100cm³ of ethane gas diffuses through a porous plug in 100 seconds. What is the molecular mass of the gas Q if 100cm³ of the gas diffuses through the same plug in 121 secknds under the same condition?(C=12.0,H=1.0) ​

The molar mass of gas Q is 43.923 g/mol

Explanation:

The given volume of ethane gas that diffuses through a porous plug in 100 seconds = 100 cm³

Therefore;

The rate of diffusion of ethane gas through the porous plug, , is given as follows;

= (100 cm³/100 s) = 1 cm³/s

The molar mass of ethane, C₂H₆ = 2×12 g/mol + 6×1 g/mol = 30 g/mol

The given volume of gas, Q, that diffuses through a porous plug in 121 seconds = 100 cm³

∴ The rate of diffusion of the gas, Q, = 100/121 cm³/s

Graham's Law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the molecular mass of the gas

Mathematically, we have;

Where;

= The rate of diffusion of gas A

= The rate of diffusion of gas B

= The molar mass of the gas A

= The molar mass of the gas B

Therefore, for ethane and gas Q, measured under the same condition, we have;

The molar mass of gas Q, = 43.923 g/mol.