# What is reaction isotherm? Describe briefly.

Jul 17, 2017

The reaction isotherm is given by

$\Delta {\overline{G}}_{r x n} = \Delta {\overline{G}}_{r x n}^{\circ} + R T \ln \left(\frac{{\Pi}_{j} {a}_{j}^{{\nu}_{j}}}{{\Pi}_{i} {a}_{i}^{{\nu}_{i}}}\right)$,

where:

• $\Delta {\overline{G}}_{r x n}$ is the molar Gibbs' free energy for the reaction.
• $\Delta {\overline{G}}_{r x n}^{\circ}$ is the molar Gibbs' free energy for the reaction at the standard pressure ($\text{1 bar}$) and at the temperature of the reference reaction.
• $R$ and $T$ are known from the ideal gas law; $T$ is in $\text{K}$.
• The argument of $\ln$ is the general form of the reaction quotient, $Q$, which for real gases and solutions, utilizes activities $a$ for the $i$th reactant and $j$th product.
An example for the activity is ${a}_{i} \equiv {f}_{i} / {P}^{\circ}$ for gases, where $f$ is the fugacity (the real-gas partial pressure). Or, if you know the mol fraction ${\chi}_{i}$ of substance $i$ in the solution, ${a}_{i} = {\gamma}_{i} {\chi}_{i}$, where ${\gamma}_{i}$ is the activity coefficient of substance $i$ at that $T$ and $P$.

This is generally useful for determining $\Delta {\overline{G}}_{r x n}$ at nonstandard temperatures.

It's also important that $\Delta {\overline{G}}_{r x n}^{\circ}$ isn't necessarily at $\text{298.15 K}$, although it is usually convenient to specify that as the standard reference temperature because $\Delta {\overline{G}}_{r x n}^{\circ}$ has been tabulated for many reactions at room temperature.

If you wish to derive this, I show it here.