Question

The volume of 5.15 mol of oxygen gas is 3.08 m3 at 300. K. What is the real pressure given that a=1.36 J m3/mol2, b=0.00320 m3/mol, and R=8.3145 J/mol K? Remember that Pascal=J/m3.

need ASAP please!!

Answer 1

Here, we will use the Van der Waals equation of real gases. The equation is,

$\left ( P+\frac{an^2}{V^2} \right )\left ( V-nb \right )=nRT$

Here, P is the real pressure, n is the no. of moles, T is the temperature, R is the universal gas constant, and a, b are the Van der waals cconstants. Putting in the values, we have,

$\left ( P+\frac{an^2}{V^2} \right )\left ( V-nb \right )=nRT\\ \Rightarrow \left ( P+\frac{an^2}{V^2} \right )= \frac{nRT}{\left ( V-nb \right )}\\ \Rightarrow P= \frac{nRT}{ V-nb}-\frac{an^2}{V^2}\\ \Rightarrow P= \frac{5.15\times 8.3145\times 300}{ 3.08-5.15\times0.00320}-\frac{1.36\times5.15^2}{3.08^2}\;J/m^3\qquad\textrm{[Putting the values]}\\ \Rightarrow P=4189.4\;J/m^3\\ \Rightarrow P \approx 4190\;Pa \qquad\textrm{[3 significant figures]}$