Gas Laws

Factors Affecting Gas Pressure• Number of Moles (Amount of gas)

– As the number of particles increases, the number of collisions with the container wall increases.

• Volume– The smaller the volume, the greater the

pressure exerted on the container.• Temperature

– As temperature increases, kinetic energy increases, increasing the frequency of collision, so pressure increases.

If Mass and Temp are Constant

Robert Boyle(1627-1691)

• Boyle was born into an aristocratic Irish family

• Became interested in medicine and the new science of Galileo and studied chemistry. 

• A founder and an influential fellow of the Royal Society of London

• Wrote extensively on science, philosophy, and theology.

#1. Boyle’s Law - 1662

Pressure x Volume = a constant

Equation: P1V1 = P2V2 (T = constant)

Gas pressure is inversely proportional to the volume, when temperature is held constant.

Boyle’s Law

P1V1=P2V2 T constant

# moles constant

P vs. V is curve

P

V

Boyle’s LawA 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..

Gas Lawspart 2

If Mass and Pressure are Constant

Jacques Charles (1746-1823) French Physicist• Part of a scientific balloon

flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans

• This is how his interest in gases started

• It was a hydrogen filled balloon – good thing they were careful!

#2. Charles’s Law - 1787The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant.

This extrapolates to zero volume at a temperature of zero Kelvin.

VT

VT

P1

1

2

2 ( constant)

Converting Celsius to Kelvin•Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the Kelvin scale.)

•Reason? There will never be a zero volume, since we have never reached absolute zero.

Kelvin = C + 273 °C = Kelvin - 273and

Charles’s original balloonCharles’s original balloon

Modern long-distance balloonModern long-distance balloon

Good example of Charles’ Law

Gas Lawspart 3

Joseph Louis Gay-Lussac (1778 – 1850)

French chemist and physicist Known for his studies on the physical properties of gases. In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

#3. Gay-Lussac’s Law - 1802•The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.• Law of expansion of gases by heat.

2

2

1

1

T

P

T

P

•How does a pressure cooker affect the time needed to cook food?

Pressure Cooker

Gay-Lussac

P1 = P2 V constant

T1 T2 # moles Constant

P

T

#4. The Combined Gas LawThe combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

= P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Ideal Gas Law

1. Brings together all the gas laws

2. Relates to Kinetic Molecular Theory

Kinetic Molecular Theory1. Gases are made of tiny particles (atoms or molecules)

2. The particles are so small, compared to the distances betweenthem, that the volume of each particle can be assumedto be negligible (zero).

3. The particles are in constant random motion, colliding with the walls ofthe container. These collisions with the walls cause the pressure exerted by the gas.

4. The particles do not attract or repel each other.

5. The average kinetic energy of the gas particles is directly proportionalto the Kelvin temperature of the gas

Ideal Gases• We are going to assume the gases behave

“ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure

• An ideal gas does not really exist, but it makes the math easier and is a close approximation.

• Particles have no volume? Wrong!

• No attractive forces? Wrong!

5. Ideal Gas Law: P V = n R T

P = pressure = kPa, atm, mmHg

V = volume measured in ml or L

n =# of moles

T = temperature °K

R=Ideal (universal) gas constant

=0.0821 L atm/(mol K)

=8.31 kPa L / (mol K)

=62.3 mmHg L/(mol K)

Ideal Gas Laws mostly hold at:

• Low pressure

• High temperature

Gas Lawspart 4

Mixtures and Movements

6.Avogadro's HypothesisEqual volumes of gases at the same T and P have the same number of molecules.

V = n(RT/P)V = n(RT/P)

•For gases this means: The number of moles goes up as volume goes up.

Amedeo Avogadro(1776 - 1856)

1 mole = 6.022 x 1023

•VV and nn are directly related.

*Lorenzo Romano Amedeo Carlo Avogadro, conte di Quaregna e Cerreto

Scheffler

Advogadro’s Law

• Equal volumes of a gas under the same temperature and pressure contain the same number of particles.

