For real gases van der Waals' equation is written as (p+(a...

For real gases van der Waals' equation is written as

\left(p+\frac{a n^2}{V^2}\right)(V-n b)=n R T

where,

a and b

are van der Waals' constants. Two sets of gases are I.

\mathrm{O}_2, \mathrm{CO}_2, \mathrm{H}_2

and

\mathrm{He}

II.

\mathrm{CH}_4, \mathrm{O}_2

and

\mathrm{H}_2

The gases given in set-I in increasing order of '

b

' and gases given in set-II in decreasing order of '

a

', are arranged below. Select the correct order from the following. For real gases van der Waals' equation is written as (p+(a n^2)/(V^2))(V-n b)=n R T where, a and b are van der Waals'

For real gases van der Waals' equation is written as (p+(a n^2)/(V^2))(V-n b)=n R T where, a and b are van der Waals'

Options

A(I) $\mathrm{He} < \mathrm{H}_2 < \mathrm{CO}_2 < \mathrm{O}_2$ (II) $\mathrm{CH}_4>\mathrm{H}_2>\mathrm{O}_2$
B(I) $\mathrm{O}_2 < \mathrm{He} < \mathrm{H}_2 < \mathrm{CO}_2$ (II) $\mathrm{H}_2>\mathrm{O}_2>\mathrm{CH}_4$
C(I) $\mathrm{H}_2 < \mathrm{He} < \mathrm{O}_2 < \mathrm{CO}_2$ (II) $\mathrm{CH}_4>\mathrm{O}_2>\mathrm{H}_2$
D(I) $\mathrm{H}_2 < \mathrm{O}_2 < \mathrm{He} < \mathrm{CO}_2$ (II) $\mathrm{O}_2>\mathrm{CH}_4>\mathrm{H}_2$

Correct answer

C. (I) $\mathrm{H}_2 < \mathrm{He} < \mathrm{O}_2 < \mathrm{CO}_2$ (II) $\mathrm{CH}_4>\mathrm{O}_2>\mathrm{H}_2$

Step-by-step solution

From experimental values of

a

and

b

, sequence of van der Waals' constant, (b) is For real gases van der Waals' equation is written as (p+(a n^2)/(V^2))(V-n b)=n R T where, a and b are van der Waals'

Hence correct order is

\mathrm{H}}_{2} < \mathrm{He} < \mathrm{O}_2 < \mathrm{CO}_2 and sequence of van der Waals' constant (a) is

\\ Hence, correct order is (II) \mathrm{CH}}_{4} \gt \mathrm{O}

}_{2} \gt

\mathrm{H}}_{2}

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