(rateO2/rateunk) = sqrt(Munk/MO2)
M = molar mass
unk = unknown
M = molar mass
unk = unknown
Thanks
First, let's determine the ratio of the rates of effusion between the unknown gas and O2 gas.
Rate of effusion of unknown gas / Rate of effusion of O2 gas = sqrt (Molar mass of O2 gas / Molar mass of unknown gas)
We are given that it took 52 s for 1.0 L of the unknown gas to effuse, and 24 s for 1.0 L of O2 gas to effuse.
Using the ratio of the rates of effusion:
Rate of effusion of unknown gas / 24 s = Rate of effusion of O2 gas / 52 s
Now, we need to solve for the molar mass of the unknown gas. Rearranging the equation:
Rate of effusion of unknown gas = (24 s / 52 s) * Rate of effusion of O2 gas
The rate of effusion of O2 gas is inverse proportion to the square root of its molar mass, so:
(24 s / 52 s) * Rate of effusion of O2 gas = sqrt (Molar mass of O2 gas / Molar mass of unknown gas)
Squaring both sides:
((24 s / 52 s) * Rate of effusion of O2 gas)^2 = Molar mass of O2 gas / Molar mass of unknown gas
After calculating the value on the left-hand side, we can rearrange the equation to solve for the molar mass of the unknown gas:
Molar mass of unknown gas = (Molar mass of O2 gas * ((24 s / 52 s) * Rate of effusion of O2 gas)^2)
Now, plug in the known values:
Molar mass of O2 gas = 32 g/mol (molar mass of O2 gas)
Rate of effusion of O2 gas = 1.0 (as we are using 1.0 L of O2 gas)
Rate of effusion of unknown gas = 1.0 (as we are using 1.0 L of the unknown gas)
Molar mass of unknown gas = (32 g/mol * ((24 s / 52 s) * 1.0)^2)
After calculating the expression on the right-hand side, you will get the molar mass of the unknown gas in grams per mole.