Solutions to the Practice Problem on Electrochemistry

1. (The steps are numbered sequentially so the numbers don't correspond directly to those from the procedure taught in class.)
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2. 1. A heat engine converts heat to work so we need to calculate the heat produced by the reaction. At constant pressure, this is just . The reaction is

      

      

      The efficiency of the heat engine is

      

      The efficiency is related to the maximum work by so the maximum work done, per mole of methanol burned is

      

   2. A fuel cell is an isothermal free energy machine that carries out oxidation under controlled conditions. Thus free energy considerations limit the maximum work that can be done. The reaction which occurs in the fuel cell is

      

      (Note the different states of methanol and water in this case. If operated well below , fuel cells produce liquid water.) We start by calculating :

      

      Then we calculate itself:

      

      The maximum work which can be obtained from this fuel cell is 702.3kJ/mol, or almost twice as much as we get from the methanol heat engine.

   3. From the oxygen half-reaction, we see that it takes four electrons per oxygen molecule reduced. In our reaction, we have oxygen molecules so oxidizing methanol requires the transfer of electrons. Therefore

      

3. The half-reactions are

   

   and

   

   The spontaneous overall reaction is the one with a positive value of . Since the term of the Nernst equation is generally a small correction, we guess

   

   (If we have guessed wrong, we will get a negative voltage and we will know that the spontaneous reaction in fact runs in the opposite direction.) The ionic strength of the zinc sulfate solution is

   

   Therefore, the mean activity coefficient at 298K is found by

   

   The ionic strength of the copper sulfate solution is

   

   Therefore, the mean activity coefficient at 298K is found by

   

   We then compute the electrochemical potential from the Nernst equation:

   

   We probably should not have used Debye-Hückel theory because the ionic strength of the zinc sulfate solution is a little beyond the range in which Debye-Hückel theory is accurate.