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Molecules can be polar because of the unsymmetrical distribution of electrons. The dipole moment, μ, is a measure of the net polarity and is defined as the charge 1.87×10−20 C , in coulombs, times the distance between the charges, which is estimated by the bond length, r, in meters: |
The percent ionic character is a comparison of the measured dipole to the expected dipole: %ionic character=measured dipoleexpected dipole×100% The expected dipole is one for which a full unit of charge (1.60×10−19 C) exists on each end of the bond. |
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The dipole measured for HI is 0.380 D. The bond length is 161 pm. What is the percent ionic character of the HI bond? |
%ionic character = 4.92 % The bond in an HI is 4.92% ionic in character. This means that the hydrogen atom carries a +0.0492 charge and the iodine atom carries a −0.0492 charge. |
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Describe the molecular dipole of OCl2. |
The molecular dipole is measurable and directed toward oxygen. |
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The dipole moment (μ) of HBr (a polar covalent molecule) is 0.790D (debye), and its percent ionic character is 11.7 % . Estimate the bond length of the H−BrH−Br bond in picometers. |
r = 140 pm The H−Br bond length is 140 pm, and its bond strength is 366 kJ/mol. |
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The dipole moment of HBr is 0.80D. What is the dipole moment of HBr in C⋅m? |
μ = 2.67×10−30 C⋅m |
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The distance between the atoms of H−Br is 1.41Å. What is the distance in meters? |
see slide above |
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What is the charge associated with each side of the HBr molecule? |
Q = 1.89×10−20 C |
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What is the percent ionic character of the H−Br bond? |
(see slide above) 11.8% |
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In a covalent bond between two atoms, the more electronegative atom will attract more electron density toward itself, causing a polar bond. The more electronegative element is the negative pole, whereas the less electronegative element is the positive pole. The direction of the dipole is always toward the more electronegative element. This is often indicated by an arrow, as shown in the figure. (Figure 1) |
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In the molecule HCl, which atom is the negative pole? |
Hydrochloric acid (HCl) is a strong acid pKa= -3. It ionizes into hydrogen ion (H+) and chloride ion (Cl-). Thus hydrogen is a positive pole since it carries positive charge and chlorine is a negative pole as it carries negative charge. |
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Of the molecules SiCl4 and SiI4, which has bonds that are more polar? |
SiCl4 |
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All three of the boron-fluorine single bonds in BF3 are polar. In which direction should the polarity arrows point? |
point away from the central boron atom. |
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A molecule can be polar or nonpolar depending upon the nature of the bonds and the shape of the molecule. For a molecule that has different outer atoms the molecular symmetry will decide the polarity. |
However, if the the molecular geometry is such that the dipole moments of each polar bond don’t cancel each other then the molecule is polar. |
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PI3Br2 is a nonpolar molecule. Based on this information, determine the I−P−I bond angle, the Br−P−Br bond angle, and the I−P−Br bond angle. |
The geometry of PI3Br2 is trigonal bipyramidal. Given that the molecule is non-polar that means three I atoms occupy equitorial positions and two Br atoms occupy axial positions in trigonal bipyramidal geometry. Then I-P-I bond angle is 1200 , Br-P-Br bond angle is 1800 and I-P-Br bond angle is 900. |
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Which statement best describes the polarity of CF2I2? |
The molecule is always polar. It will always be tetrahedral, and there is no possible way to cancel out the dipoles. |
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Which statement best describes the polarity of SCl4I2? |
Depending on the arrangement of outer atoms, this molecule could be polar or nonpolar. |
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Which molecule has a dipole moment of 0 D? ClF3 |
For future reference, you would want to draw the Lewis structure for each of these simple molecules, determine the geometry, and look to see if the molecule is symmetrical or not. A symmetrical molecule is nonpolar with a dipole moment of zero, while an asymmetrical molecule has a net dipole moment and is polar. BF3 |
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For future reference, you would want to draw the Lewis structure for each of these simple molecules, determine the geometry, and look to see if the molecule is symmetrical or not. A symmetrical molecule is nonpolar with a dipole moment of zero, while an asymmetrical molecule has a net dipole moment and is polar. You may have noticed that the compounds are listed in terms of increasing electron pair geometry complexity of the central atom, and with the molecular geometry that corresponds to the electron pair geometry. |
2 electron pairs – linear electron pair geometry BeH2 – symmetrical – linear 3 electron pairs – trigonal planar electron pair geometry BF3 – symmetrical – trigonal planar SO2 – not symmetrical – bent 4 electron pairs – tetrahedral electron pair geometry CH4 – symmetrical – tetrahedral NH3 – not symmetrical – trigonal pyramidal H2O – not symmetrical – bent 5 electron pairs – trigonal bipyramidal electron pair geometry PCl5 – symmetrical – trigonal bipyramidal SCl4 – not symmetrical – see-saw ClF3 – not symmetrical – T-shaped XeF2 – symmetrical – linear 6 electron pairs – octahedral electron pair geometry SF6 – symmetrical – octahedral IF5 – not symmetrical – square pyramidal XeF4 – symmetrical – square planar |
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Which allotrope of carbon is correctly matched to the forces that hold the structural units together? Graphite : dispersion forces |
Graphite : dispersion forces |
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The dipole moment of methanol is μ=1.70 D. Indicate the direction in which electrons are displaced. |
See picture |
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Methylamine, CH3NH2, is responsible for the odor of rotting fish. Look at the following electrostatic potential map of methylamine, and explain the observed polarity. |
The N atom is electron rich because of its high electronegativity. The C and H atoms are electron poor because they are less electronegative. |
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The dipole moment of HF is μ = 1.83 D, and the bond length is 92 pm. Calculate the percent ionic character of the H−F bond. Is HF more ionic or less ionic than HCl (Worked Example 10.1 in the textbook)? |
% ionic character = 41% more ionic than HCl |
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Tell which of the following compounds is likely to have a dipole moment, and show the direction of each. Which of the following compounds is likely to have a dipole moment? CHCl3 |
CHCl3 CH2Cl2 |
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What is the direction of dipole moment in CHCl3? |
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What is the direction of dipole moment in CH2Cl2? |
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To recognize what intermolecular forces are present in a given compound and which of those forces is predominant. Dipole-dipole forces result from the attraction of the positive end of one polar molecule to the negative end of another polar molecule. Compounds consisting of atoms with different electronegativities may have a dipole moment, or partial charge, caused by an asymmetry of electrons. |
