Gases are highly compressible and occupy the full volume of their containers. When a gas is subjected to pressure, its volume decreases. Gases always form

• Gases are highly compressible and occupy the full volume of their containers.

• When a gas is subjected to pressure, its volume decreases.

• Gases always form homogeneous mixtures with other gases.

• Gases only occupy about 0.1 % of the volume of their containers.

Characteristics of GasesCharacteristics of Gases

• Pressure is the force acting on an object per unit area:

• SI unit of force = Newton (N) = kg*m/s2

• SI unit of area = m2

• F/A = N/m2 = Pascal (Pa)• Other common units: torr (mm Hg); atm, bar. • Units: 1 atm = 760 mmHg = 760 torr = 1.01325 105 Pa

= 101.325 kPa = 1.01325 bar.

PressurePressure

AF

P

PressurePressure

Atmospheric Pressure

• Atmospheric pressure is measured with a barometer.• If a tube is inserted into a container of mercury open to

the atmosphere, the mercury will rise 760 mm up the tube.

PressurePressure

• The pressures of gases not open to the atmosphere could be measured in liquid manometers.

• Nowadays other pressure sensitive devices (solid state) are more popular: capacitance manometeres, thermal gauges, etc.

PressurePressure

Kinetic Molecular TheoryKinetic Molecular Theory

• Magnitude of pressure given by how often and how hard the molecules strike.

• Gas molecules have an average kinetic energy.

• Each molecule has a different energy.

• Theory developed to explain behavior of gases.• Theory of molecules in motion.• Assumptions:

– Gases consist of a large number of molecules in constant random motion.

– Volume of individual molecules negligible compared to volume of container.

– Intermolecular forces (forces between gas molecules) negligible.


• Assumptions:– Energy can be transferred between molecules, but total kinetic

energy is constant at constant temperature.

– Average kinetic energy of molecules is proportional to temperature.

• Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level.

• Pressure of a gas results from the number of collisions per unit time on the walls of container.


• As kinetic energy increases, the velocity of the gas molecules increases.

• Root mean square speed, u, is the speed of a gas molecule having average kinetic energy.

• Average kinetic energy, , is related to root mean square speed:


221 mu=

•There is a spread of individual energies of gas molecules in any sample of gas.

•As the temperature increases, the average kinetic energy of the gas molecules increases.

Application to Gas Laws• As volume increases at constant temperature, the average

kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases.

• If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases.


Molecular Effusion and Diffusion• As kinetic energy increases, the velocity of the gas

molecules increases.• Average kinetic energy of a gas is related to its mass• Consider two gases at the same temperature: the lighter

gas has a higher rms than the heavier gas.


M

RT3=u

Molecular Effusion and Diffusion• The lower the molar mass, M, the higher the rms.



Graham’s Law of Effusion• As kinetic energy increases,

the velocity of the gas molecules increases.

• Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion).

• The rate of effusion can be quantified.

Graham’s Law of Effusion

• Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by:

• Only those molecules that hit the small hole will escape through it.

• Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole.


1

2

2

1

M

M=

r

r

Diffusion and Mean Free Path

• Diffusion of a gas is the spread of the gas through space.• Diffusion is faster for light gas molecules.• Diffusion is significantly slower than rms speed (consider

someone opening a perfume bottle: it takes while to detect the odor but rms speed at 25C is about 1150 mi/hr).

• Diffusion is slowed by gas molecules colliding with each other.


Boyle’s Law

• Boyle’s Law: the volume of a fixed quantity of gas is inversely proportional to its pressure.

• Example: Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas.

The Gas LawsThe Gas Laws

Boyle’s Law

PV

1constant

constantPV

Charles’s Law

• Charles’s Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases.


TV constant

constantTV

Avogadro’s Law• at a given temperature and pressure, the volumes of gases

which react are ratios of small whole numbers.


Avogadro’s Law• Avogadro’s Hypothesis: equal volumes of gas at the

same temperature and pressure will contain the same number of molecules.

• Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas.

nV constant

•22.4 L of any gas at 0C contain 6.02 1023 gas molecules or 1 mol of a gas at 0C will occupy 22.4 L.

• We can combine these into a general gas law:

The Ideal Gas EquationThe Ideal Gas Equation

), (constant 1

TnP

V

), (constant PnTV

),(constant TPnV

• Boyle’s Law:

• Charles’s Law:

• Avogadro’s Law:

PnT

V

• If R is the constant of proportionality (called the gas constant), then

• The ideal gas equation is:

• R = 0.08206 L·atm/mol·K = 8.314 J/mol·K


PnT

RV

nRTPV

• We define STP (standard temperature and pressure) = 0C, 273.15 K, 1 atm.

• Volume of 1 mol of gas at STP is:


L 41.22

atm 000.1K 15.273KL·atm/mol· 0.08206mol 1

PnRT

V

nRTPV

Relating the Ideal-Gas Equation and the Gas Laws

• In general, if we have a gas under two sets of conditions, then

22

22

11

11TnVP

TnVP

Gas Densities and Molar Mass• Density has units of mass over volume. • Rearranging the ideal-gas equation with the molar mass

we get

Other derivations of the Other derivations of the Ideal-Gas EquationIdeal-Gas Equation

RT

MP=d=

V

MnRT

P=

V

n

nRT=PV

• Since gas molecules are so far apart, we can assume they behave independently.

• Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component:

• Each gas obeys the ideal gas equation:

Partial Pressures: Gas Partial Pressures: Gas MixturesMixtures

321total PPPP

VRT

nP ii

• Combing the equations

Mole Fractions

• Let ni be the number of moles of gas i exerting a partial pressure Pi, then

where i is the mole fraction (ni/nt).

