CH353 - Physical Chemistry I
Spring 2012, Unique 52135

Homework, Week 15

Homework, week 15
Answer key

1.  Explain the significance of a state function and list six properties that can be determined by state functions.

2.  When one mole of an ideal gas is compressed adiabatically and reversibly to one-half its original volume, the temperature of the gas increases from 273 K to 433 K.

a) Why does the temperature rise?

b) Determine the value of CV,m for this gas, assuming it is independent of temperature.

c)  Find q, w, deltaU, deltaH, and deltaStot of the compression.

3.  Please look at the phase diagram of H2O on pg. 1 of the pdf file.  Label each phase and provide a succinct and clear explanation of the difference in the relative slopes of each phase boundary shown.  (You don’t need to explain the origin of any curvature in these boundaries.) 


4.  Chloroform can be synthesized from natural gas and elemental chlorine according to the following reaction:

                        CH4(g) + 3 Cl2 (g) --> CHCl3(l) + 3 HCl(g)

Initially the system contains 3 bar CH3(g), 1 bar Cl­2(g), and 2 bar HCl(g), with some liquid chloroform present.  Determine the Gibbs energy, deltaGrxn for this system.

5.  (Please look at the pdf file for this question.)  Consider the figure on pg. 2 of the pdf file:

            a) What information is being represented on this figure?

b)  The four curves have slopes of -0.0125 s-1, -0.0250 s-1, -0.0500 s-1, and -0.1000 s-1.  Assign a slope to each curve.

c)  Label the magnitude of the y axis (i.e. put a number next to each tick mark and the origin). 

6.  In each of the following senarios, determine if deltaSsys is positive.  In each case the system is underlined.

            a)  A drop of ink is dispersed in a liter of water.

            b)  Ice melts in your cooler over the course of your afternoon picnic.

            c)  A heat pump cools your room from 85˚C to 78˚C.

            d)         Humpty Dumpty sat on a wall

                        Humpty Dumpty had a great fall

                        All the king’s horses and all the king’s men

                        Couldn’t put Humpty together again.

            e)  One mole of fructose (C6H12O6) is combusted in oxygen to form carbon dioxide and water.

7.  A singly-degenerate three-state system, has energy levels E1 = 0, E2 = e, E3 = 2e.  This system is filled with 4 molecules.

            a) How many individual microstates are present in this system?

            b) How many macrostates are present in this system?

            c)  What is the partition function of the system?

            d)  Plot the probability of each state vs. T.

8.  Nitric anhydride (N2O5(g)) decomposes to NO2(g) and O2(g):

                        2 N2O5(g) --> 4 NO2(g) + O2(g)

with the experimentally observed rate law

                        d[O2]/dt = k(obs)[N2O5]

The following mechanism has been proposed for this decomposition:

                        1) N2O5(g) --> NO2(g) + NO3(g)

                        2) NO2(g) + NO3(g) --> NO(g) + NO2(g) + O2(g)

                        3) NO3(g) + NO(g) --> 2 NO2(g)

where the steady-state approximation is assumed to apply to both the NO(g) and NO3(g) reaction intermediates.  Determine whether this mechanism is consistent with the experimentally observed rate law, and if so, express kobs in terms of the rate constants for the individual steps of the reaction mechanism.

9. A 2.0 kg block of copper at a temperature of 0˚C is placed in an adiabatic container containing 1.0 mol H2O(g) at 100˚C and 1 atm.  Assuming that all of the water vapor is condensed to liquid, determine the change in entropy of the water, the change in entropy of the copper, and the change in entropy of the surroundings, and the total change in entropy.  

10. Compound 1 at volume V1 is mixed with compound 2 at V2 at constant temperature and pressure.  Determine deltaV, deltaS, deltaG, deltaA, and deltaU upon mixing.