b. 20cm3 of an unknown gas Q takes 12.6 seconds to pass through small orifice.10cm3 of
oxygen gas takes 11.2 seconds to diffuse through the same orifice under the same
conditions of temperature and pressure .Calculate the molecular mass of unknown gas Q
( O=16)
To calculate the molecular mass of unknown gas Q, we can use Graham's law of diffusion which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Given:
Volume of unknown gas Q = 20 cm^3
Time taken for unknown gas Q to diffuse = 12.6 seconds
Volume of oxygen gas = 10 cm^3
Time taken for oxygen gas to diffuse = 11.2 seconds
Molar mass of oxygen (O2) = 32 g/mol (since O has a molar mass of 16 g/mol)
First, calculate the rate of diffusion for each gas:
Rate of diffusion for unknown gas Q = Volume / Time = 20 cm^3 / 12.6 seconds = 1.587 cm^3/s
Rate of diffusion for oxygen gas = 10 cm^3 / 11.2 seconds = 0.893 cm^3/s
Next, calculate the square root of the rate of diffusion for each gas:
√(rate of diffusion for unknown gas Q) = √1.587 = 1.26
√(rate of diffusion for oxygen gas) = √0.893 = 0.946
Now, calculate the ratio of the square roots of the rates of diffusion:
(√rate of diffusion for unknown gas Q) / (√rate of diffusion for oxygen gas) = 1.26 / 0.946 = 1.33
According to Graham's law, this ratio is equal to the square root of the ratio of the molar masses of the two gases:
√(Molar mass of oxygen / Molar mass of unknown gas Q) = 1.33
√(32 / Molar mass of unknown gas Q) = 1.33
32 / Molar mass of unknown gas Q = (1.33)^2
Molar mass of unknown gas Q = 32 / (1.33)^2 = 24 g/mol
Therefore, the molecular mass of unknown gas Q is 24 g/mol.