Question

A gas is contained in a cylinder with a volume of 2.9 L at a temperature of 32.7oC and a pressure of 645.3 torr. The gas is then compressed to a volume of 0.23 L, and the temperature is raised to 894.7oC. what is the new pressure of gas (in atm)

Answer 1

Answer: 41 atm

Step-by-step explanation:

Given that:

Original Volume of gas V1 = 2.9L

Temperature T1 = 32.7°C

Convert Celsius to Kelvin

(32.7°C + 273 = 305.7K)

Pressure P1 = 645.3 torr

New Volume V2 = 0.23 L

New temperature T2 = 894.7°C

Convert Celsius to Kelvin

(894.7°C + 273 = 1167.7K)

New pressure = ?

Then, apply the combined gas equation

(P1V1)/T1 = (P2V2)/T2

(645.3 torr x 2.9L)/305.7K = (P2 x 0.23L)/1167.7K

1871.37 / 305.7 = 0.23P2 / 1167.7

To get P2, Cross multiply

1871.37 x 1167.7 = 305.7 x 0.23P2

2185198.749 = 70.311P2

Divide both sides by 70.311

2185198.749/70.311 = 70.311P2/70.311

31079.045 torr = P2

Now, convert pressure in torr to atmosphere

Since 760 torr = 1 atm

31079.045 torr = Z

cross multiply

760 torr x Z = 31079.045 torr x 1 atm

Z = 31079.045 torr / 760 torr

Z = 40.89 atm (Round to the nearest whole number as 41 atm)

Thus, new pressure of gas is 41 atm