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II-13: Entropy, Gibbs energy and equilibrium

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Module II-13 · Recommended before: Before thermodynamics and spontaneity

Entropy, Gibbs energy and equilibrium

Thermodynamics combines signed energy changes. Entropy must be in compatible energy units and temperature must be in kelvin.

Learn the method

ΔG = ΔH − TΔS; ΔG° = −RT ln K

  1. Convert ΔS into kJ/K if ΔH is in kJ.
  2. Calculate TΔS.
  3. Compute ΔG = ΔH − TΔS.
  4. Interpret a negative ΔG as spontaneous under specified conditions.
  5. For standard equilibrium, use ΔG° = −RT ln K.

Common mistake: Using ΔS in J/K when ΔH is in kJ gives a thousand-fold unit error.

Worked example

Problem: At 300 K, ΔH = 20 kJ and ΔS = 0.100 kJ/K. Find ΔG.

Step-by-step solution: ΔG = 20 − (300)(0.100) = −10 kJ; favorable under the stated conditions.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Free energy and equilibrium

At 298 K, if K = 10, ΔG° = −RT ln K ≈ −(8.314)(298)(2.303) = −5.71 kJ/mol.

Temperature threshold

With ΔH=+20 kJ and ΔS=+0.050 kJ/K, ΔG changes sign near T=ΔH/ΔS=400 K (assuming ΔH and ΔS constant).

Reaction entropy from tables

Compute ΔS°rxn=ΣνS°products−ΣνS°reactants with stoichiometric coefficients; if table units are J/(mol·K), convert before combining with ΔH in kJ.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Compute ΔG for ΔH=25 kJ, ΔS=0.050 kJ/K at T=280 K.
Hint for question 1

Use consistent kJ units in both terms.

Question 2. Compute ΔG for ΔH=60 kJ, ΔS=0.200 kJ/K at T=310 K.
Hint for question 2

Use consistent kJ units in both terms.

Question 3. Compute ΔG for ΔH=10 kJ, ΔS=0.040 kJ/K at T=330 K.
Hint for question 3

Use consistent kJ units in both terms.

Question 4. Compute ΔG for ΔH=15 kJ, ΔS=0.060 kJ/K at T=360 K.
Hint for question 4

Use consistent kJ units in both terms.

Question 5. Compute ΔG for ΔH=35 kJ, ΔS=0.100 kJ/K at T=290 K.
Hint for question 5

Use consistent kJ units in both terms.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

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