Electrochemistry #1

In a galvanic cell the voltage (emf) will change with all of the following, EXCEPT:


    A. the chemical reactions occurring in the half-cells
    B. the length of the wire connecting the half-cells
    C. the concentration of the solutions in the half-cells
    D. the temperature of the solutions in the half-cells


ANSWER:  B


SHORT-AND-SWEET:


Galvanic cells convert the chemical energy of a spontaneous redox reaction into electrical energy, which enables the cell to do work.  You can imagine the voltage of a galvanic cell as a measure of galvanic cell "strength".  What makes a galvanic cell "strong"? 


1. The redox reaction which is occurring in the cell:  different redox reactions will have different intrinsic "desires" to occur.  Those that want to occur spontaneously will have a lot of chemical energy that can be converted into electric energy.  The more chemical energy a reaction has, the higher the voltage produced in the galvanic cell.
2. How concentrated the solutions in the half-cells are:  This tells you how many charged units there are in the galvanic cell;  the more charge that there is, the stronger the galvanic cell!?
3. The temperature of the half-cell solutions:  in order to understand this one, we have to recall that the spontaneity of a reaction is partially determined by the temperature in the system (ΔG = ΔH - TΔS; G-free Gibbs free energy, H-enthalpy, T-temperature, S-entropy).  If we look back to 1., the more spontaneous reactions have more free chemical energy, which corresponds to higher voltage in the galvanic cell.


This leaves us with the length of the wire connecting the half-cells as the correct answer (answer choice B).  This variable will not affect the voltage of the galvanic cell.


THE WHOLE STORY:


"Ugh, I wish I could remember that stupid Nernst equation!"  If this is your first response after reading this question, do not despair.  A good understanding of galvanic cells will enable you to answer this question without memorizing that dreaded equation.  

In fact, the MCAT will frequently test your understanding of topics that are represented by complicated equations -- which does not mean that you have to memorize these equations.  This question is a perfect example.  Instead of forcing yourself to memorize this and a bunch of other complicated equations, what you should do is spend this time understanding what these equations mean.  

Let's see how we can apply this principle to our question.  Before thinking about the voltage of a galvanic cell, it is crucial to understand the galvanic cell itself.  

Galvanic cell uses chemical energy intrinsic to a redox reaction to produce electrical energy, which enables it to do useful electrical work.  The key is that galvanic cell requires a spontaneous redox reaction, because the spontaneity of the redox reaction is where the chemical energy comes from.  An example of a spontaneous chemical reaction used to make a galvanic cell is between zinc and copper:  


Cu²⁺ + Zn    Cu + Zn²⁺


Galvanic cell will transform the chemical energy of a spontaneous redox reaction into electric energy, which manifests as the electric current.

Now, if the chemical energy comes from the spontaneity of a redox reaction, you can guess that the redox reactions that are most spontaneous will produce the most energy, therefore generating the greatest voltage (emf) in the galvanic cell.  This means that if we change which chemical redox reactions are occurring in the galvanic cell, the voltage will change (which eliminates answer A).


The voltage of a particular reaction can be calculated from standard potentials (E°) of each of the oxidation and reduction half-reactions.  What does "standard" mean?  Remember that "standard" always refers to some "standard" conditions.  In this particular case, the standard potential of a reaction is measured at standard CONCENTRATION, which is 1M, and at the standard TEMPERATURE, which is 25°C.  


Obviously, if any of these conditions were to change, the potential of the reaction would change (which eliminates answers C and D).  


This leaves answer B.  The length of the wire between the two half-cells has nothing to do with the emf of the galvanic cell.

..........

Like we mentioned in the beginning, the other way of answering this question is to memorize the equation for voltage of a galvanic cell.  This is the dreaded Nernst equation: 

E = E °  - (RT / nF)  ln (Q)

    E = voltage of a redox reaction (under non-standard conditions)

    E°  = standard voltage of a redox reaction (under standard conditions)

    R =  universal gas constant: R = 8.314 J/Kmol

    T = absolute temperature

    n = number of moles of electrons transferred in the cell reaction or half-reaction

    F = Faraday constant, which is the number of coulombs per mole of electrons: F = 96,500 C/mol

    Q = reaction quotient, determined by the concentration of reactants and products in the chemical reaction

Nernst equation looks intimidating because it has so many components, but what it shows, in the simplest terms, is that E (emf) of the galvanic cell depends on:
    -standard potential E°, which is specific to the chemical species reacting in the galvanic cell,
    -temperature T in the system, and 
    -reaction quotient Q, which depends on the concentration of chemicals in the galvanic cell.




BIG PICTURE: 


1.  When you run into a complicated-looking equation (e.g. Nernst equation), don't waste time trying to memorize it.  Look at the variables in the equation, and how they relate to each other.  Finally, practice by explaining these relations in words.


2.  Galvanic cells require a spontaneous redox reaction, whose intrinsic chemical energy the galvanic cell transforms into electric energy and electric work, i.e. current.  


3.  What redox reaction is occurring, and at which reactant concentration, as well as the temperature of the system (one of the determinants of the spontaneity of the reaction) determine what voltage (emf) the galvanic cell will produce. 


~The MCAT POD Team~