Gases and their Gases and their PropertiesProperties

Goals:

1. Use the gas law equations.2. Apply the gas laws to stoichiometric

calculations.3. Describe the states of matter based on

kinetic-molecular theory.4. Recognize why real gases do not behave like

ideal gases.

THREE STATES OF MATTERTHREE STATES OF MATTER

General Properties of GasesGeneral Properties of Gases

• There is a lot of “free” space in a gas.

• Gases can be expanded __________________.

• Gases occupy containers uniformly and completely.

• Gases diffuse and mix ___________.

Properties of GasesProperties of Gases

Gas properties can be modeled using math. Model depends on—

• V =• T =• n = • P =

PressurePressure• Pressure – force per unit area (force

divided by the area over which the force is exerted). SI unit is the pascal (Pa)

Pressure =Force

Area

SI units – Pascal (Pa)

Newton (N)

Square meter (m2)1 Pa = 1 N/m2

Newton- the force that will give a 1-kg mass an acceleration of 1 meter per second (m/s).

BarometerBarometer• Barometer – device to measure atmospheric pressure.

Invented in 1643 by Evangelista Torricelli. It is based on a column filled with mercury (Hg).

• On average, at sea level, the column supported by the air pressure is 760 mm Hg high – 1 atmosphere (atm).

1 atm = ______ mm Hg = _____ Torr

Why Hg and not H2O?

Pressure UnitsPressure Units

1 atm = 760 mm Hg = 760 Torr

1 atm = ________Pa (pascal) = ______ kPa (kilopascal)

SI unit

Units used in weather reports

Units used by engineers

1 atm = 29.921 inHg (inches of mercury) = 1013.25 mbar (millibars)

1 atm = 14.696 lb/in2 or psi (pounds per square inch)

Gas LawsGas LawsGas law Equation Variables Constant(s)

Boyle’s law

Charles’s law

Avogadro’s law

Combined gas law

Ideal gas law

P- pressure T- temperature R- universal gas constantV- volume n- number of moles

Boyle’s Law: P-V Boyle’s Law: P-V relationshiprelationship

• Robert Boyle, 1662 : Boyle’s Law– For a given amount of gas at a constant

temperature, the volume of the gas varies inversely with its pressure.

V 1 / P

V = a / P

VP = a

a- proportionalityconstant

Boyle’s Law: P-V Boyle’s Law: P-V relationshiprelationship

V = a / P

VP = a

If V increases P must decrease, and viceversa.

P1

P2

V1 V2

• A gas is enclosed in a 10.1 L tank at 1208 mmHg. Which of the following is a reasonable value for the pressure when the gas is transferred to a 30.0 L tank?

400 mmHg 3600 mmHg

Boyle’s LawBoyle’s Law

A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is

reduced, its pressure goes up, and air is forced into the tire.

Boyle’s Law: P-V Boyle’s Law: P-V relationshiprelationship

• Any units can be used for P and V (same units used throughout the calculation).

• Same sample of a confined gas at constant T.

V1P1 = V2P2

• A sample of air occupies 73.3 mL at 98.7 atm and 0oC. What volume will the air occupy at 4.02 atm and 0oC?

Boyle’s LawBoyle’s Law

P 1 / V

V 1 / P

P 1 / VP = a / V

VP = aa- proportionality

constant = slope of the line

Charle’s Law: T-V Charle’s Law: T-V relationshiprelationship

• Jacques Charles, 1787 : Charles’s Law– For a given amount of gas at a constant pressure, the

volume of the gas varies directly with its temperature.– For each oC rise in T, V expands by 1/273 of its V at

0oC; for each oC drop in T, V contracts by 1/273 of its V at 0oC.

-273.15oC Is the absolute 0 in Kelvin scale

- Volume of a fixed amount of a gas at a constant P is directly proportional to its Kelvin T.

V TV = bT

V / T = bb - proportionalityconstant

V2

V1

T1 T2

Charle’s Law: T-V Charle’s Law: T-V relationshiprelationship

• If T increases, V must also increase; when T decreases, V must also decrease.

• For the same sample of trapped gas at a constant pressure.

• For all gas law calculations involving T, absolute T in kelvins must be used.

0 oC 40 oC

V1 V2

T1 T2

=

Charle’s Law: T-V Charle’s Law: T-V relationshiprelationship

• A sample of oxygen gas occupies a volume of 2.10 L at 25oC. What volume will this sample occupy at 150oC? (Assume no change in pressure.)

Charle’s LawCharle’s Law

Charle’s LawCharle’s Law

PracticePractice

• What effect will the following changes have on the V of a fixed amount of gas?a. an increase in P at constant Tb. a decrease in T at constant Pc. a decrease in P coupled with an increase in T

• What effect will the following changes have on the P of a fixed amount of gas?a. an increase in T at constant Vb. a decrease in V at constant Tc. an increase in T coupled with a decrease in V

Avogadro’s HypothesisAvogadro’s Hypothesis

• Avogadro’s Hypothesis – equal number of molecules of different gases compared at the same T and P occupy equal V.

