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11.12: Evaluating Entropy Changes Using Thermochemical Cycles

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    As for the standard enthalpy of reaction, we can obtain the standard entropy of reaction at a new temperature by evaluating entropy changes around a suitable thermochemical cycle. To do so, we need the standard entropy change at one temperature. We also need heat capacity data for all of the reactants and products. For the reaction

    \[a\ A+b\ B\to c\ C+d\ D \nonumber \]

    we can evaluate the entropy change at a second temperature by summing the individual contributions to the change in entropy around the cycle in Figure 5. For this cycle, we have

    \[{\Delta }_rS^o\left(T_2\right)={\Delta }_rS^o\left(T_1\right)+c\int^{T_2}_{T_1}{\frac{C_P\left(C\right)}{T}dT} +d\int^{T_2}_{T_1}{\frac{C_P\left(D\right)}{T}dT}-a\int^{T_2}_{T_1}{\frac{C_P\left(A\right)}{T}dT}-b\int^{T_2}_{T_1}{\frac{C_P\left(B\right)}{T}dT} \nonumber \]

    Screen Shot 2019-10-07 at 3.13.39 PM.png
    Figure 5. Cycle relating the entropy changes for a reaction at two temperatures.

    This page titled 11.12: Evaluating Entropy Changes Using Thermochemical Cycles is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Paul Ellgen via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.