Thermodynamics relation — Interpreting ΔG° = -RTln(K): effect of a tenfold change in the equilibrium constant

Introduction:
The standard free energy change links directly to the equilibrium constant through the fundamental relation ΔG° = -RTln(K). This question checks quick, order of magnitude reasoning for decimal changes in K without a calculator.

Given Data / Assumptions:

• R is the gas constant and T is absolute temperature.
• Natural logarithm is used in the equation.
• Goal: estimate the change in ΔG° when K changes by a factor of 10.

Concept / Approach:
Use the identity ln(10) ≈ 2.303. Substituting into ΔG° = -RTln(K) shows how a tenfold change in K maps to a fixed multiple of RT independent of the actual K value, aside from sign direction.

Step-by-Step Solution:

Verification / Alternative check:
If K decreases by 10, then ln(K) decreases by 2.3, so ΔG° increases by about 2.3RT. The direction is consistent with favorable equilibria (larger K) corresponding to more negative ΔG°.

Why Other Options Are Wrong:

• 10-fold change in ΔG°: free energy is not proportional to K linearly.
• Decrease in K decreases ΔG°: sign is wrong; ΔG° becomes less negative.
• 10-fold decrease increases ΔG° by 10-fold: again mixes linear and logarithmic relations.
• 2-fold increase gives RT: ln(2) is about 0.693, not 1.0, so the magnitude is off.

Common Pitfalls:
Mixing log base 10 and natural log. Always convert decimal folds to natural logs with ln(10) ≈ 2.303 for quick estimates.

Final Answer:
a 10-fold increase in K decreases ΔG° by about 2.3RT.