Dr. Mihelcic Honors Chemistry Dr. Mihelcic Honors Chemistry

Unit 8 – GAS LAWSUnit 8 – GAS LAWS

Importance of GasesImportance of Gases

Airbags fill with NAirbags fill with N22 gas in an accident. gas in an accident. Gas is generated by the decomposition of Gas is generated by the decomposition of

sodium azide, NaNsodium azide, NaN33..

2 NaN2 NaN33 ---> 2 Na + 3 N ---> 2 Na + 3 N2 2

Three States of MatterThree States of Matter

Characteristics of GasesCharacteristics of Gases

No definable No definable shape or shape or volumevolume

LowLow mass, with a lot of “free” mass, with a lot of “free” space (leads to space (leads to lowlow density) density)

Can be expanded Can be expanded infinitelyinfinitely and and placedplaced into a container if into a container if force is exerted.force is exerted.

Occupy containers Occupy containers uniformly uniformly and completelyand completely..

Escape Escape readilyreadily from from containers, mix containers, mix rapidlyrapidly..

KINETIC MOLECULAR THEORY (KMT)

Definition:Definition:

Theory used to explain gas laws. Theory used to explain gas laws.

Treats gases as a Treats gases as a collection of collection of particles in rapid, random motionparticles in rapid, random motion..

Applies to Applies to ALLALL gases, regardless of gases, regardless of chemical identitychemical identity..

Molecular ModelMolecular Model

Gas molecules are relatively far apart (mostly Gas molecules are relatively far apart (mostly empty space).empty space).

Gas molecules are in Gas molecules are in continuous, rapid, random continuous, rapid, random motion.motion.

All collisions between gas molecules are All collisions between gas molecules are elasticelastic (no energy lost or gained in a collision).(no energy lost or gained in a collision).

Gas pressure is caused by Gas pressure is caused by collisionscollisions of molecules of molecules with the walls of the container.with the walls of the container.

Average Temperature of a gas sample is related Average Temperature of a gas sample is related to its to its kinetic energykinetic energy..

Properties of GasesProperties of Gases

Gas properties can be Gas properties can be modeledmodeled using math. using math. Model depends on—Model depends on—

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

2.2. T = temperature (K)T = temperature (K)

3.3. n = amount (moles)n = amount (moles)

4.4. P = pressureP = pressure (atmospheres) (atmospheres)

Gas PressureGas Pressure

Caused by gas molecules Caused by gas molecules hitting hitting container walls.container walls.

Definition:Definition: Force per unit area, or

ForceArea

Image from: Image from: www.indiana.edu/.../PressGasLaws.htmlwww.indiana.edu/.../PressGasLaws.html

Pressure UnitsPressure Units

SI unit: SI unit:

pascal (Pa)pascal (Pa) (equal to (equal to

N/mN/m22))

1 kPa = 1000 Pa1 kPa = 1000 Pa

Additional Units of Pressure Additional Units of Pressure

Will also see problems with:Will also see problems with:atmospheres atmospheres (atm)(atm)

millimeters of mercury millimeters of mercury (mm Hg)(mm Hg)

inches of Hg inches of Hg (in Hg)(in Hg)

torr ( = torr ( = 1 mm Hg1 mm Hg))

Less commonly used:Less commonly used:pounds per square inch (psi)pounds per square inch (psi)millibars (mb)millibars (mb)

Conversion Factors and STPConversion Factors and STP

Conversion Factors and STPConversion Factors and STP

1 atm = 1 atm = 760760 mm Hg = mm Hg = 760760 torr = torr = 101.3101.3 kPakPa

= = 29.92129.921 in Hg = 1013.25 mb = 14.969 in Hg = 1013.25 mb = 14.969 psipsi

STP – STP – Standard Temperature (0ºC) and Pressure (1 Standard Temperature (0ºC) and Pressure (1 atm)atm)

PressurePressure

BAROMETERBAROMETER (developed by (developed by Torricelli in 1643)Torricelli in 1643)

Use: Use: Measures pressure

of air

Image from Image from Dr. Walt Volland, all rights reserved Dr. Walt Volland, all rights reserved 1998-20051998-2005

Barometric Barometric PressurePressure

Column height Column height measures the pressure measures the pressure

of the atmosphereof the atmosphere

1 standard atm1 standard atm= 760 mm Hg= 760 mm Hg

= 29.921 inches Hg= 29.921 inches Hg

= about 34 feet of = about 34 feet of waterwater

ManometersManometers

Use: Use:

Measures the Measures the pressure of a gas pressure of a gas in a closed system.in a closed system.

