Question

Correct sequence ${\mathrm{U}}_{\mathrm{rms}}$ at constant temperature:

• A. ${\mathrm{U}}_{{\mathrm{N}}_2}>{\mathrm{U}}_{{\mathrm{O}}_2}>{\mathrm{U}}_{{\mathrm{CO}}_2}$
• B. ${\mathrm{U}}_{{\mathrm{O}}_2}>{\mathrm{U}}_{{\mathrm{N}}_2}>{\mathrm{U}}_{{\mathrm{CO}}_2}$
• C. ${\mathrm{U}}_{{\mathrm{CO}}_2}>{\mathrm{U}}_{{\mathrm{O}}_2}>{\mathrm{U}}_{{\mathrm{N}}_2}$
• D. ${\mathrm{U}}_{{\mathrm{CO}}_2}={\mathrm{U}}_{{\mathrm{O}}_2}={\mathrm{U}}_{{\mathrm{N}}_2}$

Answer 1

The correct option is A

${\mathrm{U}}_{{\mathrm{N}}_2}>{\mathrm{U}}_{{\mathrm{O}}_2}>{\mathrm{U}}_{{\mathrm{CO}}_2}$

Explanation for the correct option:

(A) The formula of root mean square velocity for gases is:

${\mathrm{U}}_{\mathrm{rms}}=\sqrt{3\mathrm{RT}/\mathrm{M}}$

At constant temperature,

$\mathrm{U}\mathrm{\alpha }\sqrt{1/\mathrm{M}}$

The ascending order of molar mass of gas:

${\mathrm{N}}_2<{\mathrm{O}}_2<{\mathrm{CO}}_2$

Therefore, the correct order of ${\mathrm{U}}_{\mathrm{rms}}$:

${\mathrm{U}}_{{\mathrm{N}}_2}>{\mathrm{U}}_{{\mathrm{O}}_2}>{\mathrm{U}}_{{\mathrm{CO}}_2}$

Hence, option A is correct.