Question

Which of following statement(s) is/are correct?

• A. Average velocity of molecules of a gas in a container is zero.
• B. All molecules in a gas are moving with the same speed.
• C. If an open container is heated from 300 K to 400 K the fraction of air which goes out with respect to originally present is $\frac{1}{4}$.
• D. If compressibility factor of gas at S.T.P is less than unity then its molar volume is less than 22.4 L at S.T.P.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Average velocity of molecules of a gas in a container is zero.
C If an open container is heated from 300 K to 400 K the fraction of air which goes out with respect to originally present is $\frac{1}{4}$.
D If compressibility factor of gas at S.T.P is less than unity then its molar volume is less than 22.4 L at S.T.P.

(A) Since the direction of gas molecules is random and the container is stationary, it implies that average velocity is zero but the average speed will not be zero.

(B) Speed of gas molecules follow Maxwell's distribution and hence the speed of every molecule will be different.

(C) $n_1{T}_1=n_2{T}_2$

$n\times 300=n_2\times 400$

$n_2=\frac{3}{4}n$

escape out $=\frac{n-\frac{3}{4}n}{n}=\frac{1}{4}$

(D) $\frac{PV}{RT}<1$

$Z<1$

Molar volume for Z = 1 is 22.4 L

So for Z < 1 molar volume is less than 22.4 L at S.T.P.