Diffusion of Gases

Diffusion is the process by which gas molecules move from an area of high concentration to an area of low concentration. The rate of diffusion depends on various factors including the molecular weight of the gas and the conditions under which diffusion occurs.

Diffusion of Helium

Given that 2g of helium diffuses from a porous plate in 4 minutes, we can calculate the rate of diffusion of helium using the formula:

Rate of diffusion = (Mass of gas / Time)

In this case, the rate of diffusion of helium would be:

Rate of diffusion of helium = (2g / 4 min) = 0.5 g/min

Diffusion of CH4

To determine the grams of CH4 that would diffuse through the same plate in the same time under similar conditions, we need to consider the molecular weight of CH4 and its diffusion rate relative to helium.

The molecular weight of helium is 4 g/mol, while the molecular weight of CH4 is 16 g/mol. Since the molecular weight of CH4 is four times greater than that of helium, we can expect the diffusion rate of CH4 to be slower.

Explanation

The rate of diffusion of gases is inversely proportional to the square root of their molecular weight. This is known as Graham's law of diffusion. According to Graham's law, the ratio of the diffusion rates of two gases is given by the equation:

Rate of diffusion of gas 1 / Rate of diffusion of gas 2 = √(Molecular weight of gas 2 / Molecular weight of gas 1)

In our case, the ratio of the diffusion rates of CH4 to helium can be calculated as:

Rate of diffusion of CH4 / Rate of diffusion of helium = √(Molecular weight of helium / Molecular weight of CH4)

Rate of diffusion of CH4 / 0.5 g/min = √(4 g/mol / 16 g/mol)

Rate of diffusion of CH4 = 0.5 g/min * √(4 g/mol / 16 g/mol)

Rate of diffusion of CH4 = 0.5 g/min * √(1/4)

Rate of diffusion of CH4 = 0.5 g/min * 0.5

Rate of diffusion of CH4 = 0.25 g/min

Therefore, under similar conditions, approximately 0.25 grams of CH4 would diffuse through the same plate in the same time as 2 grams of helium.