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Energetics / Thermochemistry - Entropy and spontaneity (HL only)

Grade 12IBChemistry

Review the key concepts, formulae, and examples before starting your quiz.

πŸ”‘Concepts

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Entropy (SS) is a thermodynamic function that measures the distribution of available energy among particles or the degree of disorder in a system. The units are JΒ Kβˆ’1Β molβˆ’1J\ K^{-1}\ mol^{-1}.

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A system becomes more disordered (positive entropy change, ΔS>0\Delta S > 0) when there is an increase in the number of moles of gas, a change of state from solid→liquid→gassolid \rightarrow liquid \rightarrow gas, or an increase in temperature.

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The Second Law of Thermodynamics states that for a process to be spontaneous, the total entropy of the universe must increase.

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Gibbs Free Energy (Ξ”G\Delta G) relates enthalpy and entropy to determine reaction spontaneity. For a reaction to be spontaneous at a given temperature, Ξ”G\Delta G must be negative (Ξ”G<0\Delta G < 0).

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The standard Gibbs free energy of formation (Ξ”GfβŠ–\Delta G_f^{\ominus}) is the free energy change when one mole of a compound is formed from its elements in their standard states. For elements in their standard states, Ξ”GfβŠ–=0\Delta G_f^{\ominus} = 0.

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Spontaneity depends on the balance between Ξ”H\Delta H and TΞ”ST\Delta S. If Ξ”H\Delta H and Ξ”S\Delta S have the same sign, the spontaneity of the reaction will change as the temperature (TT) changes.

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Thermodynamic spontaneity does not guarantee a fast reaction. A reaction with Ξ”G<0\Delta G < 0 may be kinetically stable if it has a very high activation energy (EaE_a).

πŸ“Formulae

Ξ”SreactionβŠ–=βˆ‘SβŠ–(products)βˆ’βˆ‘SβŠ–(reactants)\Delta S^{\ominus}_{reaction} = \sum S^{\ominus}(products) - \sum S^{\ominus}(reactants)

Ξ”GβŠ–=Ξ”HβŠ–βˆ’TΞ”SβŠ–\Delta G^{\ominus} = \Delta H^{\ominus} - T\Delta S^{\ominus}

Ξ”GreactionβŠ–=βˆ‘Ξ”GfβŠ–(products)βˆ’βˆ‘Ξ”GfβŠ–(reactants)\Delta G^{\ominus}_{reaction} = \sum \Delta G_f^{\ominus}(products) - \sum \Delta G_f^{\ominus}(reactants)

Ttransition=Ξ”HβŠ–Ξ”SβŠ–T_{transition} = \frac{\Delta H^{\ominus}}{\Delta S^{\ominus}}

πŸ’‘Examples

Problem 1:

For the reaction N2(g)+3H2(g)β†’2NH3(g)N_2(g) + 3H_2(g) \rightarrow 2NH_3(g), the enthalpy change Ξ”HβŠ–=βˆ’92.2Β kJΒ molβˆ’1\Delta H^{\ominus} = -92.2\ kJ\ mol^{-1} and the entropy change Ξ”SβŠ–=βˆ’198.7Β JΒ Kβˆ’1Β molβˆ’1\Delta S^{\ominus} = -198.7\ J\ K^{-1}\ mol^{-1}. Calculate the Gibbs free energy change (Ξ”GβŠ–\Delta G^{\ominus}) at 298Β K298\ K and determine if the reaction is spontaneous.

Solution:

  1. Convert units so they are consistent: Ξ”SβŠ–=βˆ’198.7Γ·1000=βˆ’0.1987Β kJΒ Kβˆ’1Β molβˆ’1\Delta S^{\ominus} = -198.7 \div 1000 = -0.1987\ kJ\ K^{-1}\ mol^{-1}.
  2. Use the formula Ξ”GβŠ–=Ξ”HβŠ–βˆ’TΞ”SβŠ–\Delta G^{\ominus} = \Delta H^{\ominus} - T\Delta S^{\ominus}.
  3. Ξ”GβŠ–=βˆ’92.2Β kJΒ molβˆ’1βˆ’(298Β KΓ—βˆ’0.1987Β kJΒ Kβˆ’1Β molβˆ’1)\Delta G^{\ominus} = -92.2\ kJ\ mol^{-1} - (298\ K \times -0.1987\ kJ\ K^{-1}\ mol^{-1}).
  4. Ξ”GβŠ–=βˆ’92.2+59.2=βˆ’33.0Β kJΒ molβˆ’1\Delta G^{\ominus} = -92.2 + 59.2 = -33.0\ kJ\ mol^{-1}.

Explanation:

Since Ξ”GβŠ–\Delta G^{\ominus} is negative (βˆ’33.0Β kJΒ molβˆ’1-33.0\ kJ\ mol^{-1}), the reaction is spontaneous at 298Β K298\ K. Note that because Ξ”S\Delta S is negative, the reaction will become non-spontaneous at higher temperatures.

Problem 2:

A reaction has Ξ”HβŠ–=+178Β kJΒ molβˆ’1\Delta H^{\ominus} = +178\ kJ\ mol^{-1} and Ξ”SβŠ–=+160Β JΒ Kβˆ’1Β molβˆ’1\Delta S^{\ominus} = +160\ J\ K^{-1}\ mol^{-1}. At what temperature (in KK) does the reaction become spontaneous?

Solution:

  1. The reaction becomes spontaneous when Ξ”G<0\Delta G < 0. Set Ξ”G=0\Delta G = 0 to find the threshold temperature: 0=Ξ”Hβˆ’TΞ”S0 = \Delta H - T\Delta S.
  2. Rearrange for TT: T=Ξ”HβŠ–Ξ”SβŠ–T = \frac{\Delta H^{\ominus}}{\Delta S^{\ominus}}.
  3. Convert Ξ”S\Delta S to kJkJ: +0.160Β kJΒ Kβˆ’1Β molβˆ’1+0.160\ kJ\ K^{-1}\ mol^{-1}.
  4. T=1780.160=1112.5Β KT = \frac{178}{0.160} = 1112.5\ K.

Explanation:

At temperatures above 1112.5Β K1112.5\ K, the TΞ”ST\Delta S term (which is positive) will outweigh the positive Ξ”H\Delta H term, making Ξ”G\Delta G negative and the reaction spontaneous.

Entropy and spontaneity (HL only) - Revision Notes & Key Formulas | IB Grade 12 Chemistry