A helium weather balloon, when released, has a volume of 10.0 L at 27.0 ° C and a pressure of 663 mm Hg. What volume, in liters, will the balloon occupy at an altitude where the pressure is 96 mm Hg and the temperature is - 30.0 ° C?

Question

Quizplus · Accepted Answer

To find the final volume of the helium balloon, we can use the combined gas law, which is $P_1V_1/T_1 = P_2V_2/T_2$, where $P$ is pressure, $V$ is volume, and $T$ is temperature in Kelvin. First, convert all temperatures to Kelvin by adding 273.15. The initial temperature is $27.0 °C + 273.15 = 300.15 K$, and the final temperature is $-30.0 °C + 273.15 = 243.15 K$. Then, solve for $V_2$: $V_2 = \frac{P_1V_1T_2}{P_2T_1}$. Substituting the given values, $V_2 = \frac{663 \, mmHg \times 10.0 \, L \times 243.15 \, K}{96 \, mmHg \times 300.15 \, K}$. Calculating this gives $V_2 \approx 55.9 \, L$, which is option D.

A Helium Weather Balloon, When Released, Has a Volume of 10.0