Avogadro's Law: Calculate the Initial Volume of a Balloon

Question:

A 9.79 mol sample of freon gas was placed in a balloon. Adding 3.50 mol of freon gas to the balloon increased its volume to 21.8 L. What was the initial volume of the balloon?

Answer:

16.06 L was the initial volume of the balloon.

Final answer:

The initial volume of the balloon was approximately 16.05 L, calculated by applying Avogadro's law.

Explanation:

The principle underlying this problem is Avogadro's law, which states that equal volumes of any gas, at the same temperature and pressure, contain equal numbers of moles. The volume-to-mole ratio of a gas is always constant (for example, per 1 mol, we have ~22.4 L at STP).

The initial number of moles of freon in the balloon is 9.79 mol, and then an additional 3.50 mol is added, bringing the total to 13.29 mol. The final volume after the addition is known to be 21.8 L. Hence, we can find the volume per mole as follows: V_total/n_total = 21.8 L / 13.29 mol = 1.64 L/mol.

Now, applying this to calculate the initial volume we get: V_initial = Volume per mole * Initial number of moles = 1.64 L/mol * 9.79 mol = 16.05 L approximately.

Learn more about Avogadro's law here:

Avogadro's law states that equal volumes of any gas, at the same temperature and pressure, contain equal numbers of moles. It is a fundamental principle in chemistry that helps us understand the behavior of gases under different conditions.