Gas Mixtures and Partial Gas Mixtures and Partial PressuresPressures

VRT

nnnP 321total

totalPP ii

• From the ideal gas equation, we have

• For 1 mol of gas, PV/RT = 1 for all temperatures.• As temperature increases, the gases behave more ideally.• The assumptions in kinetic molecular theory show where

ideal gas behavior breaks down:– the molecules of a gas have finite volume;

– molecules of a gas do attract each other.

Real Gases: Deviations Real Gases: Deviations from Ideal Behaviorfrom Ideal Behavior

nRTPV

• As the pressure on a gas increases, the molecules are forced closer together.

• As the molecules get closer together, the volume of the container gets smaller.

• The smaller the container, the more space the gas molecules begin to occupy.

• Therefore, the higher the pressure, the less the gas resembles an ideal gas.


• As the gas molecules get closer together, the smaller the intermolecular distance.


• The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules.

• Therefore, the less the gas resembles and ideal gas.• As temperature increases, the gas molecules move faster

and further apart.• Also, higher temperatures mean more energy available to

break intermolecular forces.


•The higher the temperature, the more ideal the gas.

The van der Waals Equation• We add two terms to the ideal gas equation one to correct

for volume of molecules and the other to correct for intermolecular attractions

• The correction terms generate the van der Waals equation:

where a and b are empirical constants.


2

2

V

annbV

nRTP

The van der Waals Equation

• General form of the van der Waals equation:


2

2

V

annbV

nRTP

nRTnbVV

anP

2

2

Corrects for molecular volume

Corrects for molecular attraction

Explaining Vapor Pressure on the Molecular Level

• Some of the molecules on the surface of a liquid have enough energy to escape the attraction of the bulk liquid.

• These molecules move into the gas phase.• As the number of molecules in the gas phase increases,

some of the gas phase molecules strike the surface and return to the liquid.

• After some time the pressure of the gas will be constant at the vapor pressure.

Vapor PressureVapor Pressure

Explaining Vapor Pressure on the Molecular Level

Volatility, Vapor Pressure, and Temperature

•The higher the temperature, the higher the average kinetic energy, the faster the liquid evaporates.

•Liquids boil when the external pressure equals the vapor pressure.

•Temperature of boiling point increases as pressure increases.

Prentice Hall © 2003David Cedeno © 2003

Pressure Effects

Factors Affecting Factors Affecting SolubilitySolubility


Pressure Effects• The higher the pressure, the more molecules of gas are

close to the solvent and the greater the chance of a gas molecule striking the surface and entering the solution.– Therefore, the higher the pressure, the greater the solubility.

– The lower the pressure, the fewer molecules of gas are close to the solvent and the lower the solubility.

• If Sg is the solubility of a gas, k is a constant, and Pg is the partial pressure of a gas, then Henry’s Law gives:


gg kPS


Pressure Effects• Carbonated beverages are bottled with a partial pressure

of CO2 > 1 atm.

• As the bottle is opened, the partial pressure of CO2 decreases and the solubility of CO2 decreases.

• Therefore, bubbles of CO2 escape from solution.



Mass Percentage, ppm, and ppb

Mole Fraction, Molarity, and Molality• Recall mass can be converted to moles using the molar

mass.

Ways of Expressing Ways of Expressing ConcentrationConcentration

910solution of mass total

solutionin component of masscomponent of ppb

solution of moles totalsolutionin component of moles

component offraction Mole

solution of literssolute moles

Molarity


Mole Fraction, Molarity, and Molality• We define

• Converting between molarity (M) and molality (m) requires density.

Ways of Expressing Ways of Expressing ConcentrationConcentration

solvent of kgsolute moles

Molality, m


• Colligative properties depend on quantity of solute molecules. (E.g. freezing point depression and melting point elevation.)

Lowering Vapor Pressure• Non-volatile solvents reduce the ability of the surface

solvent molecules to escape the liquid.• Therefore, vapor pressure is lowered.• The amount of vapor pressure lowering depends on the

amount of solute.

Colligative PropertiesColligative Properties


Lowering Vapor Pressure



Lowering Vapor Pressure

• Raoult’s Law: PA is the vapor pressure with solute, PA is the vapor pressure without solvent, and A is the mole fraction of A, then

• Recall Dalton’s Law:


AAA PP

totalPP AA


Lowering Vapor Pressure• Ideal solution: one that obeys Raoult’s law.• Raoult’s law breaks down when the solvent-solvent and

solute-solute intermolecular forces are greater than solute-solvent intermolecular forces.

Boiling-Point Elevation• Goal: interpret the phase diagram for a solution.• Non-volatile solute lowers the vapor pressure.• Therefore the triple point - critical point curve is lowered.




Boiling-Point Elevation• At 1 atm (normal boiling point of pure liquid) there is a

lower vapor pressure of the solution. Therefore, a higher temperature is required to teach a vapor pressure of 1 atm for the solution (Tb).

• Molal boiling-point-elevation constant, Kb, expresses how much Tb changes with molality, m:


mKT bb


Freezing Point Depression• At 1 atm (normal boiling point of pure liquid) there is no

depression by definition• When a solution freezes, almost pure solvent is formed

first.– Therefore, the sublimation curve for the pure solvent is the

same as for the solution.

– Therefore, the triple point occurs at a lower temperature because of the lower vapor pressure for the solution.



Freezing Point Depression• The melting-point (freezing-point) curve is a vertical line

from the triple point.

• The solution freezes at a lower temperature (Tf) than the pure solvent.

• Decrease in freezing point (Tf) is directly proportional to molality (Kf is the molal freezing-point-depression constant):


mKT ff


Freezing Point Depression


Documents

Gases are highly compressible and occupy the full volume of their containers. When a gas is subjected to pressure, its volume decreases. Gases always form