Question

A chemical reaction occurring in a cylinder equipped with a movable piston produces 0.621 mol of a gaseous product. If the cylinder contained 0.120 mol of gas before the reaction and had an initial volume of 2.18 L, what was its volume after the reaction?

Answer 1

When pressure or temperature are not mentioned, assume that they are kept constant. So, use Avogadro's Law to determine what the new volume of the cylinder will be.

Now,

According to Avogadro's Law, the volume of a gas is directly proportional to the number of moles of gas present, when temperature and pressure are kept constant. In other words, the larger the number of moles of gas present, the larger the volume.

Mathematically, this relationship is expressed like this

V₁/n₁ = V₂/n₂

where

V₁ = initial volume of the cylinder = 2.18 L

n₁ = initial number of moles = 0.120 mole

V₂ = final volume of the cylinder = ?

n₂ = final number of moles = initial moles + produced moles

The reaction produces 0.621 moles of gas, and that 0.120 moles of gas were already in the cylinder. This means that the total number of moles present in the cylinder after the reaction is completed will be

n₂ = n_total = n_initial +n_produced

              = 0.120 + 0.621

              = 0.741 moles

Now,

V₁/n₁ = V₂/n₂

= V₂ = (n₂ x V₁) / n₁

        = (0.741 mole x 2.18 L) / (0.120 mole)

        = 13.46 L