Hydrogen bonding is a particularly strong type of dipole-dipole force that occurs when hydrogen is attached to nitrogen, oxygen, or fluorine. Water is an example of a substance in which hydrogen bonding occurs. Because of oxygen’s high electronegativity and the electron deficiency of the hydrogen atom, the hydrogen atoms are attracted to the lone pairs of electrons on the oxygen of another water molecule. All substances have dispersion forces, also known as London forces. These forces are very weak and are only important in the absence of any other intermolecular force. Nonpolar covalent molecules and single-atom molecules are examples of substances that lack all other intermolecular forces except for dispersion. Dispersion forces result from shifting electron clouds, which can cause a weak, temporary dipole. |
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What is the predominant intermolecular force in the liquid state of each of these compounds: water (H2O), carbon tetrachloride (CCl4), and methyl chloride (CH3Cl)? |
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A dipole moment tends to stabilize the liquid state of the compound as molecules align to form attractive molecular interactions. A liquid state that is more stable, that is one that is held together by stronger dipole forces, will have a higher boiling point since it takes more energy to break these intermolecular forces. |
Highest boiling point sodium chloride ( NaCl ) iodomethane ( CH3I ) carbon tetrafluoride ( CF4 ) Lowest boiling point The ionic compound NaCl has the highest boiling point of the group, at 1413 ∘C. Iodomethane, CH3I, is asymmetric and polar, with a boiling point of 42 ∘C. The symmetric molecule CF4 has no net dipole moment. It is thus nonpolar and has a boiling point of -127 ∘C. |
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Watch the animation and identify the correct conditions for forming a hydrogen bond. A hydrogen bond is equivalent to a covalent bond. |
Hydrogen bonding occurs when a hydrogen atom is covalently bonded to an N, O, or F atom. A hydrogen atom acquires a partial positive charge when it is covalently bonded to an F atom. A hydrogen bond is possible with only certain hydrogen-containing compounds. Hydrogen bonding is the intermolecular force that exists between an H atom of one molecule and an electronegative atom (N, O, or F) of another molecule. If a molecule has N−H, O−H, or F−H bonds, that molecule exhibits hydrogen bonding. |
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Identify which of the following molecules can exhibit hydrogen bonding as a pure liquid. |
Hydrogen bonding has an important effect on the physical properties of compounds. The melting and boiling points of compounds are affected by hydrogen bonds. |
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Compounds that experience hydrogen bonding between molecules generally have higher boiling points. Because of hydrogen bonding, the intermolecular forces of attraction between molecules within the compound are high. Consequently, more energy is required to separate these molecules from one another through boiling. Watch the animation in the introduction to examine the effect of hydrogen bonding on the boiling points of hydrides belonging to groups 4A and 6A. The hydrides of group 5A are NH3, PH3, AsH3, and SbH3. Arrange them from highest to lowest boiling point. |
The boiling point of NH3 is higher than that predicted by periodic trends alone because of hydrogen bonding. The molecule SbH3 actually has a higher boiling point than NH3. Both intermolecular forces, such as hydrogen bonding, and molecular mass contribute to the observed boiling point of a molecule. This means that you cannot always qualitatively predict the relative boiling points of two compounds that differ greatly. You could predict that methanol (CH3OH) has a higher boiling point than methane (CH4), but decane (C10H22) has an even higher boiling point without hydrogen bonding partly due to its significantly higher molar mass. |
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Of the substances Ar, Cl2, CCl4, and HNO3, which has the largest dipole-dipole forces? |
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Of the substances Ar, Cl2, CCl4, and HNO3, which has the largest hydrogen-bond forces? |
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Of the substances Ar, Cl2, CCl4, and HNO3, which has the smallest dispersion forces? |
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Consider the kinds of intermolecular forces present in the following compounds, and rank the substances in likely order of decreasing boiling point: |
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Viscosity, Surface Tension, and Intermolecular Forces |
Intermolecular forces determine the physical properties of substances. The viscosity and surface tension of liquids are two such properties. Viscosity is the resistance of a liquid to flow. Surface tension is the energy required to increase the surface area of a liquid by a certain amount. The stronger the forces of attraction, the more difficult it is for the molecules to move past one another, thus increasing the viscosity and surface tension of the liquid. |
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Rank these liquids by their expected surface tension. |
Surface tension helps to determine whether a liquid will "wet" or spread out on a given surface. Fabrics are often treated with compounds that prevent water from spreading out on the surface and penetrating the fabric. This is a result of the cohesive forces among the water molecules being stronger than the adhesive forces between the water and the fabric. |
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The Society of Automotive Engineers has established an accepted numerical scale to measure the viscosity of motor oil. For example, SAE 40 motor oil has a higher viscosity than an SAE 10 oil. Rank the following hydrocarbons by their expected viscosity. |
The viscosity of a given liquid varies with temperature. Different grades of motor oil are often used in summer and winter because of this variation with temperature. |
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Enthalpy and Entropy for Phase Changes |
Matter can change from one physical state (phase) to another without any change in chemical identity. Each change is characterized by a specific name, a ΔH (enthalpy) value, and a ΔS (entropy) value. The energy involved in phase changes and temperature changes can be calculated by using the following equations. For a phase change (with no change in temperature) heat=ΔH×n where ΔH is the enthalpy change for that transition and n is the number of moles of the substance. For a temperature change (with no change in phase) heat=Cm×ΔT×n where Cm is the molar heat capacity, n is the number of moles, and ΔT is the temperature change in degrees Celsius. |
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For each phase change, determine the sign of ΔH and ΔS. |
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Complete the sentences describing the steps needed to calculate the energy change associated with the conversion of 333 g of water ice at −10 ∘C to steam at 125 ∘C. |
The change from ice at −10 ∘C to steam at 125 ∘C involves five steps: Raising the temperature of ice from −10 ∘C to the melting point, 0 ∘C. Melting the ice to liquid water. Raising the temperature of water from 0 ∘C to the boiling point, 100 ∘C. Boiling the liquid water to steam. Raising the temperature of the steam from 100 ∘C to 125 ∘C. To calculate the energy required for the process, you need to calculate the energy component of each step. Steps 1, 3, and 5 involve a temperature change and therefore you should use the following equation: heat=Cm×ΔT×n Steps 2 and 4 involve a phase change and therefore you should use the following equation: heat=ΔH×n |
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Calculate the amount of energy in kilojoules needed to change 333 g of water ice at −10 ∘C to steam at 125 ∘C. The following constants may be useful: |
1st transition from -10 deg C 0 deg C q = m C delta T Delta T = final T – initial T , m is mass in g , C is specific heat =333 g x (1 mol/ 18.0148 g) x 36.57 J / mol deg C x ( 0 -(-10) deg C =6759.89 J 2nd Transition From 0 to 0 deg C q = Delta H(fus) x mol = 6.01 x 1000 J /mol x (333 / 18.0148) mol =111093.66 J 3rd from 0 to 100 deg q = 333 g x (1 mol/ 18.0148 g) x 75.40 J / mol deg C x ( 100 – 0) deg C =139375.4 J 4th from 100 to 100 deg C q = Delta Hvap x mol = 40.67 x 1000 J/mol x (333 /18.0148 ) mol =751776.87 J 5th from 100 to 125 q = 333 g x (1 mol/ 18.0148 g) x 36.04 J / mol deg C x ( 125-100 0 deg C = 16654.81 J Lets add q values from all transition Total q = 6759.89 J +111093.66 J +139375.4 J +751776.87 J +16654.81 J Total q = 1025660.63 J Answer in kJ = 1025.66 kJ |
