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

Step-by-step explanation:

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

`(P_1V_1)/(T_1)=(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:

`(0.99atm* 50.0L)/(295.3K)=(0.0701atm* V_2)/(264K)\\\\V_2=(0.99* 50.0* 264)/(0.0701* 295.3)=631.3L`

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