A balloon is filled to a volume of 1.50 L with 2.50 moles of gas at 25.0°C. With pressure and temperature held constant, what will be the volume (in L) of the balloon if 0.35 mol of gas are released?
We are given an initial state of a gas in a balloon where the volume \(V_1\) is \(1.50 \text{ L}\) and the amount of substance in moles \(n_1\) is \(2.50 \text{ mol}\). The temperature and pressure remain constant throughout the process. We are told that \(0.35 \text{ mol}\) of gas is released from the balloon. To find the final volume \(V_2\), we must first determine the final number of moles \(n_2\) in the balloon. Given the amount of gas released, the final number of moles is \(n_2 = n_1 - 0.35 \text{ mol} = 2.50 \text{ mol} - 0.35 \text{ mol} = 2.15 \text{ mol}\).
Since the pressure and temperature are held constant, we can apply Avogadro's Law, which states that for a fixed amount of gas, volume is directly proportional to the number of moles. Mathematically, this relationship is expressed as:
\[\frac{V_1}{n_1} = \frac{V_2}{n_2}\]
We can rearrange this formula to solve for the final volume \(V_2\):
\[V_2 = V_1 \times \frac{n_2}{n_1}\]
Substituting the known values \(V_1 = 1.50 \text{ L}\), \(n_1 = 2.50 \text{ mol}\), and \(n_2 = 2.15 \text{ mol}\), we get:
\[V_2 = 1.50 \text{ L} \times \frac{2.15 \text{ mol}}{2.50 \text{ mol}}\]
Performing the calculation:
\[V_2 = 1.50 \times 0.86 = 1.29 \text{ L}\]
Therefore, the final volume of the balloon is \(1.29 \text{ L}\).
Avogadro's law is fundamental in understanding how gases behave in everyday life, such as in the inflation of tires or balloons. If you have a car tire that is slightly deflated and you add air to increase the number of moles of gas inside, the pressure-volume relationship helps ensure the tire reaches the correct size and pressure for safe driving. Understanding this proportional relationship allows for the precise control of gas volumes in various engineering and scientific applications.