Question

The given graph in Fig represents the variation of Z $(compressibilityfactor=\frac{PV}{nRT}$) vs P , for the 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 pressures
• B. For the gas B,b=0 and its dependence on p is linear at all pressures.
• C. For the gas C, which is typical real gas which neither a nor b=0.By konowing the minima and the point of intersection with z=1,a and b can be calculated.
• D. At high pressure,the slope is positive for all real gases.

Answer 1

Answer: (C)

Graph shows, that the value of z decreases as increasing the pressure. therefore, We can explain on the basis of van der Waals' equation. At high pressure, the value of 'p' is large, then the value of V will be small but we cannot ignore 'b' in comparison to V.

$(p+\frac{a}{V^2})(v-b)=nRT$
However, the term a/V2 be considered negligible in comparison to 'p' in van der Waals' equation

$p(v-b)=nRT$

$pv-pb=nRT$

$\frac{pv}{nRT}=1+\frac{pb}{nRT}$

$Z=1+\frac{pb}{nRT}$

Here, z is greater than 1 and it increases linearly with pressure.
Hence, statement (b) is incorrect.

NOTE:

The "a" and "b" are called van der Waals constants: The constant a provides "a" measure of the average attraction of the molecules, whereas constant "b" adjusts for the volume occupied by the gas particles.