pressure and temperature for a two phase, one component system assuming that the vapor phase is ideal and the molar volume of the condensed phase is negligible compared to vapor phase

ACS Physical Chemistry Thermochemistry Study Guide - Subjecto.com

ACS Physical Chemistry Thermochemistry Study Guide

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What is the third law of thermodynamics?

The entropy of a perfect crystal is zero.

What is the second law of thermodynamics?

As a whole, the universe always tends towards increasing entropy.

What is the relationship between number of microstates and entropy?

More microstates = higher entropy

What is the relationship between temperature and entropy?

Temperature increases, entropy increases (direct)

What is the relationship between atomic weight and entropy?

Heavier = increased entropy (direct)

What happens to entropy when a substance is dissolved in another?

Entropy increases

What is the relationship between moles of gas and entropy?

When moles of gas increase, entropy increases (direct)

What is the relationship between free energy, enthalpy, and entropy?

deltaG(system)=deltaH(system)-TdeltaS(system)

What does change in G measure?

The extent of the spontaneity of a process, and the useful energy available from it

What is the relationship between work and spontaneous processes?

Spontaneous processes produce work

What is the relationship between work and non-spontaneous processes?

Non-spontaneous processes require work

What does -w mean?

Work is being produced – spontaneous

What does a positive sign for w mean?

Work is required – non-spontaneous

Can a change be spontaneous in both directions?

No

What is an extensive property?

Value depends on the amount of substance

What does ΔG &gt; 0 mean?

Non-spontaneous process – requires work

What does ΔG &lt; 0 mean?

Spontaneous process – produces work

What does standard free energy of formation mean? ΔGo

The free energy change that occurs when 1 mole of a compound is made from its elements

What is the standard free energy of formation for an element in its standard state? ΔGf

0

What does reversing a reaction do to the standard free energy of formation? ΔG0

Changes its sign

Why are most exothermic reactions spontaneous?

Because the large negative ΔH/large energy release makes the free energy change negative.

What happens when ΔH and ΔS have opposite signs?

The reaction occurs spontaneously at all temperatures or at none.

What happens when enthalpy (ΔH) is negative and entropy (ΔS) is positive?

Spontaneous at all temperatures, negative free energy

What is the likely sign of ΔH and ΔS for a combustion reaction?

Negative ΔH, positive ΔS

What happens when ΔH is positive and ΔS is negative?

Nonspontaneous at all temperatures

What happens when ΔH and ΔS are both positive?

Reaction becomes spontaneous as temperature increases

What happens when ΔH and ΔS are both negative?

Reaction becomes spontaneous as temperature decreases

Why can the maximum work of a system never obtained from a real process?

Because such an irreversible process will always involve some free energy being converted to heat

How do you find where a reaction becomes spontaneous?

Set ΔG equal to zero and solve — use T=deltaH/deltaS to find the temperature value.

Is a chemical reaction proceeding to equilibrium a spontaneous or non-spontaneous change?

Spontaneous

How to determine reaction direction from ΔG?

ΔG<0 reaction proceeds to the right ΔG>0 reaction proceeds to the left

Which direction does the reaction proceed if ΔG is positive?

To the left / to reactants

Which direction does the reaction proceed if ΔG is negative?

To the right/ to products

How to predict ΔS(system)? (change in entropy of a system)

Positive ΔS(system) means available microstates increases/disorder increases

How to calculate the ΔSo (aka standard entropy change) of the formation of one mole of gas from its elements?

1. Write the balanced chemical equation with the proper coefficients that make the product ONE MOLE. 2. Find the value of the one mole of product in Appendix B. This is the deltaS(standard) for the product. 3. Find the value of the reactants in Appendix B for deltaS(standard) and multiply them by the coefficients you got in step 1. 4. Use total = products-reactants for your final value.

How to calculate ΔG (free energy) using enthalpy ΔH and entropy ΔS values?

ΔG=ΔH-TΔS

What is the equation that relates ΔG to K?

ΔG=-RT ln K

What is the Boltzmann constant?

ln(# of microstates)

What does a big W mean?

More microstates

What does more microstates mean?

Big ΔS – more entropy

What does fewer microstates mean?

Smaller ΔS – less entropy

What happens to entropy when volume is increased?

Microstates increase, entropy increases

What is the relationship between ΔS of a system, q, and T?

