Effusion is the process by which a gas escapes through a small hole into a vacuum. The hole size and the gas particles’ speed determine the effusion rate. The time it takes for a gas to effuse is inversely proportional to the square root of its molar mass. This means that lighter gases effuse faster than heavier gases.
In this problem, we are given that a sample of N2 effuses in 220 seconds. We can use this information to find the molar mass of N2.
The equation gives the rate of effusion:
Rate of effusion = (Volume of gas) / (Time taken to effuse)
Since the volume of gas and the size of the hole are constant, we can write:
Rate of effusion ∝ 1 / (Time taken to effuse)
Therefore, we can write:
(Time taken for N2 to effuse) / (Time taken for Cl2 to effuse) = √(Molar mass of Cl2 / Molar mass of N2)
We know that the time taken for N2 to effuse is 220 seconds. We need to find the time taken for Cl2 to effuse. We also know the molar mass of N2, which is 28 g/mol.
We can use the periodic table to find the molar mass of Cl2. The atomic mass of chlorine is 35.5, so the molar mass of Cl2 is 2 x 35.5 = 71 g/mol.
Substituting these values into the equation, we get:
(Time taken for N2 to effuse) / (Time taken for Cl2 to effuse) = √(71 / 28)
Simplifying, we get:
(Time taken for Cl2 to effuse) = (220 seconds) x √(28 / 71)
(Time taken for Cl2 to effuse) = 220 x 0.632
(Time taken for Cl2 to effuse) = 139 seconds (approx.)
Therefore, a sample of Cl2 of the same size will take approximately 139 seconds to effuse.