Ideal Gas law

The Ideal Gas law interrelates pressure, temperature, volume and number of moles of a gas sample. This law integrates the laws of Boyle, Charles and Avogadro.

Boyle's law : V ∞ 1/P
Charles' law: V ∞ T
Avogadro's law: V ∞ n

Combining these three laws will yield to a more general equation:

PV = nRT

where R is the gas constant:

R = 0.0821 L.atm / mol.K

Sample Problem:

What volume will1.27 moles of Helium gas occupy at STP?

Given:

P = 1 atm

V = ?

n = 1.27mol

R = 0.0821 L.atm / mol.K

T = 25 ºC + 273 = 298K

Solution:

PV = nRT

(1 atm)V = (1.27mol)(0.0821 L.atm/mol.K)(298K)

V = (1.27mol)(0.0821 L.atm/mol.K)(298K)

(1 atm)

V = 31.07 Liters

Exercises:

1. How many moles of gas are contained in a 50.0L cylinder at a pressure of 100.0atm and a temperature of 35.0ºC?
2. What would be the volume occupied by a 1mole gas at STP?

Gay-Lussac's Law

This relationship between pressure and temperature was studied by Joseph Louis Gay-Lussac, a French Chemist. This law states that pressure is directly proportional to the absolute temperature when volume and amount of gas is held constant.
This law is mathematically expressed as:

P1 = P2

T1 T2

Sample Problem:

A sample of gas at 3000mm Hg inside a steel tank is cooled from500ºC to 0ºC. What is the final pressure of the gas inside the steel taank?

Given:

P1 = 3000 mm Hg

T1 = 500ºC + 273 = 773K

P2 = ?

T2 = 0ºC + 273 = 273K

Solution:

P1 = P2
T1 T2

(3000 mm Hg) = P2

(773K) (273K)

P2 = (3000 mm Hg)(273K)

773K

P2 = 1,059.51 mm Hg

Exercises:

1. A gas sample has a pressure of 950 torr at 120ºC. What is the final pressure of the gas after the temperature is dropped to 10ºC?
2. Pressure of a gas in a 10.0L steel cylinder is 890torr at 56ºC. To what temperature should the gas be cooled in order to reduce the pressure to 760 torr?

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?