ΔS(system)=qrev/T

What happens to entropy ΔS when temperature increases?

It increases

What is the relationship between mass and entropy ΔS?

As mass increases, entropy increases

What is the relationship between molecular complexity and entropy ΔS?

As molecular complexity increases, entropy increases

What is the relationship between ΔG and Q?

ΔG=RTlnQ

What happens to K as ΔG becomes more positive?

It gets smaller

What happens to K as ΔG becomes more negative?

It gets bigger

What direction does a reaction proceed if ln Q/K is positive?

Reaction proceeds to the left/reactants

What direction does a reaction proceed if ln Q/K is negative?

Reaction proceeds to the right/products

Extensive Property

property which is directly proportional to the size of the system (i.e.. V, m, E )

Intensive Property

property which does not depend on the size of the system (i.e. P, T, density, molar volume)

van der Waals constants

a reflects how strong the molecules attract each other (IM forces); b reflects the size of the molecule — van der Waals equation extends beyond the ideal gas law to take into account attractive and repulsive forces

Isotherm

plot of P as a function of molar volume at constant temperature

Law of Corresponding States

Law which states "all gases have the same properties of they are compared at corresponding conditions"

Boyle Temperature

temperature at which repulsive and attractive interactions cancel and the gas appears to behave ideally

Heat (q)

the manner of energy transfer that results from temperature difference between system and surroundings ("unorganized motion")

Work (w)

the transfer of energy between system and surroundings as a result of existence of unbalanced forces between the two ("organized motion")

State Function

property that depends on the state of the system, and not upon the history of the system (i.e. energy, entropy)

Reversible Process

when pressure the pressure exerted on the system and the pressure of the system differ only infinitesimally so slight changes are able to be made

Path Function

property that depends on the path taken to reach the state of the system

Adiabatic Process

process which no energy as heat is transferred (dq = 0 ; therefore, dU=dw )

Enthalpy (H)

total heat content of a system; it is equivalent to the internal energy plus the products of pressure and volume

Heat of Combustion

the heat involved in a combustion reaction –chemical reactions that absorb heat ( dH > 0) are called endothermic –chemical reactions that release heat (dH <0) are called exothermic

Entropy (S)

unavailability of a system’s thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system —dS=0 for cyclic processes or reversible processes in isolated system —dS > 0 for spontaneous processes in isolated systems

Helmoltz Energy (A)

= U – TS —will decrease during any spontaneous process that occur at constant T and V and will achieve its minimum value at equilibrium

Gibbs Energy (G)

= H – TS = A + PV —will decrease as a result of any spontaneous process until the system reaches equilibrium

Fugacity

thermodynamic property which described the deviations of ideality; the ratio f/p is the coefficient

Gibbs Phase Rule

F = C – P + 2 —Phase (P): numer of phases ( P=1 is for within a region, P=2 is for on the coexistence curve, P=3 is for at the critical point) —Component (C): chemically independent variable describing how many components are in the system —Degrees of Freedom (F): number of intensive variables we can change yet still be in the same phase

Azeotrope

a mixture for which there is no change in composition upon boiling (not possible to achieve separation)

Colligative Property

property which depends only on the number of solute particles present, not on their identity (i.e. vapor pressure, boiling point, freezing point, osmotic pressure)

Reaction Quotient (Q) vs. Equilibrium Constant (K)

— at equilibrium dG=0 ; Qp=Kp — If Qp < P: dG <0 so reaction is moving L to R — If Qp > P: dG >0 so reaction is moving R to L

Colloids

Contains some particles that are intermediate in size between the small particles in a solution and the larger particles in a suspension

Bose-Einstein Condensate

Fifth state of matter that exists at extremely low temperatures and atoms behave as a single particle

Pressure

Result of force distributed over an area

Charles’s Law

The volume of a gas is directly proportional to its temperature in kelvins if the pressure and the # of particles of the gas are constant

Boyle’s Law

The volume of a gas is inversely proportional to its pressure if the temperature and the # of particles are constant

Endothermic

The system absorbs energy from its surroundings

Heat of Fushion

The energy a substance must absorb in order to change from a solid to liquid

Exothermic

The system releases energy to its surroundings

Deposition

When a gas changes directly to a solid

Sublimation

When a solid changes directly to a gas

Alkaline Earth Metals

The elements in group 2A; differences shown by reactivity to water

Halogens

The elements in group 7A; highly reactive nonmetals

Noble Gases

The elements in group 8A; colorless odorless and extremely unreactive

Anion

An ion with a negative charge

Cation

An ion with a positive charge

Polar Covalent Bond

A covalent bond in which electrons are not shared equally

2. An equation of state interrelates

pressure, volume, temperature, and amount of substance: p = f(T,V,n).

