Consider the decomposition of hydrogen peroxide in the gas phase:

CHEMISTRY · Multi-part · A Level · Chemistry · Thermodynamics · Thermodynamics

Problem

Consider the decomposition of hydrogen peroxide in the gas phase: 2 H2O2(g)→2 H2O(g)+O2(g)2\,\text{H}_2\text{O}_2(g) \to 2\,\text{H}_2\text{O}(g) + \text{O}_2(g). The standard enthalpy change is temperature-independent at ΔH=+196 kJ mol−1\Delta H = +196\,\text{kJ}\,\text{mol}^{-1}. The standard entropy change, however, varies with temperature according to ΔS(T)=150 J mol−1 K−1−0.050 T J mol−1 K−1\Delta S(T) = 150\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-1} - 0.050\,T\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-1}, where TT is in kelvins. (1) Part 1: Write an expression for ΔG\Delta G as a function of temperature using the information provided. (2) Part 2: Calculate the temperature at which the reaction is at equilibrium (ΔG=0\Delta G = 0). (3) Part 3: Using your expression from part (a), determine the sign of ΔG\Delta G at 500 K500\,\text{K} and explain the thermodynamic favorability of the reaction at this temperature. (4) Part 4: Briefly interpret the physical significance of the negative coefficient (−0.050 T-0.050\,T) in the entropy expression with respect to molecular motion as temperature increases.

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