Question

A gas-filled balloon having a volume of 1.00 L at 1.2 atm and 25°C is allowed to rise to the stratosphere (about 30 km above the surface of Earth), where the temperature and pressure are -23°C and 3.00 10-3 atm, respectively. Calculate the final volume of the balloon.

Answer 1

Answer: The final volume of the balloon is 335.6 L

Explanation:

To calculate the final volume of the balloon, we use the equation given by combined gas law:

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

where,

$P_1$ = Initial pressure = 1.2 atm

$P_2$ = Final pressure = $3.00\times 10^{-3}$ atm

$V_1$ = Initial volume = 1.00 L

$V_2$ = Final volume = ?

$T_1$ = Initial temperature = $25^oC=[25+273]=298K$

$T_2$ = Final temperature = $-23^oC=[-23+273]=250K$

Putting values in above equation, we get:

$\frac{1.2atm\times 1.00L}{298K}=\frac{3.00\times 10^{-3}atm\times V_2}{250K}\\\\V_2=\frac{1.2\times 1.00\times 250}{298\times 3.00\times 10^{-3}}\\\\V_2=335.6L$

Hence, the final volume of the balloon is 335.6 L