Question

A 3.5 liter sample at 20 ºC and a pressure of 650 mmHg is allowed to expand to a volume of 8570 mL. The final pressure of the gas is 0.75 atm. What is the final temperature in ºC?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can use the combined gas law, which states that for a given amount of gas at constant mass, the ratio of the pressure and volume is directly proportional to the ratio of the temperature:

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

where:
P1 = initial pressure = 650 mmHg
V1 = initial volume = 3.5 L = 3500 mL
T1 = initial temperature = 20 ºC + 273.15 = 293.15 K
P2 = final pressure = 0.75 atm
V2 = final volume = 8570 mL
T2 = final temperature = ? ºC

Plugging in the values:

(650 mmHg)(3500 mL) / 293.15 K = (0.75 atm)(8570 mL) / T2

Solving for T2:

(650)(3500) = (0.75)(8570)(293.15)
T2 = (0.75)(8570)(293.15) / (650)(3500)
T2 = 295.59 K

Converting back to ºC:

T2 = 295.59 K - 273.15 = 22.44 ºC

Therefore, the final temperature of the gas is approximately 22.44 ºC.