Gas X has a mass of 28.02 amu and gas Y has a mass of 32 amu. Which gas will diffuse faster?
The lighter gas diffuses faster.
To determine which gas will diffuse faster, you need to compare their molar masses or molecular weights. The molar mass of a substance is the mass of one mole of that substance, expressed in grams. In this case, we have Gas X with a molar mass of 28.02 amu and Gas Y with a molar mass of 32 amu.
To compare the diffusion rates, we can use Graham's Law of Effusion, which states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be represented as:
Rate of Effusion ∝ 1/√(molar mass)
Therefore, to determine which gas will diffuse faster, we can compare the square roots of their molar masses. Let's calculate:
Square root of molar mass of Gas X = √28.02 amu ≈ 5.29
Square root of molar mass of Gas Y = √32 amu ≈ 5.66
Comparing the calculated values, we see that the square root of the molar mass of Gas Y is larger than that of Gas X. According to Graham's Law, the gas with the smaller square root of its molar mass will diffuse faster. In this case, Gas X will diffuse faster since its square root is smaller than that of Gas Y.
Therefore, Gas X will diffuse faster than Gas Y.