Single Choice

According to Graham's law, at a given temperature the ratio of the rates of diffusion $$\dfrac {r_A}{r_B}$$ of gases $$A$$ and $$B$$ is given by: (where $$p$$ and $$M$$ are pressures and molecular weights of gases $$A$$ and $$B$$ respectively)

A$$\left(\dfrac {P_A}{P_B}\right)\left(\dfrac {M_A}{M_B}\right)^{\frac {1}{2}}$$
B$$\left(\dfrac {M_A}{M_B}\right)\left(\dfrac {P_A}{P_B}\right)^{\frac {1}{2}}$$
C$$\left(\dfrac {P_A}{P_B}\right)\left(\dfrac {M_B}{M_A}\right)^{\frac {1}{2}}$$
Correct Answer
D$$\left(\dfrac {M_A}{M_B}\right)\left(\dfrac {P_B}{P_A}\right)^{\frac {1}{2}}$$

Solution

According to the Graham's law of diffusion, the rates of diffusion of two gases are directly proportional to their partial pressures and inversely proportional to their molecular weights.
The expression for the relative rates of diffusion of two gases is $$\frac {r_A}{r_B}=(\frac {P_A}{P_B})(\frac {M_B}{M_A})^{\frac {1}{2}}$$.
Here, $$r_A $$ and $$r_B$$ are the rates of diffusion of two gases $$A$$ and $$B$$ respectively,
$$P_A $$ and $$P_B$$ are their partial pressures and $$M_A $$ and $$M_B$$ are their molecular weights respectively.

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