# 26.6: The Sign of ΔG and not ΔG° Determines the Direction of Reaction Spontaneity

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It is important to distinguish between the Gibbs energy of reaction, $$\Delta_rG$$ and the standard state Gibbs energy of reaction, $$\Delta_rG^\circ$$. The $$^\circ$$ refers to standard state conditions. That is, each reactant and product has a partial pressure of 1 bar if a gas, a concentration of 1 M if a solution, and they are all unmixed from each other. Such idealized conditions, while convenient for serving as a reference state, do not actually represent real reaction conditions. Consider the reaction of nitrogen with hydrogen to form ammonia:

$\sf N_2\it\left(g\right)\sf+3 H_2\it\left(g\right)\sf\rightarrow 2 NH_3\it\left(g\right) \nonumber$

$\Delta_rG^\circ=-32.9 \;\frac{\text{kJ}}{\text{mol K}} \nonumber$

If the reaction was run under standard state conditions (1 bar partial pressure of each gas), the reaction would shift towards the products since $$\Delta_rG^\circ<0$$. That is, the partial pressures of N2 and O2 will decrease and the partial pressure of NH3 will increase until equilibrium is reached. The Gibbs energy of reaction is dependent on the composition:

$\Delta_rG=\Delta_rG^\circ+RT\ln{Q}=\Delta_rG^\circ+RT\ln{\left(\frac{P_{\text{NH}_3}^2}{P_{\text{N}_2}P_{\text{H}_2}^3}\right)} \nonumber$

At equilibrium, the minimum Gibbs energy of reaction will be reached:

$\Delta_rG=0 \;\frac{\text{kJ}}{\text{mol K}} \nonumber$

And the reaction quotient will equal the equilibrium constant:

$Q=K \nonumber$

26.6: The Sign of ΔG and not ΔG° Determines the Direction of Reaction Spontaneity is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.