AP CHEMISTRYChapter 5

Gases

Slides with gray backgrounds are not tested on the AP test.

This is a schematic diagram showing gas molecules (purple) in a container. The molecules are constantly moving in random directions. When a molecule hits the container wall (green), it exerts a tiny force on the wall. The sum of these tiny forces, divided by the interior surface area of the container, is the pressure. (Longer arrows indicate higher velocities, shorter arrows indicate lower velocities)

Gas Pressure

Barometer -invented by

Evangelista Torricelli

in 1643; uses the

height of a column

of mercury to

measure gas

pressure (especially

atmospheric)

The Manometer

a device for measuring the pressure

of a gas in a container

The pressure of the gas is given by h

[the difference in mercury levels] in

units of torr (equivalent to mm Hg).

a) Gas pressure = atmospheric pressure – h

b) Gas pressure = atmospheric pressure + h

Open-tube manometer

1 mm of Hg = 1 torr

760.00 mm Hg

=

760.00 torr

=

1.00 atm

=

101.325 kPa

Know these!

kPa is not tested on the AP exam

SI unit of pressure is N/m2 or Pascal (Pa)

Boyle’s Law1st quantitative study of gases, 1600s.Pressure and volume are inversely related.P1 = V2 P1V1= P2V2

P2 V1

Memory Trick: We Boyle Peas and Vegetables

An ideal gas is expected to

have a constant value of PV,

as shown by the dotted line.

CO2 shows the largest

change in PV, and this

change is actually quite

small.

Ideal gas- gas that obeys Boyle’s law

Charles’ Law 1700’s-volume of a gas is directly proportional to Kelvin temperatureV1 = V2 Temp must be in Kelvin!!!!!!

T1 T2

Memory Trick: Charlie Brown’s Xmas is on TV

0

The volume of a gas at absolute zero is zero.

Avogadro’s Law-equal volumes of gases at

the same temperature and pressure contain the same # of particles

-for a gas at constant temp. and pressure, the volume is directly proportional to the # of moles of gas

Gay-Lussac’s Law

Pressure of a gas is directly proportional to Kelvin temperatureP1 = P2 Temp must be in Kelvin!!!!!!T1 T2

“GayLe drives a PT cruiser”

Combined Gas Law

P1V1 = P2V2

T1 T2

“Peas and Vegetables on the Table”This can be used to come up with Boyle’s, Charles’, or Gay-Lussac’s Law. Simply cover up the factors that are constant.

Ideal Gas LawCombining Boyle’s, Charles’, and Avogadro’s laws we get PV= nRT.R = 0.08206 (Latm)/(Kmol) (proportionality constant)

Most gases behave ideally at pressures less than 1 atm.

We can use the ideal gas law for all gas law problems by putting changing variableson one side and the constant on the other.

Ex. If P&V change w/ others constant: P1V1 = nRT and P2V2 = nRT so P1V1 = P2V2

If V&T change with others constant: V1 = nR and V2 = nR so V1 = V2

T1 P T2 P T1 T2

The gas pressure inside an aerosol can is 1.5 atm at 25oC. Assuming that the gas is ideal, what would the pressure be if the can were heated to 452oC?

P1=1.5 atm T1 = 25oC+273 = 298K

P2 = ? T2 = 452oC + 273 = 725K

P2 = 3.6 atm

2

2

1

1

T

P

T

P

1

212 T

TPP

298K

25K)(1.5atm)(72 P

A quantity of helium gas occupies a volume of 16.5 L at 78°C and 45.6 atm. What is the volume at STP?

P1 = 45.6 atm V1 = 16.5L T1 = 78°C + 273 = 351K

P2 = 1 atm V2 = ? T2 = 0°C + 273 = 273K

V2 = 585L

2

22

1

11

T

VP

T

VP

21

2112 PT

TVPV

(351)(1)

)(16.5)(273)6.5(42 V

Many gases are shipped in high-pressure containers. If a steel tank whose volume is 50.0L contains O2 gas at a total pressure of 1550 kPa at 23oC, what mass of oxygen does it contain?

P = 1550 kPa/101.3 = 15.3atm V = 50.0L n = ?

R = 0.08206(Latm)/(Kmol) T = 23oC + 273 = 296K

PV = nRT (15.3)(50.0) = n (0.08206)(296)

n = 31.5mol O2

1010 g O2

2

22

O mol 1

O g 32.0O mol 31.5

Molar Volume = 22.42 L of an ideal gas at STP

(Some gases behave more ideally than others.)

STP = 0oC and 1 atm

CaH2 reacts with H2O to produce H2 gas.CaH2(s) + 2H2O(l) 2H2(g) + Ca2+(aq) + 2OH-(aq)Assuming complete rxn with water, how many grams of CaH2 are required to fill a balloon to a total pressure of

1.12 atm at 15oC if its volume is 5.50 L?