• If the temperature and pressure are constant the volume of a gas is proportional to the number of moles of gas present

V = constant * n

where n is the number of moles of gas

V/n = constant

V1/n1 = constant = V2 /n2

V1/n1 = V2 /n2

29

Avogadro’s Hypothesis

N2 H2 Ar CH4

At the same temperature and pressure, equal volumes of different gases contain the same number of molecules.

Each balloon holds 1.0 L of gas at 20oC and 1 atm pressure.

Each contains 0.045 mol or 2.69 x 1022 molecules of gas.

Avogadro’s HypothesisAvogadro’s HypothesisEqual volumes of gases at the same T and P

have the same number of molecules.

V = n (RT/P) = kn

V and n are directly related.

twice as many molecules

• English Chemist and Physicist

• 1803 Law of Partial Pressures

John Dalton 1766-1844

7. Dalton’s Law of Partial Pressures

• Ptotal = P1+P2+….

• Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone.

• If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3:

2 atm + 1 atm + 3 atm = 6 atm

1 2 3 4

Dalton’s Law of Partial Pressures

What is the total pressure in the flask?

PPtotal in gas mixture = P in gas mixture = P1 + P + P2 + ... + ...

Therefore,

Ptotal = PH2O + PO2 = 0.48 atm

Dalton’s Law: total P is sum of PARTIAL pressures.

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

0.32 atm 0.16 atm

Thomas Graham

Graham's law of effusion •formulated by Scottish physical chemist Thomas Graham ,1846. •Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.

8. Graham’s Law

• The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.

• Derived from: Kinetic energy = 1/2 mv2

• m = the molar mass, and v = the velocity.

RateA MassB

RateB MassA

=

• Effusion: Gas escaping through a tiny hole in a container.

• Both of these depend on the molar mass of the particle, which determines the speed.

• Diffusion: Molecules moving from areas of high concentration to low concentration.

Example: perfume molecules spreading across the room.

Diffusion• Diffusion is the gradual mixing of two or more

gases due to their spontaneous, random motion.

When a bottle of perfume is open, some of its molecules diffuse into the air. At the same time, the molecules from the air diffuse into the bottle and mix with the gaseous scent molecules.

Effusion• Effusion is the

process where the molecule of gas confined in a

container randomly passes through a tiny opening

•Molecules may be effusing through the bag if you can smell the onions when the bag is sealed.

Effusion: a gas escapes through a tiny hole in its container

-Think of a nail in your car tire…

Diffusion and effusion are explained by:

Graham’s Law

With effusion and diffusion, the type of particle is important:– Gases of lower molar mass diffuse and

effuse faster than gases of higher molar mass.

• Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases!

Graham’s Law

Combined Gas Law

P1V1 = P2V2_

T1 T2

V1

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

P1V1 = P2V2_

T1 T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

=

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

What is the total pressure in the flask?What is the total pressure in the flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...

Therefore, Therefore,

PPtotaltotal = P = PHH22OO + P + POO22 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum ofDalton’s Law: total P is sum of PARTIALPARTIAL pressures.pressures.

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.32 atm 0.16 0.16 atmatm

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Graham’s law governs effusion and diffusion of gas molecules.

Thomas Graham, 1805-1869. Professor in Glasgow and London.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

M of AM of B

Rate for B

Rate for A

HONORS HONORS onlyonly

Scientists

• Evangelista Torricelli (1608-1647)– Published first scientific explanation of a vacuum.– Invented mercury barometer.

• Robert Boyle (1627- 1691)– Volume inversely related to pressure

(temperature remains constant)

• Jacques Charles (1746 -1823)– Volume directly related to temperature

(pressure remains constant)

• Joseph Gay-Lussac (1778-1850)– Pressure directly related to temperature

(volume remains constant)

LAWLAW RELATIONSHIPRELATIONSHIP LAWLAW CONSTANTCONSTANT

Boyle’sBoyle’s PP V V PP11VV1 1 = P= P22VV22 T, nT, n

Charles’Charles’ VV T T VV11/T/T11 = V = V22/T/T22 P, nP, n

Gay-Lussac’sGay-Lussac’s PP T T PP11/T/T11 = P = P22/T/T22 V, nV, n