How long does it take for all air molecules to come out of a 540 cm3 balloon? Assume that every second

How long does it take for all air molecules to come out of a 540 cm3 balloon? Assume that every second 10 molecules come out of it, and the number of molecules in 1 centimeter in a cube of air is 2.7 × 10 ^ 17.

The number of molecules N in a balloon is equal to the product of the number of molecules n per unit volume by the volume of the balloon V:

N = nV = 540 cm3 * 2.7 * 10 ^ 17 mol / cm3 = 1.458 * 10 ^ 20 molecules.

The time after which all the molecules leave the balloon:

t = N / v = (1.458 * 10 ^ 20 mol) / (10 mol / s) = 1.458 * 10 ^ 19 s (v is the rate of decrease in the number of molecules).

It is difficult to imagine such a number of seconds. Let’s try to express the time in years:

1 year = 364 days * 24 hours / day * 3600 s / hour = 31449600 s / year.

t = (1.458 * 10 ^ 19 s) / (31449600 s / year) = 4.6 * 10 ^ 11 years.

All the same it turns out an unimaginable amount: 460,000 thousand times over a million years.

Answer. Through 1.458 * 10 ^ 19 s.