You have a balloon filled with air. It has a volume of 5.20 gallons at 28.5'C and 745 torr. What volume, in gallons, would the balloon have at –25'C and 250 torr?
For a given number of moles of a gas (or gas mixture), it follows from the gas laws that,
`(PV)/T` = constant
In other words, `(P_1V_1)/T_1 = (P_2V_2)/T_2` ----- (i)
Here, assuming the gas mixture inside the balloon behaving ideally, `P_1` = 745 Torr.
`V_1` = 5.20 gallons
`T_1` = (273+28.5) = 301.5 K
`P_2` = 250 Torr.
`T_2` = (273-25) = 248 K
`V_2` has to be found out.
Putting the values in equation (i), we get
`(745*5.20)/301.5 = (250*V_2)/248`
`rArr V_2 = (745*5.20*248)/(250*301.5)`
= `12.7463` gallons
= `12.75` gallons (approximately).
Therefore, the balloon would have a volume of 12.75 gallons at -25°C and 250 Torr.