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Consider heating solid water (ice) until it becomes liquid and then gas (steam). (Figure 1) Alternatively, consider the reverse process, cooling steam until it becomes water and, finally, ice. (Figure 2) In each case, two types of transitions occur, those involving a temperature change with no change in phase (shown by the diagonal line segments on the graphs) and those at constant temperature with a change in phase (shown by horizontal line segments on the graphs). |
The heat energy associated with a change in temperature that does not involve a change in phase is given by q=msΔT where q is heat in joules, m is mass in grams, s is specific heat in joules per gram-degree Celsius, J/(g⋅∘C), and ΔT is the temperature change in degrees Celsius. The heat energy associated with a change in phase at constant temperature is given by q=mΔH where q is heat in joules, m is mass in grams, and ΔH is the enthalpy in joules per gram. |
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The constants for H2O are shown here: |
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How much heat energy, in kilojoules, is required to convert 55.0 g of ice at −18.0 ∘C to water at 25.0 ∘C ? |
Q1 = m*Cpice(0 –18) Q2 = m*Hmelt Q3 = m*Cpwate(25-0) Substitute all Q1 = 55*2.01(0 –18) = 1989.9 Q2 = 55*333 = 18315 Q3 = 55*4.184(25-0) = 5753 QT = 1989.9 + 18315 + 5753 = 26057.9 J QT = 26.05 kJ |
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How long would it take for 1.50 mol of water at 100.0 ∘C to be converted completely into steam if heat were added at a constant rate of 19.0 J/s ? |
1.5mol water = 27g latent heat of vaporisation of water at 100°C to steam at 100°C is: Latent heat = 2258kJ/kg You have 27g, So heat required is 2258*27/1000 = 61kJ Heat is supplied at 19J/sec It will take 61000/19 = 3,210 seconds or 53.5 minutes. |
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Which pair of molecules gives the species with the lowest viscosity first? |
CH3—O—CH3 and CH3CH2OH |
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How much energy (in kilojoules) is absorbed when 10.0 g of liquid water at 75.0 °C is converted to water vapor at 150.0 °C? (The ΔH vap of water is 40.67 kJ/mol, and the molar heat capacity is 75.3 J/K·mol for the liquid and 33.6 J/K·mol for the vapor.) |
(10.0 g H2O) / (18.01532 g H2O/mol) = 0.5551 mol H2O (75.3 J/K·mol) x (100.0 – 75.0)K x (0.5551 mol) = 1044.98 J to warm the liquid to 100°C ( 40.67 kJ/mol) x (0.5551 mol) = 22.576 kJ to vaporize the liquid (33.6 J/K·mol) x (150.0 – 100.0)K x (0.5551 mol) = 932.57 J to heat the steam to 150°C 1.04498 kJ + 22.576 kJ + 0.93257 kJ = 24.6 kJ total |
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What is the melting point in °C of 1.00 mol of H2SO4? (The ΔH fus is 10.7 kJ/mole and the ΔS fus is 37.8 J/K·mol.) |
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Which of the following processes would you expect to have a positive value of ΔS, and which a negative value? |
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Chloroform (CHCl3) has ΔHvap = 29.2 kJ/mol and ΔSvap = 87.5 J/ (K⋅mol). What is the boiling point of chloroform in kelvin? |
Use the following equation to solve the problem ΔSvap = ΔHvap / T T = ΔHvap / ΔSvap ΔHvap = 29.2KJ/mol = 29200J/mol, ΔSvap = 87.5 J/ (K⋅mol) T = 29200 / 87.5 = 333.71K |
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± Vapor Pressure and Phase Changes |
All liquids evaporate to a certain extent. The pressure exerted by the gas phase in equilibrium with the liquid is called vapor pressure, Pvap. The vapor pressure of a particular substance is determined by the strength of the intermolecular forces. But for any given substance, the vapor pressure only changes with temperature. The Clausius-Clapeyron equation expresses the relationship between vapor pressure and temperature: lnP2=lnP1+(ΔHvapR)(1T1−1T2) where P2 and P1 are the vapor pressures that correspond to temperatures T2 and T1, respectively, ΔHvap is the molar heat of vaporization, and R=8.3145J/(mol⋅K) is the gas constant. |
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Consider the following two substances and their vapor pressures at 298 K. |
1)Substance A has the higher heat of vaporization. In other words, more heat has to be applied to get it to vaporize. We really can’t tell which substance has the weaker intermolecular forces, because substance A may just be a much larger molecule with higher molecular weight than substance B. Substance A will have the higher boiling point, and therefore substance B will be a gas at 300mmHg pressure. 2)ln (P1/P2) = (?Hvap/R) (1/T2-1/T1) At the normal boiling point, the vapor pressure is 760 mm Hg. Convert your temperatures to Kelvin. Then, you have all the information you need to solve the question, so just plug in and solve for ?Hvap: ln (134/760) = ?Hvap/(8.3145 J/molK) ( 1/313K – 1/273K) ?Hvap = 3.08X10^4 J/mol = 30.8 kJ/mol |
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The vapor pressure of dichloromethane, CH2Cl2, at 0 ∘C is 134 mmHg. The normal boiling point of dichloromethane is 40. ∘C. Calculate its molar heat of vaporization. |
Clausius-Claperyon equation: ln(P2/P1) = (-DHvap/R) x (1/T2 – 1/T1) Molar gas constant R = 8.314 J/mol.K T1 = 0 deg C = 273.15 K, P1 = 134 mmHg At normal boiling point T2 = 40 deg C = 313.15 K => P2 = atmospheric pressure = 760 mmHg Substituting values into equation: ln(760/134) = (-DHvap/8.314) x (1/313.15 – 1/273.15) Heat of vaporization = DHvap = 30855 J/mol = 30.9 kJ/mol |
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The vapor pressure of a substance describes how readily molecules at the surface of the substance enter the gaseous phase. At the boiling point of a liquid, the liquid’s vapor pressure is equal to or greater than the atmospheric pressure exerted on the surface of the liquid. Since the atmospheric pressure at higher elevations is lower than at sea level, the boiling point of water decreases as the elevation increases. The atmospheric pressure at sea level is 760 mmHg. This pressure decreases by 19.8 mmHg for every 1000-ft increase in elevation. |
The boiling point of water decreases 0.05∘C for every 1 mmHg drop in atmospheric pressure. |
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What is the boiling point of water at an elevation of 9500 ft ? |
T = 90.6 ∘C The boiling point of water is said to decrease by 0.05∘C for every 1 mmHg drop in atmospheric pressure the answer should be reported to one significant figure in literature or a paper: 90 ∘C or 9×10¹∘C. |
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Learning Goal: |
Surface tension is a phenomenon that allows insects to walk on water and causes water to "bead" on windows. Surface tension is defined as the energy required to increase the surface area of a given amount of liquid by a given unit of area. Boiling point is the temperature at which a liquid becomes a gas. It is also defined as the temperature at which the vapor pressure reaches atmospheric pressure. Vapor pressure is the pressure exerted by the vapor above a liquid. Liquids that readily evaporate have relatively high vapor pressures. |
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Classify each property as associated with a liquid that has strong or weak intermolecular forces. |
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Arrange the liquids pentane (CH3CH2CH2CH2CH3), pentanol (CH3CH2CH2CH2CH2OH), and pentanal (CH3CH2CH2CH2CHO) in order of decreasing viscosity, surface tension, and boiling point. |
iscosity and surface tension are both related to intermolecular forces (IMFs) pentane is nonpolar and cannot H-bond, so only LDF is possible (London Dispersion Force) pentanal is polar, but cannot H-bond => (Dipole-Dipole) pentanol has an OH group, so it can H-bond => (Hydrogen Bonding) With higher IMFs, you get greater surface tension and greater viscosity (since the liquid molecules are more attracted to each other) In order of decreasing IMF: (and thus decreasing viscosity/surface tension) pentanol pentanal pentane |
