Carbon dioxide can be modeled by the van der Waals equation

CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures

Problem

Carbon dioxide can be modeled by the van der Waals equation, whose parameters for CO

_2

are

a=3.59\,\text{L}^2\,\text{atm}\,\text{mol}^{-2}

and

b=0.0427\,\text{L}\,\text{mol}^{-1}

. A chemist wishes to determine the amount of CO

_2

delivered to a reaction vessel by applying the ideal-gas law. To keep the percent error below

1.5\%

, the chemist must select appropriate experimental conditions. Two storage cylinders are available, both containing exactly

1.00\,\text{mol}

of CO

_2

but at different volumes: • Cylinder A:

V=24.6\,\text{L}

• Cylinder B:

V=2.46\,\text{L}

Both cylinders will be allowed to reach thermal equilibrium at

T=400\,\text{K}

before the gas is transferred. (a) Calculate the pressure inside Cylinder A predicted by (i) the ideal-gas equation and (ii) the van der Waals equation. Report both values in atmospheres. (b) Determine the compressibility factor

Z=\dfrac{PV}{nRT}

for Cylinder A and calculate the percent deviation from ideal-gas behavior. (c) Repeat calculations (a) and (b) for Cylinder B. (d) Using your results, identify which cylinder allows the chemist to meet the

1.5\%

error goal when applying the ideal-gas law. Provide quantitative justification for your choice.

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