I have a bottle at room temperature that contains water, nitrogen, and a trace amount of vinyl chloride (VC). I'm trying to determine how much the Henry's law coefficient for VC (at 25 C and 1 bar, with units of pressure/concentration) should be corrected if the bottle is pressurized to 2 bar.

A thermodynamics textbook I've borrowed states that the Henry's law coefficient $H_2$ at pressure $P_2$ can be calculated with $H_1$ at $P_1$ as follows:

$$ H_2 = H_1 \exp \left [ \int\limits_{P_1}^{P_2} \frac{\bar{V}^\infty}{RT}dP \right ] $$

where $\bar{V}^\infty$ is the partial molar volume at infinite dilution, $R$ is the gas constant, and $T$ is temperature. The textbook says that $\bar{V}^\infty$ can be approximated with the pure species molar volume $V^m$, which for VC is 45.2 mL/mol.

After making that substitution and simplifying I am left with the following approximation:

$$ H_2 \approx H_1 \exp \left [ \frac{V^m(P_2 - P_1)}{RT} \right ] $$

which for my scenario works out to a negligible adjustment of $H_2\approx1.0018H_1$. Have I interpreted this material correctly?


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