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Molecules at the surface of a liquid, if they possess enough kinetic energy, can escape to the gas state. As a result, a liquid will exert a vapor pressure. If the liquid is confined to a closed container, eventually the pressure reaches a constant value as a result of a dynamic equilibrium between molecules forming the gas state and those returning to the liquid state. The magnitude of the vapor pressure is determined by the strength of the intermolecular forces in the liquid and the temperature of the sample. |
Atmospheric pressure decreases as altitude increases. In other words, there is more air pushing down on you at sea level, and there is less air pressure pushing down on you when you are on a mountain. |
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If pentane (C5H12), heptane (C7H16), and heptanol (C7H15OH) are heated evenly at different altitudes, rank them according to the order in which you would expect them to begin boiling. |
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In the liquid and solid states, molecules are held together by attractions called intermolecular forces. There are several types of intermolecular forces. |
Physical properties such as boiling point, melting point, vapor pressure, viscosity, and surface tension are all affected by the strength of the intermolecular forces within a substance. |
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What happens to these physical properties as the strength of intermolecular forces increases? |
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Rank the following types of intermolecular forces in general order of decreasing strength (strongest to weakest). |
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Identify the predominant type of intermolecular force in each of the following compounds. |
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Place these hydrocarbons in order of decreasing boiling point. |
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Rank the following compounds in order of decreasing vapor pressure. |
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The normal boiling point of benzene is 80.1 ∘C, and the heat of vaporization is ΔHvap = 30.7 kJ/mol . What is the boiling point of benzene in ∘C on top of Mt. Everest, where P = 260 mmHg? |
Tboil = 47.2 ∘C |
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Bromine has Pvap = 400 mm at 41.0 ∘C and a normal boiling point of 331.9 K. What is the heat of vaporization, ΔHvap, of bromine in kJ/mol? |
Let us use the Clausius-Clapeyron Equation: ln (P1 / P2) = (ΔH / R) (1/T2 – 1/T1) P1 =400mm T1= 314 K P2= 760 mm natural boiling point pressure T2 =331.9 K ln (400 / 760) = (ΔH / 8.314 ) (1/331.9 – 1/314) = 3.11*104 J = 31.1 KJ |
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he physical properties such as melting point, solubility, or electrical conductivity of solid materials depend on the type of attractive force that holds the particles in the crystal lattice. The strength of these forces varies dramatically from very weak (as with dispersion forces) to very strong (as with ionic and covalent bonds). Solids are classified according to the type of forces involved. |
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Identify which of the following you would expect to be characteristic of a solid with the formula P4. |
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An unknown substance Given these properties, which of the following are possible identities for the unknown substance? |
Au |
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An unknown substance Given these properties which of the following are possible identities for the unknown substance? |
CoCl2 |
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The melting point of a solid is related to the way in which that substance is held together. Qualitatively, the relative melting points for a series of solids may be estimated using the following trends: |
It is important to keep in mind that a high or low melting point is relative, and that while this trend can be used for a quick estimation, if exact values are needed there are sources to look them up. |
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Qualitatively estimate the relative melting points for each of the solids, and rank them in decreasing order. |
While the general trend for melting points is shown in the introduction, there are deviations from this rule. Mercury is a well known exception, and is a liquid at room temperature. However, the trend is a good way to estimate how materials will behave quickly. If quantitative measures are needed, it is always good to look up the information. |
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Classify each solid as a covalent, ionic, metallic, or molecular solid. |
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Each set of solids is grouped according to a particular type of crystalline solid. In which set of solids is there one compound that is a mismatch in that set? Na, Cr, and LiCl |
Na, Cr, and LiCl |
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X-ray diffraction can be used to obtain structural information of crystalline compounds. X-ray wavelengths are about the same size as the space between atoms in solids. X-rays aimed at a crystal are diffracted by the atoms in the crystalline lattice. This results in an X-ray diffraction pattern, which can be seen on a detector placed behind the crystal. note: The units of d and λ do not matter so long as they are the same. |
Example: X-rays with a wavelength of 1.54062Å scatter at an angle of 12.251∘ from a copper crystal. If n=1, what is the distance between planes of atoms in the copper crystal that give rise to this scattering? Solution: We are given n, λ , and θ, and asked to solve for d. For an answer in units of Å, we do can calculate it directly. d = nλ2sin(θ) = (1×1.54062Å )/(2sin(12.251∘)) =3.63Å This is the distance between the planes in the bcc crystal structure of copper. |
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X-rays with a wavelength of 1.70 Å scatter at an angle of 36.5 ∘ from a crystal. |
According to Bragg’s law nλ = 2d sin θ Where n = 1 λ = wavelength of ligth used =1.70 Ao = 1.70 * 10^-10 m θ = glancing angle = 36.5 degrees d = distance between the palnes = ? Plug the values we get d = nλ / 2 sin θ = ( 1 * 1.70*10^-10 ) / ( 2*sin 36.5 ) = 1.43*10^-10 m d = 1.43 Å |
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To understand basic information about unit cells and how it relates to crystal packing. |
In a crystal, the atoms are arranged in a pattern that repeats throughout the structure. Since the spatial arrangement of the atoms repeats in a stepwise fashion in a crystal, one can define the smallest nonrepeating unit of the crystal. This is called the unit cell. The entire structure of a crystal can be recreated by translating copies of the unit cell in three dimensions. In a simple-cubic (sc) crystal lattice, the unit cell is composed of eight atoms that each take a corner of a cube. (Figure 1) Because this is such an inefficient way to pack atoms, it is a rare arrangement for metals. Only one metal is known to pack in this form: polonium, Po. The body-centered cubic (bcc) crystal lattice consists of a simple cubic unit cell and an additional atom at the center of the unit cell. (Figure 2) Metals such as iron, chromium, tungsten, and sodium pack in the bcc crystal lattice form. The face-centered cubic (fcc) unit cell consists of a simple cubic unit cell with an extra atom at the center of each of the six sides of the cube. (Figure 3) Some examples of metals that pack in this form are nickel, silver, gold, copper, and aluminum. Another crystal lattice is the hexagonal close packing (hcp) crystal lattice. (Figure 4) Some metals that pack in the hcp crystal lattice are zinc, titanium, and cobalt. |
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Rank the crystal lattice structures in order of decreasing efficiency of space in the structure. |
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Simple cubic |
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Body centered cubic |
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Face centered cubic |
