ΔG° and Keq
In the previous section, you learned that ΔG determines spontaneity. But which ΔG? There is a critical distinction between ΔG° (standard free energy change) and ΔG (actual free energy change under real conditions). Confusing the two is one of the most common mistakes on the MCAT.
ΔG° and the Equilibrium Constant
Interpreting ΔG° and K
The sign of ΔG° tells you which side of the reaction is favored at equilibrium:
| ΔG° | K | Meaning |
|---|---|---|
| Negative | K > 1 | Products favored at equilibrium |
| Zero | K = 1 | Neither side favored |
| Positive | K < 1 | Reactants favored at equilibrium |
ΔG Under Non-Standard Conditions
Real reactions rarely occur under standard conditions. The actual free energy change depends on the current concentrations via the reaction quotient Q:
How ΔG Changes as a Reaction Proceeds
When a reaction starts:
- If Q < K: ΔG < 0 (reaction proceeds forward to make more products)
- If Q > K: ΔG > 0 (reaction proceeds backward to make more reactants)
- If Q = K: ΔG = 0 (equilibrium - no net change)
As the reaction approaches equilibrium, ΔG approaches zero. At equilibrium, Q = K and:
ΔG = ΔG° + RTlnK = 0
This is exactly where the equation ΔG° = -RTlnK comes from - it is the ΔG = 0 condition rearranged.
Connecting Everything
Here is how the three big thermodynamic equations fit together:
- ΔG = ΔH - TΔS (relates free energy to enthalpy and entropy)
- ΔG° = -RTlnK (relates standard free energy to equilibrium)
- ΔG = ΔG° + RTlnQ (relates actual free energy to current conditions)
These three equations are the thermodynamic backbone of the MCAT. Know them cold.
Temperature and K
Because ΔG° depends on temperature (through the TΔS° term in ΔG° = ΔH° - TΔS°), and K depends on ΔG° (through ΔG° = -RTlnK), the equilibrium constant changes with temperature.
For an exothermic reaction (ΔH° < 0): increasing temperature makes ΔG° less negative (or more positive), which decreases K. Heat shifts equilibrium toward reactants.
For an endothermic reaction (ΔH° > 0): increasing temperature makes ΔG° more negative, which increases K. Heat shifts equilibrium toward products.
This connects directly to Le Chatelier’s principle from Chapter 6: heat acts as a reactant (endothermic) or product (exothermic).