6. A diathermic boundary is a boundary that

permits the passage of energy as heat.

7. An adiabatic boundary is a boundary that

prevents the passage of energy as heat.

7. Thermal equilibrium is a condition in which

no change of state occurs when two objects A and B are in contact through a diathermic boundary.

8. The Zeroth Law of thermodynamics states that

if A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A.

9. The Celsius and thermodynamic temperature scales are related by

T/K = θ/°C + 273.15.

10. A perfect gas obeys the perfect gas equation

pV = nRT, exactly under all conditions.

11. Dalton’s law states that the

pressure exerted by a mixture of gases is the sum of the partial pressures of the gases.

12. The partial pressure of any gas is defined as

p_J = x_J p, where x_J = n_J/n is its mole fraction in a mixture and p is the total pressure.

13. In real gases, molecular interactions affect the equation of state; the true equation of state is expressed in terms of virial coefficients

B, C, . . . : pV_m = RT(1 + B/V_m + C/V^2_m + · · · ).

14. The vapour pressure is the

pressure of a vapour in equilibrium with its condensed phase.

15. The critical point is the point at which the

volumes at each end of the horizontal part of the isotherm have merged to a single point. The critical constants p_c, V_c, and T_c are the pressure, molar volume, and temperature, respectively, at the critical point.

16. A supercritical fluid is a

dense fluid phase above its critical temperature and pressure.

17. The van der Waals equation of state is an

approximation to the true equation of state in which attractions are represented by a parameter a and repulsions are represented by a parameter b: p = nRT/(V− nb) − a(n/V)^2.

18. A reduced variable is

the actual variable divided by the corresponding critical constant.

19. According to the principle of corresponding states, real gases at the same reduced volume and reduced temperature exert

the same reduced pressure.

2. The system is the part of the world in which we have a special interest. The surroundings is the region

outside the system where we make our measurements.

3. An open system has a boundary through which matter can be

transferred.

3. A closed system has a boundary through which matter

cannot be transferred.

3. An isolated system has a boundary through which

neither matter nor energy can be transferred.

4. Energy is the capacity to

do work. The internal energy is the total energy of a system.

5. Work is the transfer of energy by motion against an opposing force,

dw = −Fdz . Heat is the transfer of energy as a result of a temperature difference between the system and the surroundings.

6. An exothermic process

releases energy as heat to the surroundings.

6. An endothermic process

absorbs energy as heat from the surroundings.

7. A state function is a property that depends only on

the current state of the system and is independent of how that state has been prepared.

8. The First Law of thermodynamics states that

the internal energy of an isolated system is constant, ΔU = q + w.

9. Expansion work is the work of expansion (or compression) of a system,

dw = −p_exdV. The work of free expansion is w = 0.

9. The work of expansion against a constant external pressure is

w = −p_exΔV.

9. The work of isothermal reversible expansion of a perfect gas is

w = −nRT ln(V_f /V_i).

10. A reversible change is a change that

can be reversed by an infinitesimal modification of a variable.

11. Maximum work is achieved in a

reversible change.

12. Calorimetry is the study of

heat transfers during physical and chemical processes.

13. The heat capacity at constant volume is defined as

C_V = (∂U/∂T) _V.

14. The heat capacity at constant pressure is

C_p = (∂H/∂T) _p.

14. For a perfect gas, the heat capacities are related by

C_p − C_V = nR.

14. The enthalpy is defined as

H = U + pV.

14. The enthalpy change is the

energy transferred as heat at constant pressure, ΔH = q_p.

15. During a reversible adiabatic change, the temperature of a perfect gas varies according to

T_f = T_i(V_i/V_f)^(1/c), c = CV,m/R. The pressure and volume are related by pV^γ = constant, with γ = C_p,m/C_V,m.

16. The standard enthalpy change is the

change in enthalpy for a process in which the initial and final substances are in their standard states. The standard state is the pure substance at 1 bar.

17. Enthalpy changes are additive, as in

Δ_subH® = Δ_fusH® + Δ_vapH® .

