Edexcel International A Level (IAL) Chemistry (YCH11) - Unit 4 - 13.8 Entropy relationship (ΔS_total = R ln K)-Study Notes - New Syllabus

Edexcel International A Level (IAL) Chemistry (YCH11) -Unit 4 – 13.8 Entropy relationship (ΔS_total = R ln K)- Study Notes- New syllabus

Edexcel International A Level (IAL) Chemistry (YCH11) -Unit 4 – 13.8 Entropy relationship (ΔS_total = R ln K)- Study Notes -International A Level (IAL) Chemistry (YCH11) – per latest Syllabus.

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Edexcel International A Level (IAL) Chemistry (YCH11) -Concise Summary Notes- All Topics

13.8 Effect of Temperature on \( \mathrm{\Delta S_{total}} \) and Equilibrium Constant

The feasibility of a reaction and the magnitude of the equilibrium constant are directly linked to entropy. Temperature plays a crucial role because it affects both the entropy of the surroundings and the value of the equilibrium constant.

(i) Effect of Temperature on \( \mathrm{\Delta S_{total}} \)

The total entropy change is given by:

\( \mathrm{\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings}} \)

and:

\( \mathrm{\Delta S_{surroundings} = -\frac{\Delta H}{T}} \)

Key Insight

  • \( \mathrm{\Delta S_{system}} \) is independent of temperature (approx.).
  • \( \mathrm{\Delta S_{surroundings}} \) depends on temperature through \( \mathrm{\frac{1}{T}} \).

Effect for Exothermic Reactions (\( \mathrm{\Delta H < 0} \))

  • \( \mathrm{\Delta S_{surroundings}} \) is positive.
  • Increasing temperature decreases \( \mathrm{\frac{1}{T}} \), so:
    • \( \mathrm{\Delta S_{surroundings}} \) becomes less positive.
    • Therefore, \( \mathrm{\Delta S_{total}} \) decreases.

Effect for Endothermic Reactions (\( \mathrm{\Delta H > 0} \))

  • \( \mathrm{\Delta S_{surroundings}} \) is negative.
  • Increasing temperature reduces magnitude of \( \mathrm{\frac{1}{T}} \):
    • \( \mathrm{\Delta S_{surroundings}} \) becomes less negative.
    • Therefore, \( \mathrm{\Delta S_{total}} \) increases.

Summary

  • Exothermic: ↑T → \( \mathrm{\Delta S_{total}} \) decreases.
  • Endothermic: ↑T → \( \mathrm{\Delta S_{total}} \) increases.

(ii) Effect of Temperature on Equilibrium Constant

The relationship between entropy and equilibrium constant is:

\( \mathrm{\Delta S_{total} = R \ln K} \)

Key Insight

  • If \( \mathrm{\Delta S_{total}} \) increases → \( \mathrm{K} \) increases.
  • If \( \mathrm{\Delta S_{total}} \) decreases → \( \mathrm{K} \) decreases.

Effect for Exothermic Reactions

  • Increasing temperature decreases \( \mathrm{\Delta S_{total}} \).
  • Therefore, \( \mathrm{K} \) decreases.

Effect for Endothermic Reactions

  • Increasing temperature increases \( \mathrm{\Delta S_{total}} \).
  • Therefore, \( \mathrm{K} \) increases.

Magnitude of \( \mathrm{K} \)

  • Large \( \mathrm{K} \) → equilibrium lies towards products.
  • Small \( \mathrm{K} \) → equilibrium lies towards reactants.
  • Temperature shifts this balance by changing \( \mathrm{\Delta S_{total}} \).

Key Features

  • Temperature affects \( \mathrm{\Delta S_{surroundings}} \), not \( \mathrm{\Delta S_{system}} \).
  • This changes \( \mathrm{\Delta S_{total}} \).
  • Since \( \mathrm{\Delta S_{total} = R \ln K} \), \( \mathrm{K} \) changes accordingly.
  • Exothermic: ↑T → ↓\( \mathrm{K} \); Endothermic: ↑T → ↑\( \mathrm{K} \).

Example 1:

Explain why increasing temperature decreases \( \mathrm{K} \) for an exothermic reaction using entropy.

▶️ Answer/Explanation

For an exothermic reaction, \( \mathrm{\Delta H < 0} \), so \( \mathrm{\Delta S_{surroundings}} \) is positive.

Increasing temperature reduces the value of \( \mathrm{\frac{1}{T}} \), making \( \mathrm{\Delta S_{surroundings}} \) less positive.

Therefore, \( \mathrm{\Delta S_{total}} \) decreases.

Since \( \mathrm{\Delta S_{total} = R \ln K} \), a decrease in \( \mathrm{\Delta S_{total}} \) leads to a decrease in \( \mathrm{K} \).

Example 2:

A reaction becomes more feasible at higher temperature. Explain this using \( \mathrm{\Delta S_{total}} \) and \( \mathrm{K} \).

▶️ Answer/Explanation

Increasing temperature increases \( \mathrm{\Delta S_{total}} \), making it more positive.

This indicates the reaction becomes more thermodynamically favourable.

Since \( \mathrm{\Delta S_{total} = R \ln K} \), an increase in \( \mathrm{\Delta S_{total}} \) increases \( \mathrm{K} \).

A larger \( \mathrm{K} \) means equilibrium lies further towards products.

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