Question

If nitrogen gas has a density of 1.14 g/L, and an unknown gas has a density of 5.11 g/L at the same temperature and pressure, what is the ratio of the rate of effusion of the known gas to the rate of effusion of nitrogen

Answer 1

The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Therefore, we can use the molar masses of the gases to calculate the ratio of their rates of effusion.

First, we need to find the molar mass of the unknown gas. Given that nitrogen gas (N2) has a molar mass of approximately 28 g/mol, we can calculate the molar mass of the unknown gas (M_unknown) using its density:

Density = (M_unknown / 22.4 L) * (1 mol / M_unknown)
1.14 g/L = (M_unknown / 22.4 L) * (1 mol / M_unknown)

Now, we can solve for M_unknown:

1.14 g/L = 1 / 22.4 mol/L
M_unknown = 1.14 g/L * 22.4 mol/L
M_unknown ≈ 25.54 g/mol

Now that we have the molar mass of the unknown gas, we can calculate the ratio of the rate of effusion of the known gas to the rate of effusion of nitrogen (N2):

Rate ratio = √(Molar mass of nitrogen / Molar mass of unknown gas)
Rate ratio = √(28 g/mol / 25.54 g/mol)

Rate ratio ≈ √(1.097)

Rate ratio ≈ 1.048

So, the ratio of the rate of effusion of the known gas to the rate of effusion of nitrogen is approximately 1.048.