Gas LawsGas Laws

NM StandardsNM Standards

Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

Ideal Ideal GasesGasesIdeal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory.

Gases consist of tiny particles that are far apart relative to their size.

Collisions between gas particles and between particles and the walls of the container are elastic collisions

No kinetic energy is lost in elastic collisions

Ideal Gases Ideal Gases (continued)

Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion

There are no forces of attraction between gas particles

The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

Real Gases Do Not Behave Real Gases Do Not Behave IdeallyIdeally

Real gases DO experience inter-molecular attractions

Real gases DO have volume

Real gases DO NOT have elastic collisions

Deviations from Ideal Deviations from Ideal BehaviorBehavior

Likely to behave Likely to behave nearly ideallynearly ideally

Gases at high temperature and

low pressure

Small non-polar gas molecules

Likely not to Likely not to behave ideallybehave ideally

Gases at low temperature and

high pressure

Large, polar gas molecules

Boyle’s LawBoyle’s Law

Pressure is inversely proportional to volume when temperature is held constant.

2211 VPVP

Boyles laws

• Animation

A Graph of Boyle’s A Graph of Boyle’s LawLaw

Charles’s LawCharles’s LawThe volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.

(P = constant)

Temperature MUST be in KELVINS!

2

2

1

1

T

V

T

V

Charles Law

• Animation

A Graph of Charles’ A Graph of Charles’ LawLaw

Gay Lussac’s LawGay Lussac’s LawThe pressure and temperature of a gas aredirectly related, provided that the volume remains constant.

Temperature MUST be in KELVINS!

2

2

1

1

T

P

T

P

Gay - Lussacs

A Graph of Gay-Lussac’s A Graph of Gay-Lussac’s LawLaw

The Combined Gas LawThe 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

• The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 P2 V2

= T1 T2

No, it’s not related to R2D2

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 Problem

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?

Set up Data Table

P1 = 0.800 atm V1 = 180 mL T1 = 302 K

P2 = 3.20 atm V2= 90 mL T2 = ??

CalculationP1 = 0.800 atm V1 = 180 mL T1 =

302 KP2 = 3.20 atm V2= 90 mL T2 = ??

P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T1 T2

T2 = P2 V2 T1

P1 V1T2 = 3.20 atm x 90.0 mL x 302 K

0.800 atm x 180.0 mL

T2 = 604 K - 273 = 331 °C

= 604 K

Learning Check

A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

Solution

T1 = 308 K T2 = ?

V1 = 675 mL V2 = 0.315 L = 315

mL

P1 = 0.850 atm P2 = 802 mm Hg = 646 mm Hg

T2 = 308 K x 802 mm Hg x 315 mL

646 mm Hg 675 mL= 178 K - 273 = - 95°C

One More Practice Problem

A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

SolutionComplete the following setup:Initial conditions Final conditionsV1 = 785 mL V2 = ?

T1 = 21°C = 294 K T2 = 0°C = 273 K

Since P is constant, P cancels out of the equation. V1 V2 V1 T2 = V1T2 = T1V2 = V2 T1 T2 T1

= 728 mLCheck your answer: If temperature decreases,

V should decrease.

And now, we pause for this commercial message from STP

OK, so it’s really not THIS kind of STP…

STP in chemistry stands for Standard Temperature and PressureStandard Pressure =

1 atm (or an equivalent) Sea Level

Standard Temperature = 0 deg C (273 K) freezing temp of water

STP allows us to compare amounts of gases between different pressures and temperatures

STP allows us to compare amounts of gases between different pressures and temperatures

Try This One

A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

P1 = 1.0 atm V1 = 15 L T1 = 273 K

P2 = 2.0 atm V2 = ?? T2 = 248 K

V2 = 15 L x 1.0 atm x 248 K = 6.8 L

2.0 atm 273 K

Avogadro’s Avogadro’s HypothesisHypothesis

Equal volumes of gases at the Equal volumes of gases at the same T and P have the same same T and P have the same number of molecules.number of molecules.

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

V and n are directly related.V and n are directly related.

twice as many twice as many moleculesmolecules

Avogadro’s Hypothesis Avogadro’s Hypothesis and Kinetic Molecular and Kinetic Molecular

TheoryTheory

Avogadro’s Hypothesis Avogadro’s Hypothesis and Kinetic Molecular and Kinetic Molecular

TheoryTheory

P proportional to nP proportional to n

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

STP and Volume

• AT STP one mole of gas has a volume of 22.4 Liters

• Standard temperature: 0°C = 273.15 K

• Standard pressure = 1 atmosphere = 760 mmHg = 101.3 kPa

• Standard volume of 1 mole of an ideal gas at STP: 22.4 liters

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

For a mixture of gases in a container,

PPTotalTotal = = PP11 + + PP22 + + PP33 + . . . + . . .

This is particularly useful in calculating the pressure of gases collected over water.

• Practice

• http://www.chm.davidson.edu/vce/gaslaws/GasConstant.html

• http://www.chm.davidson.edu/vce/gaslaws/GasConstant.html