Open Manometer: Two CasesOpen Manometer: Two Cases

Sample Manometer Problem

An open manometer is filled with Hg and connected to a container of hydrogen. The mercury level is 40.0 mm lower in the arm of the tube connected to the air. Air pressure is 1.00 atm. What is the pressure of the hydrogen gas in mm of Hg?

RELATIONSHIP BETWEEN PRESSURE AND VOLUME

Boyle’s Law

Boyle’s Law in Real Life

Popping a balloon As you squeeze the balloon, what happens

to the pressure and volume inside the balloon?

Are pressure and volume directly proportional or inversely proportional?

P V

Boyle’s Law in Real Life

Operating a syringe As you pull back on the plunger, are you

increasing or decreasing the volume? How does the pressure change?

Are P and V directly or inversely proportional?

P V

Boyle’s Law in Real Life

Marshmallow/balloon in a vacuum As we evacuate the chamber, what do you

think will happen to the pressure? What do you think will happen to the volume of the marshmallow?

Are P and V directly or inversely proportional?400 Marshmallows in a Vacuum

P V

Boyle’s Law

When temperature is held constant, pressure and volume increase and decrease as opposites If pressure increases, volume decreases If pressure decreases, volume increases

P1V1 = P2V2

Practice with Boyle’s Law

A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume temperature is held constant)P1V1 = P2V2

P1 =

V1 =

P2 =

V2 =

Practice with Boyle’s Law

At room temperature, 10.01 L of a gas is found to exert 97.0 kPa. What pressure (in atm) would be required to change the volume to 5.00 L?P1V1 = P2V2

P1 =

V1 =

P2 =

V2 = 1 atm = 101.3 kPa

Practice with Boyle’s Law

Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.50 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be?P1V1 = P2V2

P1 =

V1 =

P2 =

V2 =

CHARLES’ LAW:

Relating Volume and Temperature

Charles’ Law in Real Life

Balloons popping when kept outdoors As the balloons sits outside, what happens to

the temperature of the gas inside the balloon? What happens to the volume of the balloon?

Are volume and temperature directly proportional or inversely proportional?

V T

Charles’ Law in Real Life

A ball outside on a cold day You pump the ball up indoors. After

going outside where it’s colder, what happens to the volume of the ball?

Are volume and temperature directly or inversely proportional?

V T

Charles’ Law in Real Life

Liquid Nitrogen demo video When the balloon is placed in the liquid

nitrogen, what happened to the temperature of the gas inside the balloon? What happened to the volume?

Are volume and temperature directly or inversely proportional?

V T

Charles’ Law

If pressure is held constant (doesn’t change), volume and temperature increase or decrease together If volume increases, so does the

temperature If temperature decreases, so does the

volume

2

2

1

1

T

V

T

V ***T must

be in Kelvin!!!

Practice with Charles’ Law

A balloon inflated in a room at 24 ºC has a volume of 4.00 L. The balloon is then heated to a temperature of 58 ºC. What is the new volume if the pressure remains constant?

V1 =

T1 =

V2 =

T2 =2

2

1

1

T

V

T

V

Practice with Charles’ Law

Exactly 5.00 L of air at -50 ºC is warmed to some temperature so that the volume was 8.36 L. What temperature was the system warmed to?

V1 =

T1 =

V2 =

T2 =2

2

1

1

T

V

T

V

Practice with Charles’ Law

A 50.0 mL sample of a gas is cooled from 119 ºC to 353 K. If the pressure remains constant, what is the final volume of the gas?

V1 =

T1 =

V2 =

T2 =2

2

1

1

T

V

T

V

Avogadro’s HypothesisAvogadro’s Hypothesis

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

V = knV = kn

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

twice as many twice as many moleculesmolecules

Image from Image from

library.thinkquest.library.thinkquest.org/12596/org/12596/avogadro.htmlavogadro.html

1 mol gas @ STP = 1 mol gas @ STP = 22.422.4 L L(a new conversion factor for (a new conversion factor for

moles!!)moles!!)

Avogadro’s Hypothesis & Molar Avogadro’s Hypothesis & Molar VolumeVolume

Sample ProblemSample Problem

Example 5.3 Example 5.3 What is the mass of propane gas, C3H8, that can be held in a 5.0 L container at STP?

Combined Gas Law

Combining all four Combining all four variables:variables:

PP11VV11 = = PP22VV22

nn11TT11 n n22TT22

If any one of these variables does not change in the problem, you can eliminate it from the

equation before starting!