18. The enthalpy change for a process and its reverse are related by

ΔforwardH® = −ΔreverseH®.

19. The standard enthalpy of combustion is the

standard reaction enthalpy for the complete oxidation of an organic compound to CO2 gas and liquid H2O if the compound contains C, H, and O, and to N2 gas if N is also present.

20. Hess’s law states that the standard enthalpy of an overall reaction is the

sum of the standard enthalpies of the individual reactions into which a reaction may be divided.

21. The standard enthalpy of formation (Δ_fH® ) is the

standard reaction enthalpy for the formation of the compound from its elements in their reference states. The reference state is the most stable state of an element at the specified temperature and 1 bar.

22. The standard reaction enthalpy may be estimated by combining enthalpies of formation

Δ_rH® =ΣProducts νΔfH® −ΣReactants νΔfH® .

23. The temperature dependence of the reaction enthalpy is given by Kirchhoff’s law

Δ_rH® (T2) = Δ_rH® (T1) + Integral (T2 to T1) Δ_rC® pdT.

24. An exact differential is an

infinitesimal quantity that, when integrated, gives a result that is independent of the path between the initial and final states. An inexact differential is an infinitesimal quantity that, when integrated, gives a result that depends on the path between the initial and final states.

25. The internal pressure is defined as

π_T = (∂U/∂V) _T . For a perfect gas, π_T = 0.

26. The Joule-Thomson effect is the

cooling of a gas by isenthalpic expansion.

27. The Joule-Thomson coefficient is defined as

μ = (∂T/∂p) _H.

27. The isothermal Joule-Thomson coefficient is defined as

μ_T = (∂H/∂p) _T = −C_pμ.

28. The inversion temperature is the

temperature at which the Joule-Thomson coefficient changes sign.

2. The Second Law in terms of entropy:

The entropy of an isolated system increases in the course of a spontaneous change: ΔS_tot > 0.

3. The thermodynamic definition of entropy is

dS = dq_rev /T.

4. The statistical definition of entropy is given by the Boltzmann formula

S = k lnW.

4. A Carnot cycle is a cycle composed of a

sequence of isothermal and adiabatic reversible expansions and compressions.

5. The efficiency of a heat engine is

ε = |w|/q_h.

5. The Carnot efficiency is

ε_rev = 1 − T_c /T_h.

7. The Clausius inequality is

dS ≥ dq/T.

8. The normal transition temperature, T_trs, is the temperature at which

two phases are in equilibrium at 1 atm.

8. The entropy of transition at the transition temperature is

Δ_trsS = Δ_trsH/T_trs.

9. Trouton’s rule states that

many normal liquids have approximately the same standard entropy of vaporization (about 85 J K−1 mol−1).

10. The variation of entropy with temperature is given by

S(T_f) = S(T_i) + Integral (T_f to T_i) (C_p /T)dT.

11. The entropy of a substance is measured from the

area under a graph of C_p /T against T, using the Debye extrapolation at low temperatures, C_p = aT3 as T→0.

12. The Nernst heat theorem states that the entropy change accompanying any physical or chemical transformation

approaches zero as the temperature approaches zero: ΔS→0 as T→0 provided all the substances involved are perfectly ordered.

13. Third Law of thermodynamics:

The entropy of all perfect crystalline substances is zero at T = 0.

14. The standard reaction entropy is calculated from

Δ_rS® =ΣProducts νS® m -Σreactants νS® m .

15. The standard molar entropies of ions in solution are reported on a scale in which

S* (H+, aq) = 0 at all temperatures.

16. The Helmholtz energy is

A = U − TS.

16. The Gibbs energy is

G = H − TS.

17. The criteria of spontaneity may be written as:

(a) dS_U,V ≥ 0 and dU_S,V ≤ 0, or (b) dA_T,V ≤ 0 and dG_T,p ≤ 0.

18. The criterion of equilibrium at constant temperature and volume,

dA_T,V = 0.

18. The criterion of equilibrium at constant temperature and pressure,

dG_T,p = 0.

19. The maximum work and the Helmholtz energy are related by

w_max = ΔA.

19. The maximum additional (non-expansion) work and the Gibbs energy are related by

w_add,max = ΔG.

20. The standard Gibbs energy of reaction is given by

Δ_rG® = Δ_rH® − TΔ_rS® =ΣProducts νG® m -Σreactants νG® m .

