For a given reaction, which of the following values can be determined from the value of ΔG? 1) Enthalpy change, ΔH. 2) Cell potential, E. 3) Equilibrium constant, K eq. A) 3 only, B) 1 and 2 only, C) 2 and 3 only, D) 1, 2, and 3, or E) none of the other answers are correct.
ΔG refers to the Gibbs free energy. Mathematically, the Gibbs free energy is defined as the enthalpy minus the product of the temperature times the entropy. When the change in Gibbs free energy for a reaction or a process is negative, that process is spontaneous. The change in Gibbs free energy is also equal to the maximum amount of work that a system can do. This is why it’s called the Gibbs free energy because it tells us the amount of energy in our system that’s available or free to do work for us. This symbol in the superscript of the values in this question indicates that we’re referring to a standard state, which means the process is occurring at a temperature of 25 degrees Celsius and one-bar pressure.
In this question, we’re being asked to determine which of the values we’re given can be determined from the value of the change in the Gibbs free energy. Our first value is the change in enthalpy, ΔH. As we’ve discussed, the Gibbs free energy is related to the change in enthalpy mathematically. If we have a process that’s occurring at a constant temperature, the change in the Gibbs free energy is equal to the change in enthalpy minus the temperature times the change in entropy. So, we wouldn’t be able to determine the change in enthalpy from the value of the Gibbs free energy alone. We would also need to know the change in entropy for the reaction.
Our next value is the cell potential, which tells us how easy it is for electrons to flow from one cell to another in an electrochemical cell. When the value of the cell potential is greater than zero for an oxidation–reduction reaction in an electrochemical cell, that reaction will occur spontaneously. And we can use that reaction to perform electrical work, such as powering a light bulb. Since the change in Gibbs free energy tells us about the maximum amount of work that we can get from a process, it seems natural that it would be related to the cell potential.
This is, in fact, the case. The change in Gibbs free energy is related to the amount of electrical work that an electrochemical cell can perform. This quantity is equal to the number of electrons transferred in the reaction times Faraday’s constant, which gives us the charge per mole of electrons, times the cell potential. So, as long as we know how many electrons are being transferred in our reaction, we would be able to determine the cell potential from the value of the Gibbs free energy.
Our final value is the equilibrium constant. The Gibbs free energy is intimately related to equilibrium. When a system is at equilibrium, it’s at a minima of the Gibbs free energy. The change in Gibbs free energy is equal to the gas constant times the temperature times the natural log of the equilibrium constant. So, as long as we know the temperature of our system, we should be able to determine the equilibrium constant from the value of the change in the Gibbs free energy. Of the values we were given, 2 and 3, the cell potential and the equilibrium constant, can be determined directly from the value of the Gibbs free energy, which matches answer choice C.