MediumChemistryHigh School (11–12)States of MatterNumericalBoard Exam AP A-Level IB

One mole of nitrogen is in a 0.500 L vessel at 300 K…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

One mole of nitrogen is in a $0.500\ \text{L}$ vessel at $300\ \text{K}$ . For nitrogen, $a = 1.370\ \text{L}^2\ \text{bar mol}^{-2}$ and $b = 0.0387\ \text{L mol}^{-1}$ . Find the pressure from the ideal gas equation and from the van der Waals equation. Then find the compressibility factor, and say whether attraction or size wins.

Need a reminder? The key ideaShow

$Z = PV_m/RT$ . The van der Waals equation is $\left(P + \dfrac{an^2}{V^2}\right)(V - nb) = nRT$ . Its critical constants are $T_c = \dfrac{8a}{27Rb}$ , $P_c = \dfrac{a}{27b^2}$ and $V_c = 3b$ . From $T_c$ and $P_c$ , $b = \dfrac{RT_c}{8P_c}$ and $a = \dfrac{27R^2T_c^2}{64P_c}$ . The Boyle temperature is $T_B = a/(Rb)$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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