Question

In 1783, Charles launched his first balloon filled with hydrogen gas. He chose hydrogen because it was lighter than air. The balloon had a volume of 31,000 L at a pressure of 755 mmHg and a temperature of 22°C. When the balloon reached an altitude of 1000 m, the pressure was 658 mmHg, and the temperature was -8°C. What was the volume in liters of the balloon at these conditions, assuming the number of moles (n) is the same?

a) 28,000 L
b) 32,000 L
c) 36,000 L
d) 40,000 L

Answer 1

Using the combined gas law, we can find the volume of the balloon at the given conditions by rearranging the equation and plugging in the values. The volume of the balloon at the given conditions is approximately 36,000 L.

Step-by-step explanation:

To find the volume of the balloon at the given conditions, we can use the combined gas law equation: PV/T = PV/T. We can rearrange the equation to solve for the final volume, V2, which is what we are looking for. The equation becomes V2 = V1 * (P2 * T1) / (P1 * T2), where V1 is the initial volume, P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.

Plugging in the given values, we have V2 = 31,000 L * (658 mmHg * 295 K) / (755 mmHg * 265 K). Simplifying this equation, we find that V2 is approximately 36,006 L. Therefore, the volume of the balloon at the given conditions is approximately 36,000 L.