Question

A gas‑filled weather balloon has a volume of 50.0 L at ground level, where the pressure is 759 mmHg and the temperature is 22.3 ∘ C. After being released, the balloon rises to an altitude where the temperature is − 9.00 ∘ C and the pressure is 0.0701 atm. What is the weather balloon's volume at the higher altitude?

Answer 1

Answer: The volume of balloon at higher altitude is 631.3 L

Explanation:

To calculate the volume when temperature and pressure has changed, we use the equation given by combined gas law. The equation follows:

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1,V_1\text{ and }T_1$ are the initial pressure, volume and temperature of the gas

$P_2,V_2\text{ and }T_2$ are the final pressure, volume and temperature of the gas

We are given:

Conversion factor:  1 atm = 760 mmHg

$P_1=759mmHg=0.99atm\\V_1=50.0L\\T_1=22.3^oC=[273+22.3]K=295.3K\\P_2=0.0701atm\\V_2=?L\\T_2=-9.00^oC=[273-9]=264K$

Putting values in above equation, we get:

$\frac{0.99atm\times 50.0L}{295.3K}=\frac{0.0701atm\times V_2}{264K}\\\\V_2=\frac{0.99\times 50.0\times 264}{0.0701\times 295.3}=631.3L$

Hence, the volume of balloon at higher altitude is 631.3 L