Question

When $r,p$ and $M$ represent rate of diffusion, pressure and molecular mass, respectively, then the ratio of the rates of diffusion ($r{}_A/r_B$) of two gases A and B is given as:

• A. ${\left(p_A/p_B\right)}^{1/2}\left(M_A/M_B\right)$
• B. $\left(p_A/p_B\right)(M_A/M_B{)}^{1/2}$
• C. ${\left(p_A/p_B\right)}^{1/2}\left(M_B/M_A\right)$
• D. $\left(p_A/p_B\right)(M_B/M_A{)}^{1/2}$

Answer 1

The correct option is D $\left(p_A/p_B\right)(M_B/M_A{)}^{1/2}$

Rate of diffusion: $r\alpha p$

$r=\frac{1}{\sqrt{M}}\therefore r\alpha \frac{P}{\sqrt{M}}$

$r_A\alpha \frac{p_A}{\sqrt{M_A}}------\left(1\right)$

$r_B\alpha \frac{p_B}{\sqrt{M_B}}------\left(2\right)$

Divide eqn (1) by eqn (2) we get..,

$\frac{r_A}{r_B}=\frac{p_A}{p_B}.\sqrt{\frac{M_B}{M_A}}or\frac{p_A}{p_B}{\left(\frac{M_B}{M_A}\right)}^{{1/2}^{}}$

Hence, $\frac{p_A}{p_B}{\left(\frac{M_B}{M_A}\right)}^{{1/2}^{}}$ is the answer.