Q. A gas of unknown identity effuses at the rate of $83.3\ {mLs}^{- 1}$ in an effusion apparatus in which carbon dioxide effuses at the rate of $102\ {mLs}^{- 1}.$ Calculate molar mass of the unknown gas.
A) $6.597\ g\ {mol}^{- 1}$
B) $65.97\ g\ {mol}^{- 1}$
C) $3.650\ g\ {mol}^{- 1}$
D) $36.50\ g\ {mol}^{- 1}$
Explanation
(b)
$\frac{r_{x}}{r_{{CO}_{2}}} = \sqrt{\frac{M_{{CO}_{2}}}{M_{x}}}$
$\frac{83.3}{102} = \sqrt{\frac{M_{{CO}_{2}}}{M_{x}}} = \ \sqrt{\frac{44}{M_{x}}}$
$\ \ M_{x} = 44 \times \left( \frac{102}{83.3} \right)^{2}$
$\ \ \ \ \ \ \ \ \ = 65.97\ g\ {mol}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.