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Hexagonal close packing |
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You are a researcher for a golf club manufacturer. You are given two identical looking cubes of a metal alloy. You are informed that they are made of the exact same material, but one is crystalline, whereas the other is amorphous. It is your job to determine which one is amorphous because this one is more stress-resistant and is useful in reinforcing golf clubs. Which of the following is the best way to determine which is which? Determine the density of each cube. The less dense cube is the amorphous solid. Melt both cubes and look for a broader range of melting temperatures. The one that melts over a broader range of temperatures is the amorphous solid. Melt both cubes and measure the range of melting temperatures. The one that melts over a narrower range of temperatures is the amorphous solid. Determine the density of each cube. The more dense one is the amorphous solid. |
Determine the density of each cube. The less dense cube is the amorphous solid. It is also important to note that many crystals are made from more than one kind of atom. For example, proteins will form crystals under the right conditions, and proteins are more complex than a single metal atom. The unit cell concept applies to protein crystals as it does to single atoms. The unit cell may contain one or more proteins and weigh thousands of atomic mass units. Since it is in the form of a crystal, one of the unit cells will enable you to recreate the entire protein crystal. This fact is exploited when structural biologists perform X-ray crystallography to determine the atomic structures of proteins. |
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The atoms of crystalline solid pack together into a three-dimensional array of many small repeating units called unit cells. The simplest of the unit cells are those that have cubic symmetry, with atoms positioned at the corners of a cube. Atoms can also be found in the sides (faces) of the cube, or centered within the body of the cube. It is important to realize that a unit cell is surrounded by other unit cells in every direction. Therefore, face and corner atoms are shared with neighboring unit cells. The fraction varies with the type of atom as shown in the following table. |
The size of a unit cell in any given solid can be calculated by using its density. This and the reverse calculation are common test questions in general chemistry courses. |
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There are three main types of cubic unit cells: |
primitive cubic (or simple cubic), body-centered cubic, and face-centered cubic. |
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Identify the three types of unit cells shown. |
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Calculate the number of atoms per unit cell in each type of cubic unit cell. |
1,2,4 atoms per unit cell Simple cubic cell: 1/8 x 8 = 1 atom/cell Body centered cell: 1/8 x 8 + 1 = 2 atoms/cell Face cubic cell: 1/8 x 8 + 1/2 x 6 = 4 atoms/cell |
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Gallium crystallizes in a primitive cubic unit cell. The length of an edge of this cube is 362 pm. What is the radius of a gallium atom? |
For a cubic unit cell edge length = 2r 2r = a here a = edge of cell = 362 pm Hence r = a/2 = 181 pm |
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The face-centered gold crystal has an edge length of 407 pm. Based on the unit cell, calculate the density of gold. |
We know that density , d = (Z x atomic mass of gold ) / ( No x a 3 x 10 -30 cm 3 ) —(1) Where Z = No . of atoms in a unit cell = 4 Since it is a fcc structure atomic mass of gold = 197 g No = avagadro number = 6.023×10 23 a = edge length = 407 pm Plug these values in (1) we get d = (4×197 ) / ( 6.023×10 23 x 4073x 10 -30 cm 3 ) = 19.4 g / cm 3 |
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What is the radius of a copper atom (in picometers) that crystallizes in a face-centered cubic unit cell with an edge length of 3.62 × 10−8 cm? |
In face-centered cubic packing, the spheres touch along the face diagonal thus the face diagonal = 4r and the edge = 2*sqrt(2)*r. r = 362 pm/(2*sqrt(2)) = 127.98 pm |
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How many atoms are in the following: One body-centered cubic unit cell of a metal One face-centered cubic unit cell of a metal |
Number of atoms per unit cell in primitive cubic = 1 Number of atoms present in body centered cubic cell = 2 Number of atoms present in face centered cubic unit cell = 4 |
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Polonium metal crystallizes in a simple cubic arrangement, with the edge of a unit cell having a length d = 334 pm. What is the radius in picometers of a polonium atom? |
r = 167 pm |
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Polonium metal crystallizes in a simple cubic arrangement, with the edge of a unit cell having a length d = 334 pm. What is the density of polonium in g/cm3? |
ρ = 9.31 g/cm3 |
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The unit cell of a crystal can be described in term of its edge length, l, and the number of atoms it contains. The edge length defines the volume of a cubic unit cell, V, as |
Based on the number of atoms per unit cell and the mass of the atom, the mass m of the unit cell can be calculated. The density of the unit cell and the material as a whole can be determined from the mass mand the volume V of the unit cell as. density=mV The usual units of density are grams per cubic centimeter or g/cm3. |
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Nickel, Ni, has a face-centered cubic structure(Figure 1) with an edge length of 352 pm. What is the density of this metal? Use the periodic table as needed. |
Step 1 : To calculate volume of the unit cell Edge length, a = 352pm = 352X10-12 m Volume, V = a3 = (352X10-12 m)3 V = = 4.36X10-29 m3 Step 2: To calculate mass of an atom of Nickel Molar mass of Nickel = 58.69 g/mol 1 mole = 6.023X1023 atoms So, mass of 6.023X1023 atoms of Nickel = 58.69g mass of 1 atom of Nickel = 58.69g / (6.023X1023) = 9.744X10-23 g Step 3 : To calculate density of the unit cell / Nickel metal No. of atoms per fcc unit cell , n = 4 Mass of 4 atoms of Nickel,m = mass of 1 atom of Ni X 4 = (9.744X10-23 g) X 4 m = 38.977 X 10-23 g Density = m/V = (38.977 X 10-23 g ) / ( 4.36X10-29 m3) = 8.94 X 106 g/m3 Density = = 8.94 g/cm3 ( 1m3 = 106 cm3) |
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In ionic solids, the anions form the unit cell and the smaller cations fill the "holes" within that unit cell. Complete each statement based on the images below. Notice that the anions are represented by large red spheres and the cations are represented by smaller blue spheres. |
See next slide |
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Complete each statement based on the images below. Notice that the anions are represented by large red spheres and the cations are represented by smaller blue spheres. |
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The properties of a given metal are greatly dependent upon the way in which the atoms are arranged. A unit cell is like a "zoomed-in" view of a substance that allows us to see the basic pattern of the arrangement of atoms. In this problem you will study several types of cubic arrangements: the simple cubic,(Figure 1) the face-centered cubic,(Figure 2) and the body-centered cubic. Bismuth is a nontoxic metal that is used in pharmaceuticals and chemicals . Bismuth has a simple cubic unit cell. How many atoms of Bi are present in each unit cell? Aluminum has a face-centered cubic unit cell. How many atoms of Al are present in each unit cell? Molybdenum has a body-centered cubic unit cell. How many atoms of Mo are present in each unit cell? |
Bi: simple cubic No of atoms = 8*1/8 = 1 You have found that for the simple cubic the total number of atoms per unit cell is given by 8/8=1. Bi atoms = 1 Al: There are 8 corner atoms each contributing 1/8 atom and 6 face atoms each contributing 1/2 atom No. of Al atoms in unit cell = (8 x 1/8) + (6 x 1/2) = 4 Mo: You have found that for the body-centered cubic the total number of atoms per unit cell is given by 8/8+1=2 |
