Question

If the balloon described in Question 10.24 is released into the air and rises to an altitude of 10,000 ft where the atmospheric pressure is 523 torr and the temperature is 7.50ºC, then what is its new volume, in L?

Answer 1

The new volume will be 33.5 L.

Explanation:

The kinetic theory of gases confirm that the volume occupied by gas molecules will be directly proportional to the temperature of the molecules and inversely proportional to the pressure of the molecules. We can consider the moles to be n = 1. Then, the equation for the gases will be

PV = nRT

Here, P is the pressure, V is the volume, R is the gas constant and T is the temperature.

So, P = 523 Torr, T = 7.50 °C = 7.50+273.15 = 280.65 K and the gas constant R = 62.363 Torr L mol⁻¹K⁻¹.

$523*V = 1 * 62.363*280.65 \\\\V = 33.5 L$

Thus, the new volume will be 33.5 L.