Question

A gas-filled balloon having a volume of 3.50 L at 1.20 atm and 18°C is allowed to rise to the stratosphere (about 30 km above the surface of the Earth), where the temperature and pressure are −45°C and 5.70 × 10−3 atm, respectively. Calculate the final volume of the balloon.

Answer 1

Answer:

620.71 L the final volume of the balloon.

Explanation:

Initial volume of the gas in the balloon= $V_1=3.50 L$

Initial pressure of the gas in the balloon= $P_1=1.20 atm$

Initial temperature of the gas in the balloon= $T_1=18^oC =291.15 K$

Moles of gases = n

$n=\frac{P_1V_1}{RT_1}$...[1]

Final volume of the gas in the balloon = $V_2=3.50 L$

Final pressure of the gas in the balloon = $P_2=5.70\times 10^{-3} atm$

Final temperature of the gas in the balloon = $T_2=-45^oC =228.15 K$

Moles of gases = n

$n=\frac{P_2V_2}{RT_2}$...[2]

[1]  =  [2]

$\frac{P_2V_2}{RT_2}=\frac{P_1V_1}{RT_1}$

$V_2=\frac{P_1V_1\times T_2}{T_1\times P_2}$

$V_2=\frac{1.29 atm \times 3.50 L\times 228.15 K}{5.70\times 10^{-3} atm\times 291.15 K}=620.71 L$

620.71 L the final volume of the balloon.