Which of the following gases will escape through a hole in a balloon at the highest rate? Kr NO Ar N2O

NO.

Explanation:

The rate of diffusion of gases is inversely proportional to the square root of its density as explained by Graham's law of diffusion i.e

Rate (R) & 1/√(density (d))

R & 1/√d

But the density of a gas is proportional to the molar mass (M) of the gas.

Thus, the above equation can written as:

R & 1/√d

R & 1/√M

This implies that rate is inversely proportional to the molar mass of a gas i.e the lighter the gas, the faster the rate and the heavier the gas, the slower the rate of diffusion.

Now, to obtain the answer to the question, let us determine the molar mass of each gas.

This is illustrated below:

Molar mass of Kr = 84 g/mol

Molar mass of NO = 14 + 16 = 30 g/mol

Molar mass of Ar = 40 g/mol

Molar mass of N2O = (14x2) + 16 = 44 g/mol

Summary

Gas >>>>>>> Molar mass

Kr >>>>>>>>> 84 g/mol

NO >>>>>>>> 30 g/mol

Ar >>>>>>>>> 40 g/mol

N2O >>>>>>> 44 g/mol

From the above table, we can see the lightest gas is NO.

Therefore, NO will escape through the hole in the balloon at the highest rate.