Question

A gas is contained in a cylinder with a volume of 2.5 L at a temperature of 31.4oC and a pressure of 700.4 torr. The gas is then compressed to a volume of 0.20 L, and the temperature is raised to 663.3oC. What is the new pressure of the gas? Express your answer in atmospheres (atm).

Answer 1

We can use the combined gas law to solve for the new pressure:

(P1 x V1) / (T1) = (P2 x V2) / (T2)

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

Plugging in the given values:

P1 = 700.4 torr

V1 = 2.5 L

T1 = 31.4 + 273.15 = 304.55 K

V2 = 0.20 L

T2 = 663.3 + 273.15 = 936.45 K

(P1 x V1) / (T1) = (P2 x V2) / (T2)

(700.4 torr x 2.5 L) / (304.55 K) = (P2 x 0.20 L) / (936.45 K)

Simplifying:

P2 = (700.4 torr x 2.5 L x 936.45 K) / (304.55 K x 0.20 L)

= 43,330.0 torr

Converting to atmospheres:

P2 = 43,330.0 torr / 760 torr/atm

= 57.0 atm

Therefore, the new pressure of the gas is 57.0 atm.