Question

A container at room temperature contains two gases, oxygen, and nitrogen. The container has a small hole that allows gas molecules to escape. If the hole is big enough, which gas will escape faster and why? Calculate the ratio of their rates of effusion.

Answer 1

To determine which gas will escape faster, we can use Graham's law of effusion. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be represented as:Rate1 / Rate2 =  M2 / M1 where Rate1 and Rate2 are the rates of effusion of gas 1 and gas 2, respectively, and M1 and M2 are their molar masses.The molar mass of oxygen  O2  is 32 g/mol, and the molar mass of nitrogen  N2  is 28 g/mol. Plugging these values into the equation, we get:Rate_O2 / Rate_N2 =  28 / 32 Rate_O2 / Rate_N2 =  0.875 Rate_O2 / Rate_N2  0.935Since the ratio is less than 1, this means that nitrogen gas  N2  will escape faster than oxygen gas  O2 . The ratio of their rates of effusion is approximately 0.935:1  N2:O2 . This is because nitrogen has a lower molar mass than oxygen, and lighter gases effuse more quickly than heavier gases according to Graham's law.