Question

A weather balloon is filled with 36.7 L helium at sea level where the pressure is 1.0 atm at 20.0°C. The balloon bursts after ascending until the pressure is 26.0 torr at -50.0°C. Determine the volume (in L) at which the balloon bursts.

A) 25.5 L
B) 29.8 L
C) 32.4 L
D) 36.7 L

Answer 1

The volume at which the balloon bursts is 32.4 L.

Step-by-step explanation:

To determine the volume at which the balloon bursts, we can use the ideal gas law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. We can use a ratio of the final pressure and temperature to the initial pressure and temperature to find the ratio of the final volume to the initial volume.

First, we need to convert the initial and final temperatures to Kelvin by adding 273.15 to each. We also need to convert the final pressure from torr to atm by dividing by 760.

Using the equation, we have (36.7 L) * (1.0 atm) = (V) * (26.0 torr)/(760 torr/atm) * (273.15 K + (-50.0°C))/(273.15 K + (20.0°C)).

Simplifying this equation, we find V = 32.4 L. Therefore, the volume at which the balloon bursts is 32.4 L.