Gases

Gas Mixtures and Partial Pressures

Gas Mixtures and Partial Pressures

How do we deal with gases composed of a mixture of two or more different substances?

John Dalton (1766-1844) - (gave us Dalton's atomic theory)

The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone

The partial pressure of a gas:

• The pressure exerted by a particular component of a mixture of gases

Dalton's Law of Partial Pressures:

• Pt is the total pressure of a sample which contains a mixture of gases
• P1, P2, P3, etc. are the partial pressures of the gases in the mixture

Pt = P1 + P2 + P3 + ...

If each of the gases behaves independently of the others then we can apply the ideal gas law to each gas component in the sample:

• For the first component, n1 = the number of moles of component #1 in the sample
• The pressure due to component #1 would be:

• For the second component, n2 = the number of moles of component #2 in the sample
• The pressure due to component #2 would be:

And so on for all components. Therefore, the total pressure Pt will be equal to:

• All components will share the same temperature, T, and volume V, therefore, the total pressure Pt will be:

• Since the sum of the number of moles of each component gas equals the total number of moles of gas molecules in the sample:

At constant temperature and volume, the total pressure of a gas sample is determined by the total number of moles of gas present, whether this represents a single substance, or a mixture

Example

A gaseous mixture made from 10 g of oxygen and 5 g of methane is placed in a 10 L vessel at 25°C. What is the partial pressure of each gas, and what is the total pressure in the vessel?

(10 g O2)(1 mol/32 g) = 0.313 mol O2

(10 g CH4)(1 mol/16 g) = 0.616 mol CH4

V=10 L

T=(273+25K)=298K

Pt = PO2 + PCH4 = 0.702 atm + 1.403 atm = 2.105 atm

Partial Pressures and Mole Fractions

The ratio of the partial pressure of one component of a gas to the total pressure is:

thus...

• The value (n1/nt) is termed the mole fraction of the component gas
• The mole fraction (X) of a component gas is a dimensionless number, which expresses the ratio of the number of moles of one component to the total number of moles of gas in the sample

The ratio of the partial pressure to the total pressure is equal to the mole fraction of the component gas

• The above equation can be rearranged to give:

The partial pressure of a gas is equal to its mole fraction times the total pressure

Example

a) A synthetic atmosphere is created by blending 2 mol percent CO2, 20 mol percent O2 and 78 mol percent N2. If the total pressure is 750 torr, calculate the partial pressure of the oxygen component.

Mole fraction of oxygen is (20/100) = 0.2

Therefore, partial pressure of oxygen = (0.2)(750 torr) = 150 torr

b) If 25 liters of this atmosphere, at 37°C, have to be produced, how many moles of O2 are needed?

PO2 = 150 torr (1 atm/760 torr) = 0.197 atm

V = 25 L

T = (273+37K)=310K

R=0.0821 L atm/mol K

PV = nRT

n = (PV)/(RT) = (0.197 atm * 25 L)/(0.0821 L atm/mol K * 310K)

n = 0.194 mol

1996 Michael Blaber