A 2.39 mol sample of Freon gas was placed in a balloon. Adding 3.50 mol of Freon gas to the balloon increased its volume to 34.6 L, what was the initial volume of the balloon?

Answer 1

In order to solve this, we can use Avogadro's law in which states that:

V₁ / n₁ = V₂ / n₂

V₁ = first volume in liters

V₂ = second volume in liters

n₁ = first amount of gas in moles

n₂ = second amount of gas in moles

We know that we need to use Avogadro's law as the problem states that the ballon is filled with freon gas. Specifically, the word gas lets us know that this problem is related to the ideal gas law. The ideal gas law is PV = nRT. Additionally, as the units are given in the problem, we know that the units in this equation are liters (L) and moles (mol) in which correspond to the volume (V) and moles (n) in the ideal gas law. Since, the pressure (P), the constant (R), and temperature (T) are not present in this problem, we know that we need to use a gas law that relates only the volume (V) and moles (n) together in which is Avogadro's Law.

So, in this problem:

V₁ = first volume in liters = ?

V₂ = second volume in liters = 34.6 L

n₁ = first amount of gas in moles = 2.39 mol

n₂ = second amount of gas in moles = 2.39 mol + 3.50 mol = 5.89 mol

For n₂, we add 3.50 mol to 2.39 mol to get the number of moles that correspond to the increased volume of the balloon (34.6 L) after it gets filled up as it was stated in the problem that adding the moles made the balloon increase its volume.

Plugging the values into Avogadro's law, we get:

V₁ / n₁ = V₂ / n₂

V₁ / 2.39 mol = 34.6 L / 5.89 mol

5.89 mol * V₁ = 2.39 mol * 34.6 L Solve as a ratio

V₁ = 14.0397 L = 14.0 L (3 significant figures)