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Count the numbers of + and – charges in the CuCl unit cells (the figure given below), and show that cells are electrically neutral. |
Cu+,Cl− = 4,4 |
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Count the numbers of + and – charges in the BaCl2 unit cells (the figure given below), and show that the cells are electrically neutral. |
Ba2+,Cl− = 4,8 |
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Rhenium oxide crystallizes in the following cubic unit cell: How many rhenium atoms and how many oxygen atoms are in each unit cell? What is the formula of rhenium oxide? What is the oxidation state of rhenium? What is the geometry around each oxygen atom? What is the geometry around each rhenium atom? |
NRe, NO = 1,3 ReO₃ +6 linear octahedra |
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How many chloride anions surround a cesium cation in CsCl, which crystallizes such that the cesium cations are at the corners of the cubic cells and the anions are in the centers of the cells for the cations? |
8 |
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A phase diagram is a temperature-pressure plot that summarizes the conditions under which a substance exists as a solid, liquid, or gas. The curves that separate the phases are known as phase boundaries. Each phase boundary represents the equilibrium between the phases on either side of the curve. Identify the components of the phase diagram of water. |
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Points A to G are located on the phase diagram of water. Which of the following statements are correct regarding navigation from one point to another across the phase diagram? At point E, the temperature is less than 0∘C. Moving from point A to point C, the temperature increases. To move from point G to point B, you must increase the temperature. To move from the point G to point F, you must increase both the temperature and the pressure. To move from point C to point D, you must decrease only the pressure. To move from point D to point F, you must decrease both the temperature and the pressure. |
At point E, the temperature is less than 0∘C. Moving from point A to point C, the temperature increases. To move from the point G to point F, you must increase both the temperature and the pressure. To move from point C to point D, you must decrease only the pressure. Water is a unique molecule in that its melting point decreases as pressure is increased. This has to do with the solid structure of water, which is actually less dense than liquid water. As the pressure increases, the molecules of water are forced closer together, breaking the rigid solid lattice and liquefying ice. |
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The triple point of water is 0.0098∘C at 0.00603 atm (4.58 torr). At the triple point, ice, water, and water vapor exist in equilibrium with each other. Complete the following sentences to identify the process that ice, water, or water vapor may undergo if either the temperature or the pressure is increased. |
1. sublime, because it is going from solid to gas. 2. melt, because it goes from solid to liquid at 1atm 3. condense, because it goes from gas to liquid 4. deposit, because it goes from gas to solid. |
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Phase diagrams for water (Figure 1) and carbon dioxide (Figure 2) are given here for your reference. At 100 ∘C and 1 atm, water is in which phase? Enter the critical temperature of water. At -70 ∘C and 5.2 atm, carbon dioxide is in which phase? At -30 ∘C and 2 atm carbon dioxide is in the gas phase. From these conditions, how could the gaseous CO2 be converted into liquid CO2? |
The water will be in both liquid as well as vapour phase. There will be a liquid and gas phase equilibrium. 374°C solid Increase the pressure. |
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What is the phase change sequence that shows all of the phase changes that occur when the temperature is lowered from just below the critical-point temperature while maintaining the critical-point pressure? |
Liquid → solid. |
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Gallium metal has the following phase diagram (the pressure axis is not to scale). In the region shown, gallium has two different solid phases. Where on the diagram are the solid, liquid, and vapor regions? How many triple points does gallium have? At 1 atm pressure, which phase is more dense, solid or liquid? |
See pic 2 liquid |
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Look at the phase diagram of CO2 in the figure, and tell the minimum pressure in atmospheres at which liquid CO2 can exist. |
P = 5.11 atm |
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Look at the phase diagram of CO2 in the figure, and describe what happens to a CO2 sample when the following changes are made: The temperature is increased from -100 ∘C to 0 ∘C at a constant pressure of 2 atm. The pressure is reduced from 72 atm to 5.0 atm at a constant temperature of 30 ∘C. The pressure is first increased from 3.5 atm to 76 atm at -10 ∘C, and the temperature is then increased from -10 ∘C to 45 ∘C. |
CO2(s)→CO2(g) CO2(l)→CO2(g) CO2(g)→CO2(supercritical) |
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Ethyl acetate, CH3CO2CH2CH3, is commonly used as a solvent and nail-polish remover. Look at the following electrostatic potential map of ethyl acetate, and explain the observed polarity. |
The electronegative O atoms are electron rich, while the rest of the molecule is electron poor |
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cubic closest-packed |
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simple cubic |
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hexagonal closest-packed |
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body-centered cubic |
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Zinc sulfide, or sphalerite, crystallizes in the following cubic unit cell. What kind of packing do the sulfide ions adopt? How many S2− ions are in the unit cell? How many Zn2+ ions are in the unit cell? |
Cubic closest-packed. 4 S2− ions per unit cell. 4 Zn2+ ions per unit cell. |
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Perovskite, a mineral containing calcium, oxygen, and titanium, crystallizes in the following cubic unit cell. What is the formula of perovskite? What is the oxidation number of titanium in perovskite? |
CaTiO₃ +4 |
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Boron nitride, BN, is a covalent network solid with a structure similar to that of graphite. Choose the right structure for a small portion of the boron nitride structure. |
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What is the difference between London dispersion forces and dipole-dipole forces? |
Dipole-dipole forces arise between molecules that have permanent dipole moments. London dispersion forces arise between molecules as a result of induced temporary dipoles. |
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Of the substances Xe, CH3Cl, HF, which has: The smallest dipole-dipole forces? The largest hydrogen bond forces? The largest dispersion forces? |
Xe HF CH₃Cl |
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What are the most important kinds of intermolecular forces present in each of the following substances? Chloroform, CHCl3 Oxygen, O2. Polyethylene, CnH2n+2 Methanol, CH3OH |
Dipole-dipole intermolecular forces are most important. London dispersion forces are most important. London dispersion forces are most important. Dipole-dipole intermolecular forces and hydrogen bonds are important. |
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Which substance in each of the following pairs would you expect to have larger dispersion forces? Ethane, C2H6, or octane, C8H18 |
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Which substance in each of the following pairs would you expect to have larger dispersion forces? HCl or HI |
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Which substance in each of the following pairs would you expect to have larger dispersion forces? H2O or H2Se |
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Which of the following substances would you expect to have a nonzero dipole moment? XeF4 |
