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) and show worked examples step by step
To calculate the molecular mass of the unknown gas Q, we can use Graham's law of diffusion. Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
The formula for Graham's law of diffusion is:
Rate1/Rate2 = sqrt(MM2/MM1)
Where:
Rate1 = rate of diffusion of gas Q
Rate2 = rate of diffusion of oxygen gas
MM1 = molar mass of gas Q
MM2 = molar mass of oxygen gas
Given data:
- Volume of gas Q (V1) = 20 cm3
- Time taken for gas Q to diffuse = 12.6 seconds
- Volume of oxygen gas (V2) = 10 cm3
- Time taken for oxygen gas to diffuse = 11.2 seconds
- Molar mass of oxygen (MM2) = 32 g/mol (since O2 has a molar mass of 2*16 = 32 g/mol)
First, we calculate the rate of diffusion of gas Q and oxygen gas using the formula:
Rate1 = V1/t1
Rate2 = V2/t2
Rate1 = 20 cm3 / 12.6 s
Rate1 = 1.587 cm3/s
Rate2 = 10 cm3 / 11.2 s
Rate2 = 0.893 cm3/s
Now, substitute the rates of diffusion into Graham's law formula:
1.587/0.893 = sqrt(32/MM1)
1.78 = sqrt(32/MM1)
Square both sides:
3.17 = 32/MM1
Now, solve for MM1:
MM1 = 32 / 3.17
MM1 ≈ 10.08 g/mol
Therefore, the molecular mass of the unknown gas Q is approximately 10.08 g/mol.