# A gas occupies a volume of 200. milliliters at a pressure of 380. torr and a temperature of 298 K. At what temperature will the gas occupy a volume of 250. milliliters and have a pressure of 760....

A gas occupies a volume of 200. milliliters at a pressure of 380. torr and a temperature of 298 K. At what temperature will the gas occupy a volume of 250. milliliters and have a pressure of 760. torr? oC

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### 1 Answer

This problem can be solved using the combined gas law,

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

where P is pressure, V is volume, T is Kelvin temperature and the subscripts 1 and 2 denote initial and final conditions.

Rearranging, we get

`T_2 = (P_2V_2T_1)/(P_1V_1)`

T2 = (760 torr)(250 ml)(298K)/(380 torr)(200 ml) = **745 K**

The combined gas law comes from the Ideal Gas Law, PV=nRT.

PV/nT = a constant (R), so P1V1/n1T1 = P2V2/n2T2. We can leave out n, the number moles, if it's constant. This leaves us with the combined gas law, a combination of Boyle's and Charles' laws.

Boyle's law says that at constant temperature the pressure and volume of a gas are inversely proportional: P1V1 = P2V2

Charles' law says that at constant pressure the temperature and volume of a gas are directly proportional: V1/T1 = V2/T2