• Avogadro’s Law – at fixed T and P, the V of a gas is directly proportional to the number of molecules of a gas or to the number of moles of gas, n.– If the number of moles of gas doubles, the volume doubles.– If the mass of a gas doubles, the volume doubles.

V n

V = cn

Avogadro’s HypothesisAvogadro’s Hypothesis

The gases in this experiment are all measured at the same T and P.

2 H2 H22(g) + O(g) + O22(g) (g) 2 H2 H22O(g)O(g)

Molar VolumeMolar Volume

• Molar Volume of a gas – is the volume occupied at STP by 1 mol of any gas and it is 22.4 L .

Standard conditions of T and P (STP):T = 0oC (273K)P = 1 atm (760 Torr)

1 mol gas = 22.4 L (at STP)

Molar VolumeMolar Volume

1 mol of N2 = 28 g N2, will occupy 22.4 L at STP.

1 mol of CO2 = 44 g CO2, will occupy 22.4 L at STP.

Calculate the volume occupied by 4.11 g of methane (CH4) gas at STP.

Strategy: Convert mass of gas to moles of gas and use the molar volume relationship as conversion factor to find out the volume at STP.

1 mol gas = 22.4 L (at STP)

PracticePractice

• Solve the Charle’s Law for T2

Students should be familiar rearranging gas laws equations and applying them

in problems.

Gas LawsGas LawsGas law Equation Variables Constant(s)

Boyle’s law P1V1 = P2V2 P, V n, T

Charles’s law V1 / T1 = V2 / T2 V, T n, P

Avogadro’s law V1 / n1 = V2 / n2 V, n P, T

Combined gas law

Ideal gas law

P- pressure T- temperature R- universal gas constantV- volume n- number of moles

Combined Gas LawCombined Gas Law

V proportional to 1/PV proportional to TV proportional to n

• Therefore, V prop. to nT/P• A fixed amount of gas under a

set of initial conditions is changed to a set of final conditions. V nT

P

PV = constantnT

V1 V2

T1 T2

=V1P1 = V2P2

V1P1 V2P2

T1 T2

=

PV = nRT

What volume will occupy a 5 mL bubble of air exhaled by a deep-sea diver at 1.8 atm and at 5oC when it reaches the surface of the sea, at 0.98 atm

and at 25oC?

Ideal Gas LawIdeal Gas Law

• For varying amounts of gas (number of moles, n).• Units: P in atmospheres (atm)

V in liters (L)T in kelvins (K)

• Universal gas constant, R

• Used to calculate any of the four quantities – P, V, n or T if the other three are known.

PV = nRT

R = 0.0821L atmmol K

How much NHow much N22 (in Kg) is req’d to fill a small room with a (in Kg) is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at

25 25 ooC?C?

Gas DensityGas Density

• Reported in g/L at STP.• If you know the density, you can calculate the

molar volume.

• From the molar volume of gas, you can calculate the density of the gas using the molar mass.

1 mol gas = 22.4 L (at STP)

Gas DensityGas Density

• Density is proportional to molecular mass.

Which balloon(s) is(are) filled with the higher density gas?

The density of air at 15 The density of air at 15 ooC and 1.00 C and 1.00 atm is 1.23 g/L. What is the molar atm is 1.23 g/L. What is the molar

mass of air?mass of air?

Dalton’s LawDalton’s Law• Dalton’s experimental observation – adding H2O

vapor to a certain pressure to dry air, the P exerted by the air would increase by an amount equal to the P of the water vapor.

• Dalton’s conclusion – each gas in a mixture of gases behaves independently, exerting its own pressure.

• Dalton’s Law – The total P of the mixture is equal to the sum of the partial pressures exerted by separate gases.

Ptotal = P1 + P2 + P3 + ….

Dalton’s LawDalton’s Law

Vapor PressureVapor Pressure• Vapor pressure – is the partial pressure exerted by

the molecules of a substance in the gas phase above the liquid phase of the substance.

• Vapor pressure is T dependent (increasing T, increase the vapor pressure).

For water: T (oC) Vapor pressure (mmHg) 0 5

10 9 20 18 30 32 40 55 50 93 60 149 70 234 80 355 90 526100 760

Oxygen is collected over water at 20Oxygen is collected over water at 20ooC. The total P C. The total P inside the collection jar is 740 mmHg. What is the inside the collection jar is 740 mmHg. What is the

pressure due to the oxygen alone?pressure due to the oxygen alone?

Partial Pressures and Partial Pressures and RespirationRespiration

• Exchange of gases (CO2 and O2) between:alveoli and blood capillaries; arteriole and extracellular fluid;extracellular fluid and cells occurs by diffusion.

