Van der Waals Equation for Gas Calculations (Example 1)

The Van der Waals is like the ideal gas law, except it has a few extra constants that are given to you in the question. The constants themselves will have complicated-looking units, but pressure, volume, R, etc will have the same units as usual so don't worry.

10 mol of a gas is in a volume of 20 L at \({25^o}C\). Find the vessel's pressure using the Van der Waals equation. Use \(a = 3.61\frac{{{L^2}atm}}{{mo{l^2}}}\) and \(b = 0.0427\frac{L}{{mol}}\).

The Van der Waals equation is:

\[P = \frac{{RT}}{{{V_m} - b}} - \frac{a}{{{V_m}^2}}\]

Plug in all values, and remember to use the Kelvin temperature:

\[P = \frac{{\left( {0.08206\frac{{Latm}}{{molK}}} \right)\left( {298K} \right)}}{{\left( {2 - 0.0427} \right)\frac{L}{{mol}}}} - \frac{{3.61\frac{{{L^2}atm}}{{mo{l^2}}}}}{{{{(2)}^2}\frac{{{L^2}}}{{mo{l^2}}}}}\]

\[P = 11.59atm\]

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