For a real gas obeying vander Waal's equation a graph is plotted between ${P V}_{m}$ ( $y =$ axis) and $P (x - a x i s)$ where $V_{m}$ is molar volume. Find $y -$ intercept of the graph.

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Solution

( $P + \frac{a n^{2}}{V^{2}}$ ) (V-nb) = nRT for 'n' moles.
where a and b are Vander waals constants. The constant 'a' measures the forces of attraction between the molecules of the gas and 'b' relates to the in compressible volume of the molecules, measuring the size of the gas molecules for n = 1
PV = P(b) + $\frac{a}{v}$ - $\frac{a b}{v^{2}}$ + RT
Its of form y = mx + c
where c is Y - Intercept.
Y - Intercept : { $\frac{a}{v}$ - $\frac{a b}{v^{2}}$ + RT}

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For a real gas obeying vander Waal's equation a graph is plotted between PVm(y=axis) and P(x−axis) where Vm is molar volume. Find y−intercept of the graph.

For a real gas obeying vander Waal's equation a graph is plotted between ${P V}_{m}$ ( $y =$ axis) and $P (x - a x i s)$ where $V_{m}$ is molar volume. Find $y -$ intercept of the graph.