Gas LawsGas Laws

February 10February 10thth & 11 & 11thth, , 20102010

Ms. KomperdaMs. Komperda

The Kinetic Molecular Theory is a set The Kinetic Molecular Theory is a set of statements that describe the of statements that describe the

behavior of gasesbehavior of gasesGases are made up of a large number of Gases are made up of a large number of

small particlessmall particlesThese particles are in constant These particles are in constant randomrandom

motionmotionThe speed (kinetic energy) that these The speed (kinetic energy) that these

particles travel at is directly related to particles travel at is directly related to their temperaturetheir temperature

The particles collide with each other and The particles collide with each other and the walls of the container frequentlythe walls of the container frequently

Pressure is a measurement of how often Pressure is a measurement of how often these molecules hit the walls of the these molecules hit the walls of the containercontainer

Ideal vs Real GasesIdeal vs Real Gases

It is easier to describe the behavior of It is easier to describe the behavior of idealideal gases. To do this we assume some things gases. To do this we assume some things about gases that may not be trueabout gases that may not be true The particles in ideal gases:The particles in ideal gases:

Take up no spaceTake up no space Never attract or repel each otherNever attract or repel each other

Real gases actually do take up space and Real gases actually do take up space and can attract or repel. can attract or repel. At HIGH TEMPERATURE and LOW PRESSURE At HIGH TEMPERATURE and LOW PRESSURE

real gases behave like ideal gasesreal gases behave like ideal gases Why?Why?

Properties of GasesProperties of Gases

Chemists do not simply observe gases, they Chemists do not simply observe gases, they measure their properties. These are the measure their properties. These are the properties we measure:properties we measure:

V = volume of the gas (L)V = volume of the gas (L)

T = temperature (K)T = temperature (K) ALL temperatures MUST be in Kelvin!!! No ALL temperatures MUST be in Kelvin!!! No

Exceptions!Exceptions!

n = amount (moles)n = amount (moles)

P = pressureP = pressure (atmospheres) (atmospheres)

PressurePressure

Pressure is the force Pressure is the force exerted over a certain exerted over a certain areaarea

Because gases have mass Because gases have mass they exert pressurethey exert pressure

Pressure of air is Pressure of air is measured with a measured with a BAROMETER (developed BAROMETER (developed by Torricelli in 1643)by Torricelli in 1643)

Hg rises in tube until force Hg rises in tube until force of Hg (down) balances the of Hg (down) balances the force of atmosphere force of atmosphere (pushing up). (Just like a (pushing up). (Just like a straw in a soft drink)straw in a soft drink)

PressurePressure Column height measures Column height measures

Pressure of atmospherePressure of atmosphere

1 standard atmosphere (atm) *1 standard atmosphere (atm) *

= 760 mm Hg (or torr) *= 760 mm Hg (or torr) *

= 14.7 pounds/in2 (psi)= 14.7 pounds/in2 (psi)

= 101.3 kPa (kiloPascal)= 101.3 kPa (kiloPascal)

= about 34 feet of water!= about 34 feet of water!

* Memorize these!* Memorize these!

Pressure ConversionsPressure Conversions

= 0.9182 atm

= 0.625 atm475 mm Hg x

93.01 kPa x

Boyle’s LawBoyle’s Law

PP11VV11 = P = P22 V V22

This means Pressure and This means Pressure and Volume are INVERSELY Volume are INVERSELY PROPORTIONAL if moles PROPORTIONAL if moles and temperature are and temperature are constant (do not constant (do not change). For example, P change). For example, P goes up as V goes down.goes up as V goes down.

Robert Boyle Robert Boyle (1627-1691). (1627-1691). Son of Earl of Son of Earl of Cork, Ireland.Cork, Ireland.

Boyles Law GraphBoyles Law Graph

P

V

Boyle’s LawBoyle’s LawBoyle’s LawBoyle’s Law

A bicycle pump is a A bicycle pump is a good example of good example of Boyle’s law. Boyle’s law.

As the volume of As the volume of the air trapped in the air trapped in the pump is the pump is reduced, its reduced, its pressure goes pressure goes up, and air is up, and air is forced into the forced into the tire.tire.

Charles’s LawCharles’s Law

If n and P are constant, If n and P are constant, thenthen

V and T are DIRECTLY V and T are DIRECTLY proportional.proportional.

V1 V2 V1 V2

T1 T2T1 T2 If one temperature goes If one temperature goes

up, the volume goes up!up, the volume goes up!

Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

=

Charles Law GraphCharles Law Graph

T

V

Charles’s LawCharles’s LawThink about what happens Think about what happens

to your bike tires in the to your bike tires in the winterwinter

As the temperature As the temperature decreases the tires deflatedecreases the tires deflate

This also happens if you This also happens if you take a balloon outside on take a balloon outside on a cold daya cold day

Gay-Lussac’s LawGay-Lussac’s Law

If n and V are If n and V are constantconstant, , thenthen

P and T are DIRECTLY P and T are DIRECTLY proportional.proportional.

