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General Chemistry

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Finding the Percent Error in the Ideal Gas Law

CHEM-1JLS6T

Consider the van der Waals equation of state:

$$\left( p+\frac { { n }^{ 2 }a }{ { V }^{ 2 } } \right) \left( V-nb \right) =nRT$$

where $p$ is the pressure, $n$ is the number of moles, $V$ is the volume, $R$ is the gas constant, $T$ is the temperature, and $a$ and $b$ are the van der Waals constants.

If the volume of $1\text{ mole}$ of some gas at $STP$ calculated using the van der Waals equation is to be considered the true volume, what is the percent error in the volume calculated using the ideal gas law?

$(a=1.355\frac{{L}^{2}atm}{{mol}^{2}}, b=3.201\times {10}^{-2}\frac{L}{mol},R=0.0821\frac{L\times atm}{mole\times K})$

A

$2.44\text{%}$

B

$1.78\text{%}$

C

$3.02\text{%}$

D

$1.15\text{%}$