Imploding Can Demo

What happened to the volume of the can?

What happened to the temperature of the gas inside the can?

How did pressure play a role in the can imploding?

IDEAL GAS LAWIDEAL GAS LAW

P = pressureP = pressure

V = volumeV = volume

n = # of molesn = # of moles

R = Ideal gas constantR = Ideal gas constant

T = temperature (in Kelvin)T = temperature (in Kelvin)

P V = n R TP V = n R T

Gas Law Constant (R)Gas Law Constant (R)

RR: Universal or ideal gas : Universal or ideal gas constantconstant

Can be in different units, Can be in different units, depending on units used in the depending on units used in the

equation!equation!

0.082058 L atm/mol K0.082058 L atm/mol K62.364 L torr/mol K62.364 L torr/mol K8.3145 J/mol K8.3145 J/mol K

Sample ProblemSample Problem

Example 5.4 Example 5.4 If a fixed amount of gas occupies 2.53 m3 at -15°C and 191 Torr, what will the volume of the same gas be at 25°C and 1142 Torr?

Sample ProblemSample Problem

Example 5.5 Example 5.5 A gas cylinder is filled with 100 g of CO2 at 25oC and a pressure of 1000 mmHg. If 50 more grams of CO2 are added and the cylinder is stored at a temperature of 50oC, calculate the new pressure inside the cylinder.

Using PV = nRTUsing PV = nRTHow much N2 is required to fill a small room with a volume of 960 cubic feet (27,000 L) to a pressure of 745 mm Hg at 25°C?

Sample ProblemSample Problem

Example 5.7 Example 5.7 If 0.623 g of ethane, C2H6, is introduced into an evacuated 2.00 liter container at 23°°C, what is the pressure, in atmospheres, in the container?

Sample ProblemSample Problem

Example Example 5.8 How much gas can be placed in a gas cylinder with a volume of 10.0 L and which is designed to store gas at a maximum pressure of 75.0 atm and at a maximum of 50°°C?

Gas Density and Molar Mass

PV = nRTPV = nRTPV = nRTPV = nRT

nV

= P

RT

nV

= P

RTm

M• V =

PRT

where M = molar mass

mM• V

= P

RT

where M = molar mass

d = mV

= PMRT

d = mV

= PMRT

d and M proportionald and M proportional

and density (d) = m/Vand density (d) = m/V

Sample ProblemSample Problem

Example 5.9 Example 5.9 A sample of phosgene (a highly toxic gas) is collected in a flask with a volume of 247 mL at a pressure of 751 mmHg and a temperature of 21°°C. If the mass of the gas is 1.00 g, what is the molar mass of phosgene?

Sample ProblemSample Problem

Example 5.10 Example 5.10 What is the density of methane, CH4, at 0.940 atm and 23°°C?

Gases in Reaction Gases in Reaction StoichiometryStoichiometryReview of steps in Stoichiometry

Problems:

1. Balance equation & convert to moles for known.

2. Convert moles of known to moles of unknown quantity using coefficient ratio.

3. Convert moles of unknown to required unit (g, L)

Short-cut when dealing with all Short-cut when dealing with all gases in an equationgases in an equation

1.1. If have all gases in an equation, can go If have all gases in an equation, can go directly from V of the given to V of the directly from V of the given to V of the asked for quantity using the coefficients.asked for quantity using the coefficients.

2.2. ONLY works for equations with all gases!ONLY works for equations with all gases!

Sample ProblemSample Problem

Write the balanced equation for the synthesis of gaseous water from gaseous hydrogen and oxygen. If we start with 5.4 L of oxygen, how much water in Liters is produced?

Sample ProblemSample Problem

What is the mass, in grams, of potassium chlorate that must be used to produce 1.50 L of oxygen gas measured at 18°°C and 0.950 atm?

Sample ProblemSample Problem

How many liters of oxygen, measured at 725 mmHg and 21°C are required to burn 1.00 g of butane gas, C4H10, to produce water and carbon dioxide?

GRAHAM’S LAW &

DALTON’S LAW

Racing Gases Demo:If concentrated HCl is at one end

of the tube and concentrated NH3 is at the other end, which

gas do you think will move farthest and fastest down the

tube?

Racing Gases Demo

HCl (g)

NH3 (g)

RACING GASES DEMOThe gases will diffuse down the tube

Diffusion – tendency of molecules to move from areas of higher concentration towards areas of lower concentrationExample: spraying perfume and

smelling it across the room

DIFFUSION

Originally

Over Time

RACING GASES DEMOThe gases diffused at different rates

If the white ring forms closer to the HCl end of the tube, which gas moved farthest and fastest?

