Question

Intermolecular forces, heating curves, phase diagrams, Clausius-Clapyron equation, and Unit cell calculations

1.     If 42.0 kJ of heat is added to a 32.0 g sample of liquid methane under 1 atm of pressure at a temperature of -170 ^oC, what are the final state and temperature of the methane once the system equilibrates? Assume no heat is lost to the surroundings. The normal boiling point of methane is -161.5 ^oC. The specific heats of liquid and gaseous methane are 3.48 and 2.22 J/g-K, respectively.

2.     The phase diagram for a hypothetical substance is shown below:

                a) Estimate the normal boiling point and freezing point of the substance.
                b) What is the physical state of the substance under the following conditions?
                    i) T = 150 K, P = 0.2 atm
                     ii) T = 100 K, P = 0.8 atm
                     iii) T = 300 K, P = 1.0 atm
                c) What is the triple point of the substance?

3.     Benzoic acid, C₆H₅COOH, melts at 122 ^oC. The density in the liquid state at 130 ^oC is 1.08 g/cm³. The density of solid benzoic acid at 15 ^oC is 1.266 g/cm³.

                a) In which of these two states is the average distance between molecules greater?

                b) Explain the difference in densities at the two temperatures in terms of the relative kinetic                           energies of the molecules.

4.     At standard temperature and pressure the molar volume of Cl₂ and NH₃ gases are 22.06 L and 22.40 L, respectively.
                a) Given the different molecular weights, dipole moments, and molecular shapes, why are their                                         molar volumes nearly the same?
                b) On cooling to 160 K, both substances form crystalline solids. Do you expect the molar                                                       volumes to decrease or increase on cooling to 160 K?
                c) The densities of crystalline Cl₂ and NH₃ at 160 K are 2.02 and 0.84 g/cm³, respectively.                                                         Calculate their molar volumes.
                d) Are the molar volumes in the solid state as similar as they are in the gaseous state? Explain. e) Would you expect the molar volumes in the liquid state to be closer to those in the solid or                                     gaseous state?

5.     Draw a heating curve for the conversion of 100 g of ice at -25 ^oC to steam at 125 ^oC. Temperatures should be labled but the sketch does not have to be to scal and the values for q do not need to be identified.

                a) Comparing the heating of water to the heating of steam, these lines should have a different                                        slope. Explain why that is.
                b) The length of the line for the conversion of water to steam should be much longer than the                                       line representing the amount of heat required to convert ice to water. Explain why that is.
                c) The specific heat capacities for ice, water, and steam are 2.03, 4.18, and 2.01 J/g-^oC.
                     The DH_vap of water is 40.65 kJ/mol and the DH_fus of water is 6.01 kJ/mol.
                     Calculate the amount of heat required to convert 100 g of ice at 0 ^oC to steam at 100 ^o.

6. The following quote about ammonia (NH₃) is from a textbook of inorganic chemistry: �It is estimated that 26% of the hydrogen bonding in NH₃ breaks down on melting, 7% on warming from the melting to the boiling point, and the final 67% on transfer to the gas phase at the boiling point.� From the standpoint of the kinetic energy of the molecules, explain
                a) why there is a decrease of hydrogen-bonding energy on melting and
                b) why most of the loss in hydrogen bonding

7. Name the phase transition in each of the following situations and indicate whether it is exothermic or endothermic:
                a) Bromine vapor turns to bromine liquid as it is cooled.
                b) Crystals of iodine disappear from an evaporating dish as they stand in a fume hood.
                c) Rubbing alcohol in an open container slowly disappears.
                d) Molten lava from a volcano turns into solid rock.

8. Compounds like CCl₂F₂ are known as chlorofluorocarbons, or CFC's. These compounds were once widely used as refrigerants but are now being replaced by compounds that are believed to be less harmful to the environment. The heat of vaporization of CCl₂F₂ is 289 J/g. What mass of this substance must evaporate to freeze 200 g of water initially at 15 ^oC? (The heat of fusion of water is 334 J/g; the specific heat of water is 4.184 J/g-^oC.)

9. The critical temperatures (K) and pressures (atm) of a series of halogenated methanes are as follows:

                a) List the intermolecular forces that occur for each compound.
                b) Predict the order of increasing intermolecular attraction, from least to most, for this series of                                      compounds.
                c) Predict the critical temperature and pressure for CCl4 based on the trends in this table.

10. Explain how each of the following affects the vapor pressure of a liquid:
                a) volume of the liquid,
                b) surface area,
                c) intermolecular attractive forces,
                d) temperature,
                e) density of the liquid.

11. Explain the following observations:
                a) Water evaporates more quickly on a hot, dry day than on a hot, humid day.
                b) It takes longer to cook an egg in boiling water at high altitudes than it does at lower altitudes.

12.         a) What is the significance of the critical point in a phase diagram?
                b) Why does the line that separates the gas and liquid phases end at the critical point?

13. The normal boiling point of acetone, an important laboratory and industrial solvent, is 56.2 ^oC and its DH_vap is 25.5 kJ/mol. At what temperature (in ^oC) does acetone have a vapor pressure of 375 torr?

14. Selenium tetrafluoride, SeF₄, is a colorless liquid. It has a vapor pressure of 757 mmHg at 105 ^oC and 522 mmHg at 95 ^oC. What is its heat of vaporization in kJ/mol?

15. Iron has a body-centered unit cell with a cell dimension of 286.65 pm.
            a) How many iron atoms are in each unit cell?
            b) Calculate the density of iron in g/cm³. (1 pm = 10^-12 m)

16. Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell).
            a) How many aluminum atoms are in each unit cell?
            b) Estimate the edge of the unit cell from the atomic radius of Aluminum
                     (1.43 �, 1 � = 10^-10 m).
            c) Calculate the density of aluminum metal.

Answer 1

1.

3.The average distance between molecules is the greatest in liquid state.

At higher temperatures, molecules have more available energy. With enough energy, the molecules can break free from the solid lattice to form a liquid. Interionic attraction in liquid is less strong than in the solid. With more energy, the molecules can also overcome more of the intermolecular forces that hold them together. This results in more void space, and lower density.

4.

a.MOlar volume of ideal gases depend only on the no of particles. Since one mole of any gas contain Avogadro no f particles, molar volume of all gases are same. Ideal gas molecules do not have volume and no intermolecular attraction is there between the molecules. So dipole moments or molecular shape do not affect the volume. Real gases differ slightly in molar volumes because the factors such as intermolecular attraction or the effect of molecular shape are not negligible.

b. Molar volume will decrease in the crystalline state because in solid state the effect of intermolecular attraction cannot be neglected.

c. density = mass/volume

Molar volume of crystalline Cl₂ = 71/2.02 = 35.12 cm³

Molar volume of crystalline NH₃ = 17/2.02 = 20.24 cm³

d. No. Interionic attraction decreases the volume.

e. The molar volumes in the liquid state will be closer to those in the solid state.