Question

A sample of gas is contained in a 245 mL flask at a temperature of 23.5°C. The gas pressure is 37.8 mm Hg. The gas is moved to a new flask, which is then immersed in ice water, and which has a volume of 54 mL. What is the pressure of the gas in the smaller flask at the new temperature?

Answer 1

We can use the combined gas law to solve this problem:

(P1V1/T1) = (P2V2/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.

We are given that the initial pressure is P1 = 37.8 mm Hg and the initial volume is V1 = 245 mL. The initial temperature is T1 = 23.5°C, which we need to convert to Kelvin by adding 273.15:

T1 = 23.5°C + 273.15 = 296.65 K

We are also given that the final volume is V2 = 54 mL, and the final temperature is the temperature of the ice water, which is 0°C or 273.15 K.

Now we can solve for the final pressure, P2:

(P1V1/T1) = (P2V2/T2)

P2 = (P1V1T2) / (V2T1)

P2 = (37.8 mm Hg * 245 mL * 273.15 K) / (54 mL * 296.65 K)

P2 = 24.4 mm Hg

Therefore, the pressure of the gas in the smaller flask at the new temperature is 24.4 mm Hg.