The rate of diffusion of two gases X and Y is in the ratio 1 : 3 and that of Y and Z in the ratio of 3 : 2. The ratio of the rate of diffusion of Z with respect to X is

Rate of diffusion of two gases X and Y, is in the ratio of 1:3.  So,

$\frac{{\mathrm{r}}_{\mathrm{x}}}{{\mathrm{r}}_{\mathrm{y}}}=\frac{1}{3}$

Rate of diffusion of two gases X and Y, is in the ratio of 1:3.  So,

$\frac{{\mathrm{r}}_{\mathrm{y}}}{{\mathrm{r}}_{\mathrm{z}}}=\frac{3}{2}$

$\frac{r_x}{r_z}=\frac{{\mathrm{r}}_{\mathrm{x}}}{{\mathrm{r}}_{\mathrm{y}}}\times \frac{r_y}{r_z}=\frac{1}{3}\times \frac{3}{2}=1:2$

∴  The ratio of the rate of diffusion of Z with respect  to X is

$\frac{{\mathrm{r}}_{\mathrm{z}}}{{\mathrm{r}}_{\mathrm{x}}}=\frac{2}{1}=2:1$