21. The standard Gibbs energy of formation (Δ_fG®) is the

standard reaction Gibbs energy for the formation of a compound from its elements in their reference states.

22. The standard Gibbs energy of reaction may be expressed in terms of

Δ_fG®, Δ_rG® =ΣProducts νΔfG® −ΣReactants νΔfG®.

23. The standard Gibbs energies of formation of ions are reported on a scale in which

Δ_fG® (H+, aq) = 0 at all temperatures.

24. The fundamental equation is

dU = TdS − pdV.

25. The Maxwell relations are

.

26. A thermodynamic equation of state is an

expression for pressure in terms of thermodynamic quantities, π_T = T(∂p/∂T) _V − p.

27. The Gibbs energy is best described as a function of pressure and temperature,

dG = Vdp − SdT.

27. The variation of Gibbs energy with pressure and temperature are, respectively,

(∂G/∂p) _T = V and (∂G/∂T) _p = −S.

28. The temperature dependence of the Gibbs energy is given by the Gibbs-Helmholtz equation,

(∂(G/T)/∂T) _p = −H/T2.

29. For a condensed phase, the Gibbs energy varies with pressure as

G(p_f) = G(p_i) + V_mΔp. For a perfect gas, G(p_f) = G(p_i) + nRT ln(p_f/p_i).

1. A phase is a form of matter that is

uniform throughout in chemical composition and physical state.

2. A transition temperature is the temperature at which the two phases are in

equilibrium.

3. A metastable phase is a

thermodynamically unstable phase that persists because the transition is kinetically hindered.

4. A phase diagram is a diagram showing the

regions of pressure and temperature at which its various phases are thermodynamically stable.

5. A phase boundary is a

line separating the regions in a phase diagram showing the values of p and T at which two phases coexist in equilibrium.

6. The vapour pressure is the

pressure of a vapour in equilibrium with the condensed phase.

7. Boiling is the condition of

free vaporization throughout the liquid.

8. The boiling temperature is the temperature at which the

vapour pressure of a liquid is equal to the external pressure.

9. The critical temperature is the temperature at which a liquid surface

disappears and above which a liquid does not exist whatever the pressure. The critical pressure is the vapour pressure at the critical temperature.

10. A supercritical fluid is a

dense fluid phase above the critical temperature.

11. The melting temperature (or freezing temperature) is the temperature at which, under a specified pressure, the liquid and solid phases of a substance

coexist in equilibrium.

12. The triple point is a point on a phase diagram at which

the three phase boundaries meet and all three phases are in mutual equilibrium.

13. The chemical potential μ of a pure substance is the

molar Gibbs energy of the substance.

14. The chemical potential is

uniform throughout a system at equilibrium.

15. The chemical potential varies with temperature as

(∂μ /∂T) _p = −S_m and with pressure as (∂μ /∂p) _T = V_m.

16. The vapour pressure in the presence of applied pressure is given by

p = p*e^(V_mΔP/RT).

17. The temperature dependence of the vapour pressure is given by the Clapeyron equation,

dp/dT = Δ_trsS/Δ_trsV.

18. The temperature dependence of the vapour pressure of a condensed phase is given by the Clausius-Clapeyron equation,

d ln(p/dT) = Δ_vapH/RT^2.

19. The Ehrenfest classification is a classification of

phase transitions based on the behavior of the chemical potential.

1. The partial molar volume is the

change in volume per mole of A added to a large volume of the mixture: V_J = (∂V/∂n_J)_p,T,n′.

1. The total volume of a mixture is

V = n_AV_A + n_BV_B.

2. The chemical potential can be defined in terms of the partial molar Gibbs energy,

μ_ J = (∂G/∂n_J) _p,T,n′.

2. The total Gibbs energy of a mixture is

G = n_Aμ_A + n_Bμ_B.

3. The fundamental equation of chemical thermodynamics relates the change in Gibbs energy to changes in pressure, temperature, and composition:

dG = Vdp − SdT + μ_Adn_A + μ_Bdn_B + · · ·.

4. The Gibbs-Duhem equation is

Σn_Jdμ_J = 0.

5. The chemical potential of a perfect gas is

μ = μ+ RT ln(p/pp*), where μ* is the standard chemical potential, the chemical potential of the pure gas at 1 bar.

6. The Gibbs energy of mixing of two perfect gases is given by

Δ_mixG = nRT(x_A ln x_A + x_B ln x_B).