• Gases go from higher partial pressure to lower partial pressure.

• Diffusion – the flow of a substance from a region of higher concentration to a region of lower concentration.

• CO2 is the trigger; if too high we take a breath, if too low, there is no breathing.

Gases and StoichiometryGases and Stoichiometry

2 H2O2(liq) ---> 2 H2O(g) + O2(g)

1.1 g of H2O2 decompose in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O?

2 H2O2(liq) ---> 2 H2O(g) + O2(g)Decompose 1.1 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O?

Kinetic-Molecular TheoryKinetic-Molecular Theory

Theory used to explain gas laws. KMT assumptions are

• Gases consist of _______________________________________________.

• P arises from _______________________.• No __________ or __________ forces between

molecules. Collisions elastic.• Volume of molecules is ____________.

Kinetic-Molecular TheoryKinetic-Molecular TheoryBecause we assume molecules are in

motion, they have a kinetic energy.

KE = (1/2)(mass)(speed)2

At the same T, all gases have the same average KE.

At the same T, all gases have the same average KE.

As T goes up for a gas, KE also As T goes up for a gas, KE also increases — and so does speed.increases — and so does speed.As T goes up for a gas, KE also As T goes up for a gas, KE also increases — and so does speed.increases — and so does speed.

Kinetic-Molecular TheoryKinetic-Molecular Theory

At the same T, all gases have the same average KE.As T goes up, KE also increases — and so does

speed.

Maxwell’s equationMaxwell’s equation

where u is the speed and M is the molar mass.– speed INCREASES with T– speed DECREASES with M

root mean square speed

2u M3RT

Speed’s DistributionSpeed’s Distribution

• Boltzmann plots• Named for Ludwig

Boltzmann doubted the existence of atoms.

• This played a role in his suicide in 1906.

Velocity of Gas MoleculesVelocity of Gas Molecules

Molecules of a given gas have a range of speeds.

Average velocitydecreases withincreasing mass.

Gas Diffusion and EffusionGas Diffusion and Effusion

DIFFUSION is the gradual mixing of molecules of different gases.

EFFUSION is the movement of molecules through a small hole into an empty container.

Gas EffusionGas Effusion

Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is

• proportional to T• inversely proportional to M.Therefore, He effuses more

rapidly than O2 at same T.

Graham’s LawGraham’s Law

• Rate of effusion is inversely proportional to its molar mass.– HCl and NH3 diffuse from

opposite ends of tube. – Gases meet to form NH4Cl

– HCl heavier than NH3

– Therefore, NH4Cl forms closer to HCl end of tube.

M of AM of B

Rate for B

Rate for A

Kinetic-Molecular TheoryKinetic-Molecular Theory Model used to explain de behavior of gases. Postulates:

1. All matter is composed of tiny, discrete particles called molecules (N2, Ar).

2. The molecules are in rapid, constant motion and move in straight lines (strike the walls of the container, exert pressure).

3. The molecules of a gas are small compared with the distances between them (low density, compressibility).

4. There is little attraction between molecules of a gas.

5. Molecules collide with one another, and energy is conserved in these collisions (elastic- the sum of the kinetic energies before and after collision is equal).

6. Temperature is a measure of the average kinetic energy of the gas molecules (on average, the particles of a cold sample move more slowly than the particles of a hot sample).

Deviations from Ideal Gas Deviations from Ideal Gas LawLaw

• Real molecules have volume.

• There are intermolecular forces.– Otherwise a gas could not become a

liquid.Account for volume of molecules and

intermolecular forces with VAN DER WAALS’s EQUATION.

Van Der Waals’s EquationVan Der Waals’s Equation

ClCl22 gas has a = 6.49, b = 0.0562 gas has a = 6.49, b = 0.0562

For 8.0 mol ClFor 8.0 mol Cl22 in a 4.0 L tank at 27 in a 4.0 L tank at 27 ooC.C.

P (ideal) = nRT/V = 49.3 atmP (ideal) = nRT/V = 49.3 atm

P (van der Waals) = 29.5 atmP (van der Waals) = 29.5 atm

Measured V = V(ideal)Measured P

intermol. forcesvol. correction

nRTV - nbV2

n2aP + ----- )(

P V = n R T

Deviations from Ideal Gas Deviations from Ideal Gas LawLaw

• PV = nRT• PV = constant

PV

P

y = mx + b

m = slopecorrection to

Volumem = -1.5Vc = V – mVc = 20 + 1.5 =

21.5 mL

RememberRemember

• Go over all the contents of your textbook.

• Practice with examples and with problems at the end of the chapter.

• Practice with OWL tutor.• Work on your OWL assignment for

Chapter 12.• Practice with the quiz on CD of

Chemistry Now.