Question

A gas mixture contains HBr, NO2, and C2H6 at STP.If a tiny hole is made in the container, which gas will effuse fastest?Which gas molecules have the highest average kinetic energy at this temperature?

Answer 1

Explanation:

Molar mass of HBr = 81 g/mol

Molar mass of nitrogen dioxide gas = 46 g/mol

Molar mass of ethane = 30 g/mol

Graham's Law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

$\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}$

So, the gas with least molar mass will effuse out fastest from the container and that is ethane gas.

The formula for average kinetic energy is:

$K.E=\frac{3}{2}kT$

where,

k = Boltzmann’s constant = $1.38\times 10^{-23}J/K$

T = temperature = 273.15 K ( at STP)

As we can see from the formula that kinetic energy depends upon only temperature of the gas molecule.

So, from this we can say that all the gas molecules have the same average kinetic energy at this temperature.