A 22.4-L sealed chamber at 273 K is filled with air at a pressure of 1.00 atm. A solid state chemical reaction in the chamber adds 1.25 mol hydrogen gas. The temperature of the chamber must be decreased to ________ to maintain the pressure at 1.00 atm.

Question

Quizplus · Accepted Answer

The initial conditions are a volume of 22.4 L, a temperature of 273 K, and a pressure of 1.00 atm. The addition of 1.25 mol of hydrogen gas increases the amount of gas in the chamber. To maintain the pressure at 1.00 atm while the amount of gas increases, the temperature must decrease. Using the ideal gas law (PV=nRT) and assuming the volume and pressure remain constant, the temperature must decrease proportionally to the increase in the amount of gas. Initially, the chamber contains 1 mol of gas (since 22.4 L at 273 K and 1 atm is the molar volume of an ideal gas). Adding 1.25 mol of hydrogen increases the total moles of gas to 2.25 mol. To maintain the same pressure, the temperature must decrease in the same ratio as the initial conditions to the final conditions, which is 273 K * (1 mol / 2.25 mol) = 121 K.

A 224-L Sealed Chamber at 273 K Is Filled with Air