7. The entropy of mixing of two perfect gases is given by

Δ_mixS = -nR(x_A ln x_A + x_B ln x_B).

8. The enthalpy of mixing for perfect gases is

Δ_mixH = 0 for perfect gases.

9. An ideal solution is a solution in which all components obeys Raoult’s law

(p_A = x_Ap_A*) throughout the composition range.

10. The chemical potential of a component of an ideal solution is given by

μ_A = μ_A* + RT ln x_A.

11. An ideal-dilute solution is a solution for which the solute obeys Henry’s law

(p_B = x_BK_B*) and the solvent obeys Raoult’s law.

12. The Gibbs energy of mixing of two liquids that form an ideal solution is given by

Δ_mixG = nRT(x_A ln x_A + xB ln xB).

13. The entropy of mixing of two liquids that form an ideal solution is given by

Δ_mixS = -nR(xA ln xA + xB ln xB).

14. An excess function (XE) is the

difference between the observed thermodynamic function of mixing and the function for an ideal solution.

16. A colligative property is a property that

depends only on the number of solute particles present, not their identity.

17. The elevation of boiling point is given by

ΔT = K_bb, where Kb is the ebullioscopic constant.

17. The depression of freezing point is given by

ΔT = K_fb, where Kf is the cryoscopic constant.

21. The activity is defined as

a_A = p_A/p_A*.

22. The solvent activity is related to its chemical potential by

μ_A = μ_A* + RT ln a_A. The activity may be written in terms of the activity coefficient γ_A = a_A/x_A.

26. The Debye-Hückel theory of activity coefficients of electrolyte solutions is based on the assumption that

Coulombic interactions between ions are dominant; a key idea of the theory is that of an ionic atmosphere.

5. Thermal analysis is a technique for

detecting phase transitions that takes advantage of the effect of the enthalpy change during a first-order transition.

6. The vapour pressure of an ideal solution is given by

p = p_B + (p_A − p*_B)x_A.

6. The composition of the vapour of an ideal solution,

y_A = x_Ap_A/{p_B + (p_A − pp*_B)x_A}, y_B = 1 − yA.

7. The total vapour pressure of a mixture is given by

p = p_A p_B/{p_A + (p_B − p*_A)y_A}.

8. An isopleth is a line of

constant composition in a phase diagram. A tie line is a line joining two points representing phases in equilibrium.

9. The lever rule allows for the calculation of the relative amounts of two phases in equilibrium:

nαlα = nβlβ.

10. A temperature-composition diagram is a phase diagram in which the boundaries show the

composition of the phases that are in equilibrium at various temperatures.

11. An azeotrope is a mixture that

boils without change of composition.

12. Partially miscible liquids are liquids that

do not mix in all proportions at all temperatures.

13. The upper critical solution temperature is the

highest temperature at which phase separation occurs in a binary liquid mixture.

13. The lower critical solution temperature is the

temperature below which the components of a binary mixture mix in all proportions and above which they form two phases.

14. A eutectic is the mixture with the

lowest melting point; a liquid with the eutectic composition freezes at a single temperature. A eutectic halt is a delay in cooling while the eutectic freezes.

15. Incongruent melting occurs when a compound

melts into its components and does not itself form a liquid phase.

1. The extent of reaction (ξ) is defined such that,

when the extent of reaction changes by a finite amount Δξ, the amount of A present changes from n_A,0 to n_A,0− Δξ.

2. The reaction Gibbs energy is the slope of the graph of the Gibbs energy plotted against the extent of reaction:

Δ_rG = (∂G/∂ξ) _p,T; at equilibrium, Δ_rG = 0.

3. An exergonic reaction is a reaction for which

Δ_rG < 0; such a reaction can be used to drive another process. An endergonic reaction is a reaction for which ΔrG > 0.

4. The general expression for ΔrG at an arbitrary stage of the reaction is

Δ_rG = Δ_rG* + RT ln Q.

5. The equilibrium constant (K) may be written in terms of Δ_rG* as

Δ_rG* = −RT ln K.

6. The standard reaction Gibbs energy may be calculated from standard Gibbs energies of formation,

ΔrG=ΣProducts νΔfG −ΣReactants νΔfG=Σν_JΔ_fGΣν_JΔ_fG* (J).

