**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:**

is the**P**_{t}**total pressure**of a sample which contains a mixture of gases, etc. are the**P**_{1}, P_{2}, P_{3}**partial pressures**of the gases in the mixture

**P _{t}**

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,
**n**= the number of moles of component #1 in the sample_{1} - The pressure due to component #1 would be:

- For the second component,
**n**= the number of moles of component #2 in the sample_{2} - The pressure due to component #2 would be:

And so on for all components. Therefore, the total pressure **P _{t}** will be equal to:

- All components will share the same temperature,
**T**, and volume**V**, therefore, the total pressure P_{t}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 O_{2})(1 mol/32 g) = 0.313 mol O_{2}

(10 g CH_{4})(1 mol/16 g) = 0.616 mol CH_{4}

V=10 L

T=(273+25K)=298K

*P _{t} = P_{O2} + P_{CH4}* = 0.702

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 (n
_{1}/n_{t}) is termed theof the component gas__mole fraction__ - The mole fraction (
) 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*X*

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 CO_{2}, 20 mol percent O_{2} and 78 mol percent N_{2}. 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 O_{2} are needed?

P_{O2} = 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)

*1996 Michael Blaber*