Question

If a gas diffuses at a rate of one-half as fast as oxygen (O2), find the molecular mass of the gas.

Answer 1

To find the molecular mass of the gas, we need to compare the rates of diffusion of the gas and oxygen (O2).

The rate of diffusion of a gas is inversely proportional to the square root of its molecular mass. Therefore, if the gas diffuses at a rate of one-half as fast as oxygen (O2), we can set up the following equation:

rate of gas / rate of O2 = sqrt(Molar mass of O2 / Molar mass of gas)

Given that the gas diffuses at one-half the rate of oxygen (O2), the left side of the equation is 1/2. The molar mass of oxygen (O2) is 32 g/mol.

1/2 = sqrt(32 / molar mass of gas)

Squaring both sides of the equation, we get:

(1/2)^2 = 32 / molar mass of gas
1/4 = 32 / molar mass of gas
molar mass of gas = 32 / (1/4)
molar mass of gas = 32 * 4
molar mass of gas = 128 g/mol

Therefore, the molecular mass of the gas is 128 g/mol.