7. Thermodynamic equilibrium constant is an equilibrium constant K expressed in terms of activities (or fugacities):

K = Πa_J ν_J Equilibrium .

8. A catalyst does not affect the

equilibrium constant.

9. Changes in pressure do not affect the equilibrium constant:

(∂K/∂p) _T = 0. However, partial pressures and concentrations can change in response to a change in pressure.

10. Le Chatelier’s principle states that a system at equilibrium, when subjected to a disturbance,

responds in a way that tends to minimize the effect of the disturbance.

11. Increased temperature favors the ____ in exothermic reactions and the _____ in endothermic reactions.

Reactants and Products.

12. The temperature dependence of the equilibrium constant is given by the van ‘t Hoff equation:

d(ln K/dT) = Δ_rH/RT^2. To calculate K at one temperature in terms of its value at another temperature, and provided ΔrHH* is independent of temperature, we use ln K2 − ln K1 = −(Δ_rH*/R)(1/T_2 − 1/T_1).

13. A galvanic cell is an electrochemical cell that

produces electricity as a result of the spontaneous reaction occurring inside it.

13. An electrolytic cell is an electrochemical cell in which a

non-spontaneous reaction is driven by an external source of current.

14. Oxidation is the

removal of electrons from a species.

14. Reduction is the

addition of electrons to a species

14. A redox reaction is a reaction in which there is a transfer of

electrons from one species to another.

15. The anode is the electrode at which

oxidation occurs.

15. The cathode is the electrode at which

reduction occurs.

16. The electromotive force (emf) is the cell potential when

it is balanced by an exactly opposing source of potential so that the cell reaction occurs reversibly, the composition is constant, and no current flows.

17. The cell potential and the reaction Gibbs energy are related by

−νFE = Δ_rG.

18. The standard emf is the standard reaction Gibbs energy expressed as a potential:

E® = Δ_rG® /νF.

19. The Nernst equation is the equation for the emf of a cell in terms of the composition:

E = E® − (RT/νF) ln Q.

20. The equilibrium constant for a cell reaction is related to the standard emf by

ln K = νFE® /RT.

21. The standard potential of a couple (E®) is the standard emf of a cell in which a couple forms the ______ and the standard hydrogen electrode is the _____.

Right-hand electrode and Left-hand electrode.

22. To calculate the standard emf, form the difference of electrode potentials:

E® = E® (right) − E® (left).

23. The temperature coefficient of cell potential is given by

dE® /dT = Δ_rS® /νF.

24. The standard reaction entropy and enthalpy are calculated from the temperature dependence of the standard emf by:

Δ_rS ® = νFdE® /dT, Δ_rH® = −ν(FE ® − TdE® /dT).

Calorimetry

Method of determining heat change in a system by measuring heat exchanged in the surroundings

What enthalpy sign do exothermic reactions have?

Negative

What enthalpy sign do endothermic reactions have?

Positive

Le Châtelier’s Principle

States that if an equilibrium system is subject to change, the equilibrium shifts in the direction which tends to counter that change

Isobaric

Constant P

Isothermal

Constant T

Isochoric

Constant V

Adiabadic

No heat flows in or out of the system (Q =0; ∆U = W)

Relationship between heat and work

∆U = Q + W

Work Equation

W = -Pext (Vf – Vi)

Enthalpy

H = U + PV

Change in enthalpy at constant presssure

∆H = ∆U + P∆V

Equation for Cv for monoatomic gas

Cv = (3/2)R

Equation for Cp for monoatomic gas

Cp = (5/2)R

Equation for Cv for diatomic gas

Cv = (5/2)R

Equation for Cp for diatomic gas

Cp = (7/2)R

Gibb’s phase rule

f = c – p + 2 (f is the number of degrees of freedom of a system; c is the number of components is the system; p is the number of phases present)

Boyle’s Law

At constant T and for a given sample of gas, the pressure of a gas is inversely proportional to its volume

Boyle’s Law

, P∝1/V

Charles’ Law

The volume of a given sample of gas at constant pressure is proportional to its absolute temperature

V∝T

Charles’ Law

The Kinetic Model of Gases is based on what assumptions?

1) Gas consists of molecules in ceaseless random motion moving in straight linesbetween collisions , 2) The size of the molecule is negligible , 3) The molecules do not interact with each other or the wall of the vessel

Root-mean-square (r.m.s) speed

c=√(3RT/M), Molar mass must be in kg mol-1, Temperature must be in K, Units = ms-1

What is the van der Waals equation of state?

