# correcting Henry's Law coefficient for higher pressure

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?