First slide

Vanderwaal's equation

Question

At moderately low pressures (or) intermediate pressures, a graph is plotted between compressibility factor(Z) on y-axis Vs $\frac{1}{V}$ on x-axis at constant temperature. Correct statement regarding the graph is

Moderate

A

It is a straight line with positive y-intercept and a positive slope
B

It is a straight line with positive y-intercept and a negative slope
C

It is a straight line with negative y-intercept and a positive slope
D

It is a straight line with negative y-intercept and a negative slope

Solution

At moderately low pressures (or) intermediate pressures, the factor ‘b’ of Vanderwaals equation can be neglected. ‘b’ is covolume (or) volume occupied by molecules which becomes significant only at high pressures.
Vanderwaals equation for one mole can be written as
$\begin{array}{l} (P + \frac{a}{V^{2}}) (V) = RT \\ PV + \frac{a}{V} = RT \\ PV = RT - \frac{a}{V} \\ \frac{PV}{RT} = 1 - \frac{a}{RTV} \\ \underset{y}{Z} = \underset{c}{1} - \underset{m}{\frac{a}{RT}} \times \underset{x}{\frac{1}{V}}; \\ A straight line with negative slope and positive y - intercept; \end{array}$

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