PP11 PP22

==

TT11 TT22

If one temperature goes If one temperature goes up, the pressure goes up!up, the pressure goes up!

Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

Gay-Lussac’s GraphGay-Lussac’s Graph

T

P

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

PP11 V V11 P P22 V V22 = =

TT11 T T22

No, it’s not related to R2D2

Combined Gas LawCombined Gas Law

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

= =

P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas LawCombined Gas Law

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

Notice how this problem still has TWO sets of conditions- before Notice how this problem still has TWO sets of conditions- before and afterand after

List what you know:P1 = 0.800 atm V1 = .180 L T1 = 302 KP2 = 3.20 atm V2= .090 L T2 = ??

Combined Gas Law Combined Gas Law ProblemProblem

PP1 1 = 0.800 atm V= 0.800 atm V11 = .180 L T = .180 L T11 = 302 K = 302 K

PP22 = 3.20 atm V = 3.20 atm V22= 0.090 L T= 0.090 L T2 2 = ??= ??

PP11 V V11 P P22 V V2 2 Cross multiply to get rid of the fraction: Cross multiply to get rid of the fraction: PP11 V V11 TT2 2 = P= P22 V V2 2 TT11

TT11 = = TT2 2

Solve for Solve for TT22 T T2 2 = P= P22 V V2 2 TT1 1 = = 3.20 atm x 0.090 L x 3.20 atm x 0.090 L x 302 K302 K

PP11 V V1 1 0.800 atm 0.800 atm x .180 Lx .180 L

T2 = 604 K - 273 = 331 °C

T2 = 604 K

CalculationsCalculations

Brings together all gas properties, including moles.

What is the difference between a real and an ideal gas?

PV = nRTPV = nRT

Ideal Gas LawIdeal Gas Law

P = PressureP = Pressure

V = VolumeV = Volume

T = TemperatureT = Temperature

n = number of molesn = number of moles

R is a constant, called the R is a constant, called the Ideal Gas ConstantIdeal Gas Constant

R = 0.08206L * atm

mol * K

Using the Ideal Gas Using the Ideal Gas LawLaw

How much N2 is required to fill a small room with a volume of 27,000 L to 745 mm Hg at 25 oC?

List knowns (change units if needed)

V = 27,000 L

T = 25 oC + 273 = 298 K

P = 745 mm Hg * (1 atm/760 mm Hg) = 0.98 atm

And we always know R, 0.08206 L*atm / mol*K

Ideal Gas CalculationIdeal Gas Calculation

RT RTRT RT

Rearrange the equation and solve for the unknown

PV = nRT n = (0.98 atm)(2.7 x 104 L)

(0.0821 L• atm/K • mol)(298 K)n =

(0.98 atm)(2.7 x 104 L)

(0.0821 L• atm/K • mol)(298 K)

n = 1082 moln = 1082 mol

How many grams of NHow many grams of N22 is this? is this?

1082 mol * (28 g/ 1mol) = 30,296 g!1082 mol * (28 g/ 1mol) = 30,296 g!

Ideal Gas CalculationIdeal Gas Calculation

What is the

total pressure in

the cylinder?

Ptotal in gas mixture = P1 + P2 + ...

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

Dalton’s Law of Partial Dalton’s Law of Partial PressurePressure

DiffusionDiffusion

Think about a time you were in a room with Think about a time you were in a room with somebody wearing too much perfume…somebody wearing too much perfume…

Why don’t you smell it immediately? Why don’t you smell it immediately?

What about people across the room?What about people across the room? This is because the smell spreads out. This is because the smell spreads out.

This rapid dispersion of particles from high This rapid dispersion of particles from high concentration to low concentration is concentration to low concentration is DIFFUSION in action!DIFFUSION in action!

Think about when a nail makes a small puncture in Think about when a nail makes a small puncture in a tire and the air escapes? Isn’t that diffusion too? a tire and the air escapes? Isn’t that diffusion too? When this happens, we are looking at EFFUSION, When this happens, we are looking at EFFUSION,

or the motion of a gas through a small openingor the motion of a gas through a small opening

Since the opening is small, gas particles have to Since the opening is small, gas particles have to “wait in line” for other particles to pass through. “wait in line” for other particles to pass through. Like a grocery checkout, it’s first come, first Like a grocery checkout, it’s first come, first

served. served. Lighter particles travel faster and escape more Lighter particles travel faster and escape more

often than more massive particles. often than more massive particles. Difference between having a full cart (heavy and Difference between having a full cart (heavy and

slow) and 10 items or less (light and fast)slow) and 10 items or less (light and fast)

EffusionEffusion

Graham’s law governs effusion

and diffusion of gas molecules.

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

Rate of effusion is inversely proportional to

molar mass.

High mass = low speedLow mass = high speed

Rates of Effusion & Rates of Effusion & DiffusionDiffusion