Gas Mixtures--Partial Pressure

• So far: pure gases

• Many gases are actually mixtures of two or more gases:– air: O2, N2 , H2O, etc

• How do mixtures of gases behave?

Gas Mixtures--Partial Pressure

P= 8 psi

N2 (g)

P= 6 psi

O2 (g)

P= 9 psi

CO2 (g)

Gas Mixtures--Partial PressureWhat happens when you put all three samples of gas together into one container (the same size container as each was in alone)?

•The gases form a homogeneous mixture.

•The pressure in the container increases, V and T stay the same

– How do you know what the new pressure will be?

P

Gas Mixtures--Partial Pressure

• Each gas in a mixture behaves independently of the other gases present.– Each gas exerts its own pressure on the

container.• PO = pressure exerted by O2

• PN = pressure exerted by N2

• PCO = pressure exerted by CO2

2

2

2

Gas Mixtures--Partial Pressure

• Partial pressure: the pressure exerted by a particular gas present in a mixture

• Dalton's Law of Partial Pressure: The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.

Ptotal = P1 + P2 + P3 + ………

Gas Mixtures--Partial Pressure

• Ptotal = PO + PN + PCO

• So for this example:

Ptotal = 6 psi + 8 psi + 9 psi

= 23 psi

2 2 2

Partial Pressure

• In other words, at constant T and V,

– Ptotal depends only on the total number of moles of gas present

– Ptotal is independent of the type (or types) of gases present.

Partial Pressure-Mole Fraction

• When describing a mixture of gases, it is useful to know the relative amount of each type of gas.

• Mole fraction (X): a dimensionless number that expresses the ratio of the number of moles of one component compared to the total number of moles in a mixture.

Mole Fraction

• If a gas mixture contains 5.0 mol O2 (g), 3.0 mol H2O (g), and 12.0 mol N2 (g),

XO=

• On the exam, you must be able to calculate the mole fraction of each component of a gas mixture.

nO2

nt=

5.0 mol

20.0 mol= 0.25

Partial Pressure

• The partial pressure of a gas in a mixture can be found:

PA = XA Ptotal

where PA = partial pressure of gas A

XA = mole fraction of gas A

Ptotal = total pressure of mixture

Partial Pressure Calculation

A mixture of gases contains 0.51 mol N2, 0.28 mol H2, and 0.52 mol NH3. If the total pressure of the mixture is 2.35 atm, what is the partial pressure of H2?

PH2 = XH2

Ptotal

XH2=

0.28 mol0.28 mol + 0.51 mol + 0.52 mol

= 0.21

PH2 = 0.21 x 2.35 = 0.50 atm

In the lab

• Chemical reaction producing gas

eg: NH4NO2 (s) N2(g) + H2O (l)

Determine number of moles (amount) of gas collected?

Partial Pressures

• When one collects a gas over water, there is water vapor mixed in with the gas. Ptotal = Pgas + PH2O

• To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

• Table p1111 shows water vapor pressure (T dep)

Gas Mixtures--Partial Pressure

What is the partial pressure of O2 in a sample of gas collected over water if the total pressure was 745 torr at 25oC?

Given: Ptotal = 745 torr

T = 25oC

Find: Poxygen

Ptotal = PO2 + PH2O

Must find Pwater

first.

Partial Pressure

Ptotal = Poxygen + Pwater

To find Pwater, look in Appendix (p 1111):

At 25C, Pwater = 23.76 torr

So:

745 torr = PO2 + 23.76 torr

PO2 = 745 torr - 23.76 torr = 721 torr

What is happening?

Effusion

Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Diffusion

Diffusion is the spread of one substance throughout a space or throughout a second substance.

Molecular Effusion & Diffusion

• The rate of effusion (r) of a gas is inversely proportional to the square root of its molar mass, M.

rA = 1MA

Molecular Effusion & Diffusion

• What does this all mean?

– “Lighter” molecules will escape faster than “heavier” molecules.

– If you want your balloons to stay inflated longer, use N2 instead of He because N2 has a higher molar mass.

Real Gases

• Real gases do not completely follow the ideal gas law.

• In kinetic molecular theory, the following assumptions are made:– gas molecules occupy no space– gas molecules have no attraction for each

other

Real Gases

• Neither assumption is correct.

– Real gas molecules have a finite volume.

– Real gas molecules do attract each other.

Real Gases

• The greatest deviation from ideal gas behavior occurs at:high pressure

higher density of gas molecules– Molecules are closer together so:

» finite volume of gas molecules more important» attraction between molecules more important

Real Gases

In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

Curves for 1 mol of gas

Real Gases

– Low temperatureAttractive forces between molecules becomes more

important.

– Average kinetic energy decreases.

– Gas molecules have less energy to overcome attractive forces.

Real Gases

Even the same gas (e.g. nitrogen) will show wildly different behavior under high pressure at different temperatures.