Kaplan MCAT General Chemistry Review

Note that there are two ways to express emf. The first allows us to use only reduction potentials. The second asks us to change the sign of the “E_red” value in order to use an oxidation potential, which is the exact opposite of a reduction potential. Be careful on the MCAT to pay close attention to the value and sign of the numbers you are using ... and DON’T multiply by the coefficients!

Thermodynamics of Redox Reactions

Throughout our discussion of electrochemistry and the different types of electrochemical cells, we have been making references to the spontaneity or nonspontaneity of the redox reactions housed in each of the different cell types. Let’s now look more formally at this topic by relating the state function of free energy to emf and the concentrations of the redox reactants and products to the voltage of a cell at a given point in time.

Bridge

Recall that if G is positive, the reaction is not spontaneous; if G is negative, the reaction is spontaneous. Go back to Chapter 6 if you need a review.

emf AND GIBBS FREE ENERGY

As you know well by now, the thermodynamic criterion for determining the spontaneity of a reaction is the change in Gibbs free energy, G, which is the change in the chemical potential of a reaction or the change in the amount of energy of a chemical system available to do work. In an electrochemical cell, the work done is dependent on the number of coulombs and the energy available. Thus, G and emf are related as follows:

G = -nFE_cell

where n is the number of moles of electrons exchanged, F is Faraday’s constant, and E_cell is the emf of the cell. Keep in mind that if Faraday’s constant is expressed in coulombs (J/V), then G must be expressed in J, not kJ. (The astute student will notice the similarity of this relationship to that expressed by the physics formula W = q V for the amount of work available or needed in the transport of a charge q across a potential difference V! And if you didn’t notice it before, you do now, so that means you are now astute!)

If the reaction takes place under standard conditions (298 K, 1 atm pressure, and all solutions at 1 M concentration), then the G is the standard Gibbs free energy, and E_cell is the standard cell potential. The above equation then becomes

G° = -nFE°_cell

You should notice the significance of the negative sign on the right side of the equation. Being mindful of it will help you eliminate wrong answer choices that have the wrong sign for either the G° or the E°_cell. For example, if you are asked to calculate the change in Gibbs function for a galvanic cell, you will immediately be able to eliminate the answer choices that have positive values, because you know that voltaic cells have positive emfs and the equation tells you the change in Gibbs will have the opposite sign.

THE EFFECT OF CONCENTRATION ON emf

So far, we have considered the calculation of cell emf only under standard conditions (all the ionic species are 1 M, and all gases are at a pressure of 1 atm). However, electrochemical cells may have ionic concentrations that are greater or lesser than 1 M. In fact, for the concentration cell, the concentrations of the ion in the two compartments must be different, even if one of them is 1 M, for there to be a voltage and current. Concentration does have an effect on the emf of a cell: emf varies with the changing concentrations of the species involved. It can be determined by the use of the Nernst equation:

where Q is the reaction quotient for the reaction at a given point in time. For example, for the following reaction,

aA + bB cC + dD

the reaction quotient can be calculated as follows:

Although the expression for the reaction quotient Q has two terms for the concentrations of reactants and two terms for the concentrations of products, you need to remember that only the species in solution are included. When considering the case of the Daniell cell, for example, we need to think about which species of the redox reaction are in solution. Upon oxidation, the resulting cation will enter into solution, so the product concentration is the concentration of the oxidized species. Because the electrons are captured by the cations that surround the cathode in the reduction half-reaction, these cations are the reactants of the redox reaction, so the reactant concentration is the concentration of the species that gets reduced.

The emf of a cell can be measured by a voltmeter. A potentiometer is a kind of voltmeter that draws no current, and it gives a more accurate reading of the difference in potential between two electrodes.

emf AND THE EQUILIBRIUM CONSTANT (K_eq)

For reactions in solution, G° can determined in another manner, as follows:

G° = -RT ln K_eq