Chapter 56

Which expression below describes the mathematical relationship between \(\Delta G T\) and \(K^{?}\) a) Is \(\Delta G \Upsilon \propto K ?\) (That is, does \(\Delta G Y=c K\), where " \(c^{\prime \prime}\) is some proportionality constant? If so, then \(\frac{\Delta G \mathrm{C}}{K}=\) same number for all entries in Table \(1 .\) ) b) Is \(\Delta G \mid \propto-K ?\) c) Is \(\Delta G^{*} \propto-\sqrt{K}\) ? d) Is \(\Delta G \mid \propto-\ln K ?\)

Recall that \(\Delta G \Upsilon\) can be written as a function of \(\Delta H^{\circ}\) and \(\Delta S T\). Assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are not temperature dependent and answer each of the following: a) Derive an expression relating \(\ln K, \Delta H^{*}\), and \(\Delta S r .\) That is, derive an expression that looks like \(\ln K=\) some function of \(\Delta H \mathrm{Y}\) and \(\Delta \mathrm{ST}\). The temperature, \(T\), should appear only once in this equation. b) How are the equilibrium constants for reactions with \(\Delta H^{\prime}>0\) affected by an increase in temperature? c) How are equilibrium constants for reactions with \(\Delta H \Upsilon<0\) affected by an increase in temperature?

How does temperature affect the equilibrium \(\mathrm{H}_{2} \mathrm{O}(\boldsymbol{\ell}) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) ?\) Explain in terms of \(\Delta H \Upsilon\).