Question

A weather balloon is infated to a volume of 26.5 L at a pressure of 745 mmHg and a temperature of 23.3 °C. The balloon rises in the atmosphere to an altitude where the pressure is 360. mmHg and the temperature is -13.7°C Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Answer 1

Answer: 48 Liters.

Step-by-step explanation:

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

The combined gas equation is,

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

where,

`P_1` = initial pressure of gas = 745 mmHg

`P_2` = final pressure of gas =360 mmHg

`V_1` = initial volume of gas = 26.5 L

`V_2` = final volume of gas = ?

`T_1` = initial temperature of gas =
`23.3^oC=(273+23.3)K=296.3K`

`T_2` = final temperature of gas =
`-13.7^oC=273+(-13.7)K=259.3K`

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

`(745mmHg* 26.5L)/(296.3K)=(360mmhg* V_2)/(259.3K)`

`V_2=48L`

Therefore, the volume of the gas will be 48 Liters.