Adding helium to a balloon increased its volume from 832.3 mL to 4.266 L

Question

Adding helium to a balloon increased its volume from 832.3  mL to 4.266  L. If the final number of moles of helium in the balloon is 20.4 mol, what was the initial number of moles of helium in the balloon? Assume the balloon contained only helium initially.

Answer 1

Hi, Noah,

A great question!! So, this is an application of Avogadro's law (which is derived from the ideal gas law or PV = nRT where P is the gas pressure, V is the volume occupied by the gas, n is the moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin). Assuming no change in pressure or in temperature reduces this problem to

, where k is a constant for any given temperature and pressure.

In this case, since the volume and molar quantity of the gas are changing, you need to solve the following equation:

So, for this particular problem:

0.8323 L = 4.266 L

n₁ 20.4 mol, or n₁ = (20.4)(0.8323) ÷ 4.266,

or n₁ = 3.98 mol of helium initially.