Chapter 17: Problem 15
Define free energy. What are its units?
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Chapter 17: Problem 15
Define free energy. What are its units?
These are the key concepts you need to understand to accurately answer the question.
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Consider two carboxylic acids (acids that contain the \(-\mathrm{COOH}\) group \(): \mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid, \(\left.K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) and \(\mathrm{CH}_{2} \mathrm{ClCOOH}\) (chloroacetic acid, \(K_{\mathrm{a}}=1.4 \times 10^{-3}\) ). (a) Calculate \(\Delta G^{\circ}\) for the ionization of these acids at \(25^{\circ} \mathrm{C}\). (b) From the equation \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ},\) we see that the contributions to the \(\Delta G^{\circ}\) term are an enthalpy term \(\left(\Delta H^{\circ}\right)\) and a temperature times entropy term \(\left(T \Delta S^{\circ}\right) .\) These contributions are listed below for the two acids: $$ \begin{array}{lcc} \hline & \Delta H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & T \Delta S^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) \\ \hline \mathrm{CH}_{3} \mathrm{COOH} & -0.57 & -27.6 \\ \mathrm{CH}_{2} \mathrm{ClCOOH} & -4.7 & -21.1 \\ \hline \end{array} $$ Which is the dominant term in determining the value of \(\Delta G^{\circ}\) (and hence \(K_{\mathrm{a}}\) of the acid)? (c) What processes contribute to \(\Delta H^{\circ} ?\) (Consider the ionization of the acids as a Brønsted acid-base reaction.) (d) Explain why the \(T \Delta S^{\circ}\) term is more negative for \(\mathrm{CH}_{3} \mathrm{COOH}\)
State the second law of thermodynamics in words and express it mathematically.
From the values of \(\Delta H\) and \(\Delta S,\) predict which of the following reactions would be spontaneous at \(25^{\circ} \mathrm{C}\) : reaction \(\mathrm{A}: \Delta H=10.5 \mathrm{~kJ} / \mathrm{mol}, \Delta S=30 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} ;\) reaction \(\mathrm{B}: \Delta H=1.8 \mathrm{~kJ} / \mathrm{mol}, \Delta S=-113 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\) If either of the reactions is nonspontaneous at \(25^{\circ} \mathrm{C}\), at what temperature might it become spontaneous?
Why is it more convenient to predict the direction of a reaction in terms of \(\Delta G_{\text {sys }}\) instead of \(\Delta S_{\text {univ }}\) ? Under what conditions can \(\Delta G_{\text {sys }}\) be used to predict the spontaneity of a reaction?
A \(74.6-\mathrm{g}\) ice cube floats in the Arctic Sea. The temperature and pressure of the system and surroundings are at 1 atm and \(0^{\circ} \mathrm{C}\). Calculate \(\Delta S_{\text {sys }}, \Delta S_{\text {surr }}\) and \(\Delta S_{\text {univ }}\) for the melting of the ice cube. What can you conclude about the nature of the process from the value of \(\Delta S_{\text {univ }} ?\) (The molar heat of fusion of water is \(6.01 \mathrm{~kJ} / \mathrm{mol} .)\)
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