A balloon occupies a volume of 352 cm3 at 615 Torr and 19 oC. If the pressure is changed to 410 Torr, what temperature must the gas in the balloon have to occupy the same volume?
(P1/T1) = (P2/T2)
P1 = 615 torr
T1 = 19 C (change to kelvin)
P2 = 410 torr
Tw = ?
To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, initial volume, and initial temperature of a gas to the final pressure, final volume, and final temperature of the gas is constant at constant moles of gas.
The formula for the combined gas law is:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
Given values:
P1 = 615 Torr
V1 = 352 cm3
T1 = 19 oC
P2 = 410 Torr
V2 = 352 cm3 (same volume as before)
We can rearrange the formula to solve for T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
Substituting the given values into the formula:
T2 = (410 Torr * 352 cm3 * 19 oC) / (615 Torr * 352 cm3)
Canceling out the units:
T2 = (410 * 19) / 615 oC
T2 ≈ 12.64 oC
Therefore, the gas in the balloon must have a temperature of approximately 12.64 oC to occupy the same volume when the pressure is changed to 410 Torr.