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.