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The entropy \left(S^{\circ}\right) of the following substances are:

\begin{aligned} & \mathrm{CH}_4(\mathrm{g}): 180 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ \\& \mathrm{O}_2(\mathrm{g}): 200 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ \\& \mathrm{CO}_2(\mathrm{g}): 210 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ \\& \mathrm{H}_2 \mathrm{O}(\mathrm{l}): 65 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \end{aligned}

The entropy change S^{\circ} for the reaction \mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{l}) is :

Option: 1

\begin{aligned} & -240 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ \end{aligned}


Option: 2

\begin{aligned} & -340 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ \end{aligned}


Option: 3

\begin{aligned} & -440 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ \end{aligned}


Option: 4

\begin{aligned} & -540 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \end{aligned}


Answers (1)

best_answer

Given :

\begin{aligned} & \mathrm{CH}_4(\mathrm{g}): 180 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ & \mathrm{O}_2(\mathrm{g}): 200 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ & \mathrm{CO}_2(\mathrm{g}): 210 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \\ & \mathrm{H}_2 \mathrm{O}(\mathrm{l}): 65 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \end{aligned}

The entropy change \left(S^{\circ}\right) for the reaction \mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(1)
Entropy of a reaction = entropy of products - entropy of reactants
Here, entropy change

\mathrm{\Delta S=(210+2 \times 65)-(180+2 \times 200)}

\begin{aligned} & =340-580 \\& =-240 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \end{aligned}

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