Chapter 18: Problem 15
Define free energy. What are its units?
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For each pair of substances listed here, choose the one having the larger standard entropy value at \(25^{\circ} \mathrm{C}\). The same molar amount is used in the comparison. Explain the basis for your choice. (a) \(\operatorname{Li}(s)\) or \(\operatorname{Li}(l)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) or \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(l)\) (c) \(\operatorname{Ar}(g)\) or \(\operatorname{Xe}(g)\) (d) \(\mathrm{CO}(g)\) or \(\mathrm{CO}_{2}(g)\) (e) \(\mathrm{O}_{2}(g)\) or \(\mathrm{O}_{3}(g)\) (f) \(\mathrm{NO}_{2}(g)\) or \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\)
Derive the following equation $$ \Delta G=R T \ln (Q / K) $$ where \(Q\) is the reaction quotient and describe how you would use it 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 \(\Delta S_{\text {uniy }}\) 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 \(6.01 \mathrm{~kJ} / \mathrm{mol} .)\)
As an approximation, we can assume that proteins exist either in the native (or physiologically functioning) state and the denatured state $$\text { native } \rightleftharpoons \text { denatured }$$ The standard molar enthalpy and entropy of the denaturation of a certain protein are \(512 \mathrm{~kJ} / \mathrm{mol}\) and \(1.60 \mathrm{~kJ} / \mathrm{K} \cdot \mathrm{mol}\), respectively. Comment on the signs and magnitudes of these quantities, and calculate the temperature at which the process favors the denatured state.
State the second law of thermodynamics in words and express it mathematically.
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