Chapter 11Gas Laws

11.1 and 11.2 Development of the Kinetic Theory of Gases

• The kinetic Theory of Gases– Gases are made up of molecules with lots of empty

space between– Particles move quickly - pressure is caused by this

motion– Collisions are completely elastic– There are no attractive or repulsive forces between

molecules– KE = ½ mv2

Development of the Kinetic Theory of Gases

• Properties of Gases resulting from the KTG– Expansion - no definite shape or definite volume– Fluidity - particles glide past each other ( gases and

liquids are both fluids)– Low Density - gases are roughly 1/1000 the density of

solids and liquids– Compressibility– Diffusion - spontaneous mixing of 2 substances due

to random molecular motion– Effusion - a gas spreads through a small opening

between containers

Development of the Kinetic Theory of Gases

• A qualitative description of gases:– P = Pressure (mmHg, kPa, atm)– T = Temperature (K, Co)– V = Volume (mL, L)– n = moles

Combined Gas Law• Describes the relationship between Pressure,

Temperature, and Volume.• Formula:

– P1V1 = P2V2

T1 T2

• STP = standard temperature and pressure:– Pressure units: 101.3 kPa, 760 torr, 1 atm, 760 mmHg– Temperature units: 273 K, O C0 ( must use K with gas

laws)– Volume: if one mole is present, then 22.4 L

Practice of Conversions

• 2.0 atm = ______ Kpa

• 560mmHg = ______ torr

• 35 oc = _____ K

• 298 K = _____ co

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11.3 Boyle’s Law

• The volume of a gas varies inversely with pressure at constant temperature.– Formula: P1V1 = P2V2

T1 T2

• P1V1 = P2V2

– As the applied (outside pressure) increases, the volume decreases.

• Graph:V

P

Boyle’s Law• Ex1: If 150. ml of a sample of O2 at 720.0 mm Hg

has the pressure increased to 750.0 mm Hg, what is the new volume?

x = 144 mL

Charles’ Law• The volume of a fixed mass of gas varies directly with

temperature at constant pressure.– Formula: P1V1 = P2V2

T1 T2

• V1 = V2

T1 T2

• As the temperature increases, the volume increases. (hot air balloon)

v

t

When the graph is extrapolated to 0 K, the volume is 0. This is impossible as the gas would have volume of all the particles with no space between them. Of course, this is impossible to test since no gases exist at - 273 C0 (only solids and liquids).

Charles’ Law• If 753 ml of nitrogen at 25 C0 is heated to

50. C0, then what is the new volume?

820 mL

Gay-Lussac’s Law

• The pressure of a fixed mass of gas varies directly with temperature at constant volume – Formula: P1V1 = P2V2

T1 T2

• P1 = P2

T1 T2

– As the temperature increases, the pressure increases.

p

t

Gay-Lussac’s Law• If a gas at 3.0 atm and 25 C0 is heated to

52 C0, what is the new pressure?

3.3 atm

Combine Gas Law• The relationship between pressure, volume, and

temperature when the amount of gas is fixed– Formula

P1V1 = P2V2

T1 T2

Combine Gas Law• If a sample of gas at 22.0oc and 31 kPa occupies

200.0 cm3, what space will it occupy at STP?

Combine Gas Law• A 350 mL air sample collected at 35oC has a

pressure of 550 mmHg. What pressure will the air exert if it is allow to expand to 425 mL and 57oC?

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Dalton’s Law of Partial Pressures

• The total pressure of a collection of gases in a mixture is equal to the sum of the pressures that each gas would exert by itself in the same volume.

– Formula: PT = P1 + P2 .....

– Collecting gas over water:

H2O(g) H2O(g)

H2O(g)

Zn(s) + H2SO4(aq) ZnSO4(aq) + H2(g)

Ptotal = Pwater + Phydrogen

Dalton’s Law of Partial Pressures

• A student collects oxygen gas over water at an atmospheric pressure of 100.0 kPa and a temperature of 29.0 C0. What is the partial pressure of the oxygen?

At 29.0 C0 water has a pressure of 30.0 mmHg (or 4.00 kPa).

100.0 kPa = 4.00 kPa + Poxygen

Poxygen = 96.0 kPa

Graham’s Law of Diffusion

• Graham noticed that gases with low densities diffuse faster than gases with higher densities.

• Under the same conditions of temperature and pressure, gases diffuse at a rate inversely proportional to the square roots of their densities (or molecular mass).

Graham’s Law of Diffusion

• Formulas:rate of gas “A” = density of gas “B”rate of gas “B” density of gas “A”

velocity of gas “A” = molecular weight of gas “B”velocity of gas “B” molecular weight of gas “A”

This comes from KE = ½ mv2

Graham’s Law of Diffusion

• If CO2 molecules travel at 200.0 mph, how fast do H2 molecules go?

x = 938.1 mph

Graham’s Law of Diffusion

• If He atoms travel at 800.0 mph, how fast do nitrogen molecules go?

x = 330.8 mph

The Kinetic Theory and the Gas Law

• In Boyle’s Law, Pressure = Force/Area. So….

• In Charle’s Law, temperature is proportional to KE. So....

½ the volume means 2x the particles So, 2x the pressure

-doubling temperature = doubling KE-doubling KE = doubling pressure (doubles the number of collisions)

-in order to keep pressure the same (constant), volume must double instead

The Kinetic Theory and the Gas Law

• In Gay-Lussac’s Law, temperature is proportional to KE. So...– doubling temperature = doubling KE– doubling KE = doubling pressure (doubles the

number of collisions)– volume is constant, so the pressure does change

• In Dalton’s Law of Partial Pressures, if gas A exerts a pressure of 5 collisions/second and gas B exerts a pressure of 5 collisions/second, then the total # of collisions/second should = 10 (their sum).

Practice!!!!• To what temperature must a sample of nitrogen

at 27oC and 0.625 atm be heated so that its pressure becomes 855 mmHg at constant volume?

• If the pressure exerted on a 240 mL sample of hydrogen gas at constant temperature is increased from 325 mmHg to 550 mmHg, what will be the final volume of the sample?

Practice!!!!• A sample of gas is collected over water at a

temperature of 35.0o when the barometric pressure reading is 742 mmHg. What is the partial pressure of the dry gas?

• A sample of air has a volume of 140 mL at 67oC. To what temperature must the gas be lowered to reduce its volume to 50 mL at constant pressure?

Practice!!!!• If CO atoms travel at 300.0 mph, how fast

do chlorine molecules go?

• A gas measures of 1.75 L at -23oC and 150 kPa. At what temperature would the gas occupy 1.30 L at 210 kPa?

Ideal Gas Law

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