Question

A high-altitude balloon is filled with 1.41×10^4 L of hydrogen at a temperature of 21°C and a pressure of 745torr . What is the volume of balloon at a height of 20 km, where the temperature is - 48'C and the pressure is
63.1 torr?​

Answer 1

Answer: $12.7\times 10^4L$

Explanation:

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

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

where,

$P_1$ = initial pressure of gas = 745 torr

$P_2$ = final pressure of gas = 63.1 torr

$V_1$ = initial volume of gas = $1.41\times 10^4L$

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $21^oC=273+21=294K$

$T_2$ = final temperature of gas = $-48^oC=273+(-48)=225K$

Now put all the given values in the above equation, we get the final pressure of gas.

$\frac{745\times 1.41\times 10^4L}{294K}=\frac{63.1\times V_2}{225K}$

$V_2=12.7\times 10^4L$

Therefore, the final volume of the gas will be $12.7\times 10^4L$