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When we have an isotherm isomerism reaction

$\ce{A(g) -> A^*(g)}$ with $\ce{ΔH^0 = 0}$

is the ratio of preassures $\ce{P_A^* / P_A}$ independent from temperature?

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The van't Hoff equation would predict that the equilibrium constant is not dependent on temperature, since in this case:

$$\frac{\mathrm{d}}{\mathrm{d}T}\ln K_{eq} = \frac{\Delta H^\circ}{RT^2}=0$$

Strictly speaking the equilibrium constant is a function of fugacities, but it is probably safe to assume that the pressures are also independent of T, so the answer would be yes.

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