Question

The given graph represent the variations of compressibility factor (z) = pV/nRT versus p, for three real  gases A, B and C. Identify the only incorrect statement

(a) For the gas A, a = 0 and its dependence on p is linear at all pressure.

(b) For the gas B, b = 0 and its dependence on p is linear at all pressure.

(c) For the gas C, which is typical real gas for which neither a nor b = 0, By knowing the minimum and point of the intersection, with z =1, a and b can be calculated.

(d) At high pressure, the slope is positive for all real gases.

Answer 1

The incorrect statement is (b) For the gas B, b = 0 and its dependence on p is linear at all pressure.

Explanation:

From the graph it is clear that the value of z decreases with increase of pressure. We can explain as follows on the basis of van der Waals' equation.

At high pressure, when 'p' is large, V will be small and one cannot ignore 'b' in comparison to V. However, the term a/V² be considered negligible in comparison to 'p' in van der Waals' equation

Here z  is greater than one and it increases linearly with pressure. Hence, statement (b) is false.

Answer 2

The incorrect statement is (b)

The van der Waals equation for n moles of a real gas is

Thus the compressibility shows linear dependence on P with a positive slope. i.e., z increases linearly with pressure.