Question

For real gases, the relation between P, V and T is given by van der Waals equation, $\left(P + \frac{a n^{2}}{V^{2}}\right)\left(V - n b\right)=nRT.$ For the following gases $CH_{4},CO_{2},O_{2},H_{2}$ which gas will have
(i) highest value of '$a$' and (ii) lowest value of '$b$' respectively?

• A. (i) $CO_{2}$ , (ii) $H_{2}$
• B. (i) $CH_{4}$ , (ii) $CO_{2}$
• C. (i) $H_{2}$ , (ii) $CO_{2}$
• D. (i) $O_{2}$ , (ii) $H_{2}$

Answer 1

Answer: (A)

(i) Order of intermolecular attraction is $CO_{2}>CH_{4}>O_{2}>H_{2}$
In $CO_{2}$ value of '$a$' will be maximum. Value of '$a$' is directly proportional to intermolecular attraction of gas molecules.
(ii) Size increases in order of $H_{2} < O_{2} < CH_{4} < CO_{2}$
Hence, $H_{2}$ will have lowest value of '$b$'. Value of '$b$' is directly proportional to molecular size of gas molecules.