Question

If the initial temperature of an ideal gas at 2.250 atm

is 62.00 ∘C,
what final temperature would cause the pressure to be reduced to 1.700 atm?

Answer 1

To determine the final temperature of the ideal gas, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas.

P1V1/T1 = P2V2/T2

where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.

We can assume that the volume of the gas is constant, so V1 = V2.

Converting the initial conditions to SI units:

P1 = 2.250 atm * 101.325 kPa/atm = 228.04 kPa
T1 = 62.00 + 273.15 = 335.15 K

Converting the final conditions to SI units:

P2 = 1.700 atm * 101.325 kPa/atm = 172.24 kPa

Solving for T2:

P1/T1 = P2/T2
T2 = P2 * T1 / P1
T2 = 172.24 * 335.15 / 228.04
T2 = 252.4 K

Converting the final temperature to Celsius:

T2 = 252.4 - 273.15 = -20.8 °C

Therefore, the final temperature that would cause the pressure of the ideal gas to be reduced to 1.700 atm is -20.8 °C