(p+a(n/v)^2)(V-nb) = RT , a and b are van der Waals parameters, specific for a given gas but independent of temperature

What is the equation for the molar heat capacity and give its units?

q = Cm x n x ∆T , Units: J K-1 mol-1

What is the equation for the specific heat capacity and give its units?

, q = Cs x m x ∆T , Units: J K-1 g-1 , The specific heat capacity of liquid water is 4.18 JK-1 g-1 Calculate the energy required to heat 1 mol of water from 25 °C to 90 °C , q = Cs x n x ∆T = 4.18 x 18 x (90-25) = 4.9kJmol-1

When a gas expands and moves a piston, how do you calculate the work done ?

Work done = external pressure x change in volume, The system is losing energy the external pressure is negative

work done = -p(ex) x ∆V , Calculate the work done when a gas is compressed from 750cm3 to 500cm3 by an external pressure of 100kPa , work done = external pressure x change in volume , = 100×10^3 (Pa) x 250×10^-6 (m3) = 25J , Because the gas is compressed the external pressure is positive

What type of property is internal energy?

Both extensive and a state function

What is internal energy, give its symbol and give the equation for a change in internal energy

Internal energy is the total energy of a system, It has the symbol U, ∆U = q + w

What is the relationship between enthalpy change and internal energy?

∆U = ∆H -p∆V p is pressure (constant)

What is the equation for the variation of entropy with temperature?

∆S = q(rev) / T , q(rev) = quantity of heat added reversibly ∆S = Cp ln (Tf/Ti)

What is the difference between K and Q?

K is the thermodynamic equilibrium constant and is calculated at equilibrium whereas Q although calculated in the same way it doesn’t have to be at equilibrium

What relationship between Q and K has a tendency to form products?

Q < K

What relationship between Q and K has a tendency to form reactants?

Q > K

What is the relationship between ∆rG and K?

∆rG = -RT lnK

What is the van’t Hoff equation for a reaction at a given temperature

lnK = (∆rS/R) – (∆rH/RT)

The equilibrium for the dissociation of one mole of iodine vapour is 3.94 x10-4 at 900K and the standard enthalpy is 154 kJmol-. Calculate the equilibrium constant at 1200K assuming the standard enthalpy remains constant

ln(K2/K1) = – ∆rH/R(1/T2 – 1/T1) , ANS = 6.7 x 10-2 at 1200K

At low vapour pressure, it is easy for a liquid to transition into a gas, true or false?

True

What is a Daniell cell’s cell diagram?

Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s)

What is a Galvanic Cell?

An electrochemical cell that produces electricity as a result of a spontaneous reaction

What is an Electrolytic Cell?

A non-spontaneous reaction is forced by an external source of current

What is a Fuel Cell?

Galvanic cells in which the reagents are supplied continuously

During cell notation where is the oxidation half reaction?

Left

During cell notation where is the reduction half reaction?

Right

What side does the anode appear in the cell notation?

Left

What side does the cathode appear in the cell notation?

Right

What is the cell notation for a calomel electrode?

Hg(l) | Hg2Cl2(s) | Cl-(aq)

Standard electrode potentials are given as? (oxidation/reduction)

reduction

What is the relationship between electrical work and standard gibbs energy change for a reaction?

∆rG = we = -VQ, 1J = 1V x 1C

If Ecell is positive what will ∆rG be?

∆rG will be negative therefore the reaction is spontaneous

What is the energy per photon and what is its units?

E = hv = hc/ λ , Units: Joules

What is the equation for transmittance?

T = It/I0 , light intensity emmitted / light intensity added

What is the equation for absorbance?

A = – log T

If a sample absorbs 20% of light what is T and A?

T = 0.8 , A= – log (0.8) = 0.1

What is Beer-Lambert Law? Give units

A = εcl , A has no units so the units must cancel out , ε usually in dm3 mol-1 cm-1 , c has to be in mol dm-3 , l has to be in cm

Repulsive

Force exist between the molecules of gasses when Z>1

Clapeyron equation

Governs the temperature dependence of pressure in a two-phase, one component system

Clausius-Clapeyron equation

Gives the relationship between pressure and temperature for a two phase, one component system assuming that the vapor phase is ideal and the molar volume of the condensed phase is negligible compared to vapor phase

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