P = 1.12 atm V= 5.50 L T= 15oC + 273 = 288K

n= ? R = 0.08206 Latm/Kmol

PV=nRT (1.12)(5.50)=n(0.08206)288

n = 0.2606 mol H2

0.2606 mol H2 1 mol CaH2 42.10g CaH2

2 mol H2 1 mol CaH2

= 5.49g CaH2

How many liters of N2 are required to produce 115 g of NH3 at STP?

N2 + 3H2 2NH3

115g NH3 1 mol NH3 1 mol N2 22.42L N2

17.04g NH3 2 mol NH3 1 mol N2

= 75.7 L N2

Molecular Weight and Density of a Gas

n = mass so P = mRT MW V(MW)Since m/V = density (g/L), P = dRT MW MW = dRT P “Molecular Weight Kitty Cat”

Meow = dirt/pee

Calculate the molar mass of a gas if 0.608g occupies 750 mL at 385 mm Hg and 35oC.

V = 750 mL = 0.75L P = 385/760 = 0.507 atm

T = 35oC + 273 = 308 K

d = 0.608g/0.75L = 0.811g/L

MW = dRT/P

MW = (0.811)(0.08206)(308) = 40.4 g/mol 0.507

Dalton’s Law of Partial PressuresFor a mixture of gases in a container, the

total pressure exerted is the sum of the pressures that each gas would exert if it were alone.

Ptot = P1 + P2 + P3 + …

Ptot = n1RT + n2RT + n3RT +… V V V Ptot = ntotal (RT) (It doesn’t matter what the gas is.)

V

Mole Fraction-the ratio of the number of

moles of a given component in a mixture to the total number of moles in the mixture.

is used to symbolize mole fraction.

1 = n1

n1 + n2 + n3 + ...

The partial pressure of a particular component of a gaseous mixture is the mole fraction of that component times the total pressure. P1 = 1 (Ptotal)

When gases are collected over water, we must adjust for the pressure of the water vapor.

PH2O + Pgas = Ptotal

If a 0.20 L sample of O2 at 0oC and 1.0 atm pressure and a 0.10 L sample of N2 at 0oC and 2.0 atm pressure are both placed in a 0.40 L container at 0oC, what is the total pressure in the container?

P1V1=P2V2

1.0(0.20) = P2 (0.40) P2 = 0.50 atm = PO2

(2.0)(0.10) = P2 (0.40) P2 = 0.50 atm = PN2

PO2 + PN2 = Ptotal

0.50 + 0.50 = 1.00 atm

Kinetic Molecular Theory of Gases

-a simple model that attempts to explain properties of an ideal gas

Gases consist of particles which have the following properties:

1. The particles are so small compared to the distances between them that the volume of the individual particles can be assumed to be negligible (zero).

2. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

3. The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.

4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

-real gases don’t conform to these assumptions!!!

Kelvin temp. is an index of the random motions of the particles of a gas, with higher temp. meaning greater motion.

KE (avg) = 3/2 RT R = 8.314 J/K molUnits of KE are J/mol

KE = 1/2 mv2

Remember that mass has to be in kg and velocity in m/s!

Since we are working with energy, we need the energy R, not the gas R. Temp must be in Kelvin. Formula is not on AP exam.

Real gases have many collisions between particles. The average distance a particle travels between collisions in a particular gas sample is called the mean free path. These collisions produce a huge variation in velocities. As temperature increases, the range of velocities is greater.

Path of One Particle in a Gas

A Plot of the Relative Number of O2 Molecules That Have a Given Velocity at STP

A Plot of the Relative Number of N2 Molecules That Have a Given Velocity at Three Temperatures

This is called a Boltzmann Distribution graph

Effusion and Diffusion

Diffusion- mixing of gases

Effusion- the passage of a gas through a tiny orifice into an evacuated chamber

The Effusion of a Gas into an Evacuated Chamber

Graham’s Law of Effusion-The rate of effusion of a gas is

inversely proportional to the square root of the mass of its particles.

____Rate of effusion for gas 1 = MW2

Rate of effusion for gas 2 MW1

MW1 and MW2 represent the molar

masses of the gases. These calculations are not tested on the AP test.

-lighter gases effuse & diffuse faster than heavier gases

HCl(g) and NH3(g) Meet in a Tube

Because NH3 has a lower molar mass than HCl, it moves faster and farther in the tube. Solid NH4Cl is formed closer to the HCl.

Real gases

*No gas exactly follows the ideal gas law. *A real gas exhibits behavior closest to ideal behavior at low pressures and high temperatures.

Students also behave most ideally under these conditions. (Summer vacation!)

At high temperatures, there is less interaction between particles because they are moving too fast.

At high concentrations, gases have much greater attractive forces between particles. This causes particles to hit the walls of the container with less force (producing less pressure than expected).

At high pressure (small volume), the volume of the particles becomes significant, so that the volume available to the gas is significantly less than the container volume.

Attractive forces are greatest for large, complex molecules and polar molecules.

Volume Taken up by Gas Particles

We can use the Van der Waals equation to adjust for departures from ideal conditions.

PV = nRT becomes: [Pobs + a(n/V)2]V-nb = nRTcorrected correctedpressure volume You don’t need

to memorize this!