The Initial Volume of a Balloon Filled with Freon Gas

Problem:

A 3.63 mol sample of freon gas was placed in a balloon. Adding 3.50 mol of freon to the balloon increased its volume to 30.2 L. What is the initial volume of the balloon?

Final answer:

Using the direct relationship between volume and the amount of gas when temperature and pressure are constant, the initial volume of the balloon filled with freon gas is calculated to be approximately 15.27 liters.

Explanation:

To determine the initial volume of the balloon filled with freon gas, we can use the ideal gas law under the assumption that temperature and pressure conditions remained constant during the addition of the freon gas. The ideal gas law is stated as PV = nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is temperature. However, for this problem, we specifically use the direct relationship of volume and amount of gas, V/n = k, where k is a constant when pressure and temperature are held constant.

When 3.50 moles of freon gas are added to the initial 3.63 moles, the total becomes 7.13 moles, and the volume of the balloon increases to 30.2 liters. Using the direct ratio, we can set up a proportion: (initial volume/3.63 mol) = (30.2 L/7.13 mol). Solving for the initial volume, we get: initial volume = (3.63 mol * 30.2 L) / 7.13 mol, which calculates to approximately 15.27 liters.