Chemistry 2720 Spring 1998 Test 2 Solutions

1. The reaction is

   

   Start by calculating the equilibrium constant:

   

   The equilibrium constant is related to the equilibrium activities by . In a rigid container at constant temperature, . It follows (by stoichiometry) that . We therefore get the quadratic equation

   

   or

   

   This equation has two solutions:

   

   One solution ( ) leads to a negative activity for the nitrogen dioxide and is therefore physically inadmissible. The other solution is which gives . Thus the equilibrium ratio of to is 0.92.

2. For the process

   

   at the boiling point. At the normal boiling point, . Thus we have

   

   or

   

   This temperature is sufficiently high that liquid water could still exist on this planet.

3. 1.   We can read this off directly from the differential of A:

      

   2. We start with the answer to question 3a:

      

   3. For an ideal gas, P = nRT/V so

      

4. We need , which is the equilibrium constant for the process

   

   

   The equilibrium constant at 298K is therefore

   

   Therefore

   

   at 298K, giving us a of 10.1.

   To get the , we need to know the equilibrium constant at this temperature. For this we need .

   

5. 1. Two reactions are coupled if they can be made to occur together in such a way that one reaction drives the other. This requires that the overall free energy change for the two reactions taken together be negative. For example, fructose-6-phosphate is made from fructose by reaction with phosphate:

      

      This reaction can be made to yield more product if it is coupled to a reaction with a very negative free energy change which produces phosphate such as ATP hydrolysis:

      

      The overall process is

      

   2. Le Chatelier's principle states that a chemical system will react in such a way as to partially offset an applied stress. For example, increasing the temperature shifts the equilibrium of exothermic reactions toward the reactants because exothermic reactions absorb heat when reactants are formed from the products. Coupled reactions also rely on Le Chatelier's principle: In the example above, we might say that production of fructose-6-phosphate is increased because ATP hydrolysis supplies one of the reactants of the other reaction. The system responds by reacting away some of this phosphate.
6. The overall process is

   

   Maximum transport (requiring the minimum ratio of ATP to ADP) is achieved when , i.e. when

   

   However,

   

   In the biochemists' standard state, , and . Therefore