Question on: JAMB Chemistry - 2014

According to Graham's Law of Diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this is expressed as:

$\frac{Rate_X}{Rate_Y} = \sqrt{\frac{M_Y}{M_X}}$

Where:

• $Rate_X$ is the rate of diffusion of gas X
• $Rate_Y$ is the rate of diffusion of gas Y
• $M_X$ is the molar mass of gas X
• $M_Y$ is the molar mass of gas Y

Given that gas X diffuses twice as fast as gas Y, $Rate_X = 2 \times Rate_Y$. The relative molecular mass of X ($M_X$) is 32.

Substitute the known values into the equation:

$\frac{2 \times Rate_Y}{Rate_Y} = \sqrt{\frac{M_Y}{32}}$

Simplify:

$2 = \sqrt{\frac{M_Y}{32}}$

Square both sides:

$4 = \frac{M_Y}{32}$

Multiply both sides by 32 to solve for $M_Y$:

$M_Y = 4 \times 32 = 128$

Therefore, the relative molecular mass of Y is 128.