Chemistry 2720 Fall 1999 Test 2 Solutions

1. For the reaction

   

   

   The equilibrium constant is related to by

   

   However,

   

2. The process is . There are two ways to tackle this problem:
   1. At the boiling point, the liquid is in equilibrium with vapor at 1atm. Equilibrium is obtained when so that . For this process, . For the pure liquid, . At the boiling point, . Therefore . However, so that

      

      At 298.15K,

      

      or about .

   2. At 298.15K, . Therefore

      

      At the boiling point, . Using the relationship between equilibrium constants and temperatures, we have

      

3. We begin by calculating the number of moles of sodium acetate:

   

   The formal (total) acetate concentration in this solution is therefore 0.305mol/L. Acetic acid arises from the reaction

   

   for which the equilibrium constant is :

   

   neglecting factors of the standard concentration. The very small value of and the significant initial concentration of acetate together suggest that only a negligible amount of acetate will react. It follows that, at equilibrium, . It follows that

   

   This product is much larger than so the autoionization of water is not significant. Accordingly, by stoichiometry, so that

   

   The activity of is therefore

   

   which corresponds to a pH of 9.1.

4. The overall reaction is

   

   The standard free energy change for this reaction is

   

   If is negative, the reaction is spontaneous. We can reduce the ratio of ATP to ADP only to the extent that remains negative. Beyond that, the reaction is no longer spontaneous and G6P will not be produced. Thus, the critical minimum ratio is reached when , i.e.\ when the reaction is at equilibrium.

   

5. Step 1:

   The maximum work at 350K is wanted, so this calculation at 298K is not needed.

   Step 2:

   For the reaction as written, we should have

   

   Steps 2-3:

   The units of and of the term don't match.

   Steps 5-6:

   This should be a calculation of from and . It is improper to do this calculation with .

   Step 6:

   The units of and don't match. Also, the sign of wasn't properly carried through this calculation. Finally, the units of are wrong.

   Step 8:

   The units are again mishandled.

   Step 9:

   Maximum work is , not .

   Step 10:

   The reaction ratio is again wrong.

   Step 12:

   The free energy change calculated in step 11 is positive so, according to the student's answer, work must be done on this system for this reaction to proceed. To be consistent, the student should therefore report that no work can be obtained.