Derive the equation that is equivalent to Eqs. (15-32b) and (15-32c) in terms of a partial pressure

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Derive the equation that is equivalent to Eqs. (15-32b) and (15-32c) in terms of a partial pressure driving force and a \(\log\) mean partial pressure difference:

\[ \begin{equation*} \left(\mathrm{p}_{\mathrm{B}}\right)_{\operatorname{lm}}=\frac{\left(\mathrm{p}_{\mathrm{B}, 2}-\mathrm{p}_{\mathrm{B}, 1}\right)}{\ln \left(\mathrm{p}_{\mathrm{B}, 2} / \mathrm{p}_{\mathrm{B}, 1}\right)} \tag{15-32g} \end{equation*} \]

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