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Van der Waals Equation for Gas Calculations (Example 1)
The Van der Waals is an equation of state, it’s 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.
The constants should generally be provided in the question itself on an exam or on a cheat sheet.
Sample question: 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:
\[P = \frac{{\left( {0.08206\frac{{Latm}}{{molK}}} \right)\left( {298K} \right)}}{{\left( {2 – 0.0427} \right)\frac{L}{{mol}}}} – \frac{{3.61\frac{{{L^2}atm}}{{mo{l^2}}}}}{{{{(2)}^2}\frac{{{L^2}}}{{mo{l^2}}}}}\]
\[P = 11.59atm\]
Click here to see an solved examples with the regular ideal gas law!