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

620.71 L the final volume of the balloon.

Step-by-step 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=(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* 10^(-3) atm`

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

Moles of gases = n

`n=(P_2V_2)/(RT_2)`...[2]

[1] = [2]

`(P_2V_2)/(RT_2)=(P_1V_1)/(RT_1)`

`V_2=(P_1V_1* T_2)/(T_1* P_2)`

`V_2=(1.29 atm * 3.50 L* 228.15 K)/(5.70* 10^(-3) atm* 291.15 K)=620.71 L`

620.71 L the final volume of the balloon.