CL2O and CH3CH2CL has non zero dipole moments The molecular geometry of Cl2O is similar to that of H2O, except the bond angle is about 111 degrees. The polar bonds, plus the bent molecular geometry produces a polar molecule with the oxygen having a slight negative charge and the chlorine atoms a slight positive charge. The dipole moment is 0.78D Each B-F has a dipole moment because electronegativity (EN) of B is 2 and EN of F is 4. However, the symmetry of the Molecule negates these individual dipoles and Net dipole of molecule is zero. This is a trigonal planar molecule (sp2 boron atom). XeF4 is a square planar molecule and has no dipole moment. Ethyl chloride (CH3CH2Cl) is covalent, with a carbon chain ("greasy" hydrophobic, non-polar), and little dipole moment overall |
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Which of the following substances would you expect to have a nonzero dipole moment? NF3 |
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Which of the following substances would you expect to have a nonzero dipole moment? CH3NH2 |
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Which of the following substances would you expect to have a nonzero dipole moment? XeF2 |
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Which of the following substances would you expect to have a nonzero dipole moment? PCl5 |
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The dipole moment of ClF is 0.887 D and the distance between atoms is 162.8 pm. |
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The class of ions PtX2−4, where X is a halogen, has a square planar geometry. Choose a structure for a PtBr2Cl2−2 ion that has no dipole moment. |
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Of the two compounds SiF4 and SF4, which is polar and which is nonpolar? |
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1,3-Propanediol can form intra molecular as well as intermolecular hydrogen bonds. Choose the right structure of 1,3-propanediol showing an intramolecular hydrogen bond. |
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Water flows quickly through the narrow neck of a bottle, but maple syrup flows sluggishly. Is this different behavior due to a difference in viscosity or in surface tension for the liquids? |
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Why is ΔHvap usually larger than ΔHfusion? |
ΔHvap is usually larger than ΔHfusion because ΔHvap is the heat required to overcome all intermolecular forces. |
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Why is the heat of sublimation, ΔHsubl, equal to the sum of ΔHvap and ΔHfusion at the same temperature? |
Sublimation is the direct conversion of a solid to a gas. A solid can be converted to a gas in two steps: melting followed by vaporization. The energy to convert a solid to a gas must be the same regardless to the path. |
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Mercury has mp = -38.9∘C and bp = 356.6∘C. What, if any, phase changes take place under the following conditions at 1.0 atm pressure? The temperature of a sample is raised from -30∘C to 365∘C. |
Hg(l)→Hg(g) |
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Mercury has mp = -38.9∘C and bp = 356.6∘C. What, if any, phase changes take place under the following conditions at 1.0 atm pressure? The temperature of a sample is lowered from 291K to 238K. |
There are no frase changes at this conditions. |
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Mercury has mp = -38.9∘C and bp = 356.6∘C. What, if any, phase changes take place under the following conditions at 1.0 atm pressure? The temperature of a sample is lowered from 638K to 231K. |
Hg(g)→Hg(l)→Hg(s) |
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Ether at room temperature is placed in a flask connected by a rubber tube to a vacuum pump, the pump is turned on, and the ether begins boiling. Explain. |
The normal boiling point for ether is relatively low. As the pressure is reduced by the pump, the relatively high vapor pressure of the ether equals the external pressure produced by the pump, and the liquid boils. |
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How much energy (in kilojoules) is released when 13.0 g of steam at 130.0 ∘C is condensed to give liquid water at 62.0 ∘C? The heat of vaporization of liquid water is 40.67 kJ/mol, and the molar heat capacity is 75.3 J/(K⋅mol) for the liquid and 33.6 J/(K⋅mol) for the vapor. What is ΔHvap for SiCl4 in kJ/mol? |
Clausius-Claperyon equation: ln(P2/P1) = (-DHvap/R) x (1/T2 – 1/T1) Molar gas constant R = 8.314 J/mol.K P1 = 100 mmHg, T1 = 5.4 deg C = 278.55 K At normal boiling point: P2 = 1 atm = 760 mmHg, T2 = 56.8 deg C = 329.95 K ln(760/100) = (-DHvap/8.314) x (1/329.95 – 1/278.55) Heat of vaporization = DHvap = 3.02 x 10^4 J/mol = 30.2 kJ/mol |
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What is the vapor pressure of SiCl4 (in mm Hg) at 26.5 ∘C? The vapor pressure of SiCl4 is 100mm Hg at 5.4∘C, and ΔHvap = 30.2kJ/mol. |
P = 250 mm Hg |
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Choose any two temperatures and corresponding vapor pressures in the table given, and use those values to calculate ΔHvap for mercury (in kJ/mol). |
Clausius-Claperyon equation: ln(P2/P1) = (-DHvap/R) x (1/T2 – 1/T1) Molar gas constant R = 8.314 J/mol.K Choosing a pair of (P,T) values from table (you can choose any pair but here we have used the values at 500 K and 600 K): P1 = 39.3 torr, T1 = 500 K P2 = 432.3 torr, T2 = 600 K Substituting values into equation: ln(432.3/39.3) = (-DHvap/8.314) x (1/600 – 1/500) Heat of vaporization = DHvap = 5.98 x 10^4 J/mol = 59.8 kJ/mol |
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What kinds of particles are present in each of the four main classes of crystalline solids? |
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Which of the substances diamond, Hg, Cl2, glass, and KCl best fits each of the following descriptions? amorphous solid |
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Which of the substances diamond, Hg, Cl2, glass, and KCl best fits each of the following descriptions? ionic solid |
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Which of the substances diamond, Hg, Cl2, glass, and KCl best fits each of the following descriptions? molecular solid |
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Which of the substances diamond, Hg, Cl2, glass, and KCl best fits each of the following descriptions? covalent network solid |
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Which of the substances diamond, Hg, Cl2, glass, and KCl best fits each of the following descriptions? metallic solid |
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Silicon carbide is very hard, has no known melting point, and diffracts X rays. What type of solid is it: amorphous, ionic, molecular, covalent network, or metallic? |
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Which of the substances Na3PO4, CBr4, rubber, Au, and quartz best fits each of the following descriptions? amorphous solid |
rubber |
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Which of the substances Na3PO4, CBr4, rubber, Au, and quartz best fits each of the following descriptions? ionic solid |
Na3PO4 |
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Which of the substances Na3PO4, CBr4, rubber, Au, and quartz best fits each of the following descriptions? molecular solid |
CBr4 |
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Which of the substances Na3PO4, CBr4, rubber, Au, and quartz best fits each of the following descriptions? covalent network solid |
quartz |
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Which of the substances Na3PO4, CBr4, rubber, Au, and quartz best fits each of the following descriptions? metallic solid |
Au |
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Diffraction of X rays with = 154.2 pm occurred at an angle θ=22.5∘C from a metal surface. What is the spacing (in pm) between the layers of atoms that diffracted the X rays? |
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What is a unit cell? |
The unit cell is the smallest repeating unit in a crystal. |
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Which of the four kinds of packing used by metals makes the most efficient use of space? Which makes the least efficient use? |
hexagonal closest-packed hexagonal closest-packed simple cubic |
