Combined Gas Law

The Combined Gas Law integrates the Boyle's and Charles' Law as one. This gives the relationship between temperature, pressure and volume considering the amount of gas in held constant.

It states that "for a given mass of gas, the volume is inversely proportional to the pressure and directly proportional to its absolute temperature".

Derived from Boyle's law:

P1V1 = P2V2

and Charles' law:

V1 = V2

T1 T2

will give us the Cobined Gas Law Equation:

P1V1 = P2V2

T1 T2

Sample Problem #1:

A gas occupies a volume of 3 liters at 50 degrees Celcius and 1.50 atm. Compute its volume at 25 degrees C and 1 atmosphere.

Given:

P1 = 1.50atm

V1 = 3 L

T1 = 50ºC + 273 = 323K

P2 = 1 atm

V2 = x

T2 = 25ºC + 273 = 298K

Solution:

P1V1 = P2V2
T1 T2

(1.50atm)(3L) = (1atm)V2

323K 298K

V2 = (1.50atm)(3L)(298K)

(323K)(1atm)

V2 = 4.15 liters

Sample Problem #2:

A quantity of gas exerts a pressure of 2.4atm when its volume is 4.0L at 40ºC. Calculate the pressure exerted by the same gas if the temperature is raised to 50ºC and the volume is reduced to 1.5 liters.

Given:

P1 = 2.4 atm

V1 = 4.0 L

T1 = 40ºC + 273 = 313K

P2 = ?

V2 = 1.5 L

T2 = 50ºC + 273 = 323K

Solution:

P1V1 = P2V2

T1 T2
(2.4 atm)(4.0 L) = P2 (1.5 L)
313K 323K
P2 = (2.4 atm)(4.0L)(323K)
(313K)(1.5 L)
P2 = 6.60 atm

STP = Standard Temperature and Pressure

These are standard sets of conditions for experimental measurements to allow comparisons between sets of data. These measurements are usually that of the International Union of Pure ans Applied Chemistry (IUPAC).

Standard Temperature = 25ºC

Standard Pressure = 1 atm

Exercises:

1. A gas sample occupies a volume of 20m3at 40ºC and at a pressure of 1.60 atm. What volume will it occupy at STP?
2. A certain amount of gas has a volume of 85cm3 at a temperature of 15ºC and a pressure of 800 torr. Calculate its temperature, in Kelvin, if the volume is increased to 120cm3 annd the pressure is changed to 700 torr.
3. A gas has a volume of 38 Liters at 10ºC and a pressure of 1.24atm. At what pressure will its volume be 50 Liters if the temperature is increased to 25ºC?