Questions: A balloon is filled to a volume of 1.50 L with 2.50 moles of gas at 25°C. With pressure and temperature held constant, what will be the volume of the balloon if 0.45 moles of gas are released?

Solution Steps

We are given a balloon with an initial volume of 1.50 L containing 2.50 moles of gas at a constant temperature of \(25^{\circ} \mathrm{C}\) and constant pressure. We need to find the new volume of the balloon after releasing 0.45 moles of gas.

Avogadro's Law states that the volume of a gas is directly proportional to the number of moles of gas when temperature and pressure are held constant. Mathematically, this is expressed as:

\[ \frac{V_1}{n_1} = \frac{V_2}{n_2} \]

where:

• \(V_1 = 1.50 \, \text{L}\) is the initial volume,
• \(n_1 = 2.50 \, \text{moles}\) is the initial number of moles,
• \(V_2\) is the final volume,
• \(n_2\) is the final number of moles.

The initial number of moles is 2.50 moles, and 0.45 moles are released. Therefore, the final number of moles is:

\[ n_2 = 2.50 - 0.45 = 2.05 \, \text{moles} \]

Using Avogadro's Law, we can solve for \(V_2\):

\[ \frac{1.50}{2.50} = \frac{V_2}{2.05} \]

Solving for \(V_2\), we get:

\[ V_2 = \frac{1.50 \times 2.05}{2.50} = 1.23 \, \text{L} \]

Final Answer