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Copper crystallizes in a face-centered cubic unit cell with an edge length of 362pm. What is the radius of a copper atom (in picometers)? |
Edge length a = 362 pm In face – centerd cubic unit cell radius = \sqrt{2} a / 4 = 1.414 x 362 / 4 = 128 pm radius of copper atom = 128 pm |
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What is the density of copper in g/cm3? |
Copper metal has a density of 8.92 g/cm3 at 20.0 °C and 8.83 g/cm3 at 100.0 °C. Calculate the change in volume that occurs when a 10.0 cm3 piece of copper is heated from 20.0 °C to 100.0 °C. 2. |
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Lead crystallizes in a face-centered cubic unit cell with an edge length of 495 pm. What is the radius of a lead atom (in picometers)? What is the density of lead in g/cm3? |
r = 175 pm ρ = 11.3 g/cm3 |
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4.Aluminum has a density of 2.699 g/cm3 and crystallizes with a facecentered cubic unit cell. What is the length of the edge of the unit cell in picometers? |
V=n×MW/ d×N =404.9pm |
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Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 317pm. What is the length (in picometers) of a unit-cell diagonal that passes through the center atom? |
Lenght of diagonal = √3 a = √3 x 317 pm = 549 pm |
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The length of a unit-cell diagonal that passes through the center atom in tungsten is equal to 549pm. What is the radius (in picometers) of a tungsten atom? |
137 |
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Sodium has a density of 0.971g/cm3 and crystallizes with a body-centered cubic unit cell. What is the radius of a sodium atom (in picometers)? What is the edge length of the cell (in picometers)? |
r = 186 pm d = 429 pm |
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Titanium metal has a density of 4.54g/cm3 and an atomic radius of 144.8 pm. How many Ca atoms are in one unit cell? In what cubic unit cell does titanium crystallize? |
4 atoms Face-centred cubic. |
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Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl. How many Na+ ions touch each H− ion? How many H− ions touch each Na+ ion? |
6 ions 6 ions |
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Cesium chloride crystallizes in a cubic unit cell with Cl− ions at the corners and a Cs+ ion in the center. Count the numbers of + and − charges. Is the unit cell electrically neutral? |
+ charges, − charges = 1.00,1.00 per unit cell yes |
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Look at the phase diagram of H2O in Figure 10.28 in the textbook, and tell what happens to an H2O sample when the following changes are made. The temperature is reduced from 48∘C to -4.4∘C at a constant pressure of 6.5 atm. The pressure is increased from 85 atm to 226atm at a constant temperature of 380∘C. |
H2O(l)→H2O(s) Water will be a supercritical fluid. |
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Using the bromine phase diagram, tell what phases are present under the following conditions: T=−10∘C, P = 0.0075 atm T=25∘C, P= 16 atm |
Br2(g) Br2(l) |
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Fluorine is more electronegative than chlorine, yet fluoromethane (CH3F; μ=1.86 D) has a smaller dipole moment than chloromethane (CH3Cl; μ=1.90 D). Explain. |
Because chlorine is larger than fluorine, the charge separation is larger in CH3Cl compared to CH3F, resulting in CH3Cl having a slightly larger dipole moment. |
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Magnesium metal has ΔHfusion = 9.037 kJ/mol and ΔSfusion = 9.79 J/(K⋅mol). What is the melting point (in ∘C) of magnesium? |
Mg(s) ⇋ Mg(l) ΔG = ΔH – TΔS At equilibrium ΔG = 0 and hence ΔH = TΔS Convert ΔHfus into J mol^-1 and we have: 9037 = 9.79T T = 923.08 K = 650°C |
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The dipole moment of ClF is 0.88 D, and its bond length is 163 pm. What is the percent ionic character of the Cl-F bond? |
11 |
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Solids having no ordered long-range structure are classified as |
amorphous. |
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When a liquid is heated at its boiling point, the |
temperature of the liquid remains the same as long as any liquid is present. |
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If figure (1) represents the vapor pressure of water at 25°C, which figure represents the vapor pressure of ethanol, CH3CH2OH at 25°C? |
figure (3) |
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An ionic compound crystallizes in a unit cell having a face-centered cubic array of anions, X-, and half of the tetrahedral holes filled with metal ions, Mn+ The empirical formula of this ionic compound is |
MX. |
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Which transition could occur if a solid is heated at a pressure above the triple point pressure? |
melting |
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Which drawing best represents hydrogen bonding? |
drawing (3) |
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Which of the following statements is not consistent with the properties of a molecular solid? |
a compound that conducts electricity when molten |
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Molecules of a liquid can pass into the vapor phase only if the |
molecules have sufficient kinetic energy to overcome the intermolecular forces in the liquid. |
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An element forms a body-centered cubic crystalline substance. The edge length of the unit cell is 287 pm and the density of the crystal is 7.92 g/cm3. Calculate the atomic weight of the substance. |
56.4 amu |
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Which of the following forms a molecular solid? |
C9H8O4 |
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Silver crystallizes in a face-centered cubic structure. What is the edge length of the unit cell if the atomic radius of silver is 144 pm? |
407 pm |
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In liquid methanol, |
Dispersion, hydrogen bonding and dipole-dipole forces are present. |
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The intermolecular forces responsible for CH3CH2OH being at liquid at 20°C are ________ bonds. |
hydrogen |
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Which of the following exhibits ion-dipole forces? |
NaCl(aq) |
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A certain mineral crystallizes in the cubic unit cell shown below. M represents the cations and A represents the anions. What is the empirical formula of the mineral? |
MA |
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MgO crystallizes in a cubic unit cell with O2- ions on each corner and each face. How many Mg2+ and O2- ions are in each unit cell of MgO? |
4 Mg2+ ions and 4 O2- ions |
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Cesium has a radius of 272 pm and crystallizes in a face-centered cubic unit cell. What is the edge length of the unit cell? |
769 pm |
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Which is expected to have the largest dispersion forces? |
C8H18 |
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Identify the packing in the figure shown below. |
simple cubic |
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An ionic compound crystallizes in a unit cell having a face-centered cubic array of metal ions, M n+, and all of the tetrahedral holes occupied by anions, X-. The empirical formula of this ionic compound is |
MX2 |
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Which of the following forms an ionic solid? |
NH4Cl |
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The vapor pressure of a pure liquid increases as the |
temperature of the liquid phase increases. |
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Which of the following compounds exhibits hydrogen bonding? |
NH3 |
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Which substance in each of the following pairs is expected to have the larger dispersion forces? |
2 in set I and n-butane in set II |
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