Multiple choice

The ratio of rate of diffusion of gases $A$ and $B$ is $1 : 4$. If the ratio of their masses present in the mixture is $2 : 3$, what is the ratio of their mole fraction?

  1. $\dfrac {1}{8}$
  2. $\dfrac {1}{12}$
  3. $\dfrac {1}{16}$
  4. $\dfrac {1}{24}$
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AI explanation

By applying Graham's law of diffusion, the ratio of the rates of effusion of gases A and B is inversely proportional to the square root of their molar masses. Given the rate ratio of 1:4, the square root of the molar mass of A divided by the molar mass of B equals 4, meaning the molar mass of A is 16 times that of B. If the mass ratio of A to B is 2:3, taking 2 grams of A and 3 grams of B gives 2 divided by 16M for the moles of A and 3 divided by M for the moles of B, which simplifies to 1/8 and 3. The mole fraction ratio is calculated by dividing the moles of A by the moles of B, yielding (1/8) divided by 3, which results in 1/24. The ratio of their mole fraction is therefore 1/24.

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