What if it was closer to the NH3 end?

RACING GASES DEMOWhat happened in the tube?

Was the reaction closer to the HCl or NH3 end of the tube?

Calculate the molar mass of NH3(g) and HCl(g). Did the lighter or heavier gas move faster?

GRAHAM’S LAW OF EFFUSION

The demo is related to Graham’s Law of Effusion – gases of lower molar masses effuse faster than gases with higher molar massesEffusion – when a gas escapes through a

tiny hole in its containerExample: Helium balloons shrinking

compared to normal balloons

GRAHAM’S LAWGraham’s Law can also be applied to the

diffusion of a gasGases with lower molar masses (lighter

gases) diffuse faster than gases with higher molar masses (heavier gases)

The lighter the gas, the faster it moves

GRAHAM’S LAWWhich gas would both diffuse and

effuse faster…Methane (CH4) or carbon dioxide

(CO2)?Chlorine (Cl2) or oxygen (O2)?Hydrogen sulfide (H2S) or carbon

monoxide (CO)?

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Graham’s law calculates: Graham’s law calculates:

rate of effusion and rate of effusion and diffusion of gas diffusion of gas molecules.molecules.

Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.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 1

M of 2

Rate(Gas 2)

Rate (Gas 1)

Sample ProblemSample ProblemIf they are compared under the same conditions, how much faster than helium does hydrogen effuse through a tiny hole?

Sample Sample ProblemProblem

The rate of a volume of an unknown gas to effuse through a pinhole was 4.00 moles/sec. The rate calculated for the

same volume at the same temperature and pressure of oxygen was 2.00 moles/sec. Calculate the molar mass of

the unknown gas.

REVIEW - PRESSURE OF A GAS If the gas molecules in a sample

collide more with the walls of the container, will the pressure increase or decrease?

If the number of gas molecules increases, what will happen to the pressure?

DALTON’S LAW

DALTON’S LAWPartial pressure – the contribution of each

gas in a mixture to the total pressureDalton’s Law of Partial Pressures – for a

mixture of gases, the total pressure is the sum of the partial pressure of each gas in the mixture

Ptotal = P1 + P2 + P3 + …

(at constant volume and temperature)

PRACTICE – DALTON’S LAWDetermine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are: PO2

= 20.0 kPa, PN2=46.7 kPa, and PHe=26.7 kPa.

Ptotal = P1 + P2 + P3 + …

PRACTICE – DALTON’S LAWAir contains O2, N2, CO2, and trace amount of other gases. What is the partial pressure of oxygen (PO2

) if the total pressure of the system is

101.3 kPa and the partial pressures of N2, CO2, and the other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

Ptotal = P1 + P2 + P3 + …

Vapor Pressure of WaterVapor Pressure of Water

PPtotaltotal = P(gas) + P(H = P(gas) + P(H22O) = 788 mm HgO) = 788 mm Hg

If the total pressure is 788 mm Hg at 25oC, what is the partial pressure of hydrogen collected over water?

Deviations from Ideal Gas Law occur Deviations from Ideal Gas Law occur because of two main factors:because of two main factors:

1. Real molecules have 1. Real molecules have volumevolume..

2. There are 2. There are forces between forces between moleculesmolecules.. Otherwise a gas could not Otherwise a gas could not

become a liquid.become a liquid.

These factors are important These factors are important at at HIGHHIGH pressures and pressures and

LOW LOW temperatures.temperatures.

Deviations from Ideal Gas Law occur because of two main factors:

1. Real molecules have 1. Real molecules have volumevolume..

2. There are 2. There are forces between forces between moleculesmolecules.. Otherwise a gas could not Otherwise a gas could not

become a liquid.become a liquid.

In general, the closer a gas is In general, the closer a gas is to theto the LIQUIDLIQUID state, the more state, the more it will deviate from the Ideal it will deviate from the Ideal

Gas Law.Gas Law.

Deviations from Ideal Gas Deviations from Ideal Gas LawLaw

Account for volume of molecules Account for volume of molecules and intermolecular forces with and intermolecular forces with

VAN DER WAALS’s EQUATIONVAN DER WAALS’s EQUATION..

Measured V = V(ideal)Measured P

intermol. forcesvol. correction

J. van der Waals, J. van der Waals, 1837-1923, 1837-1923, Professor of Professor of Physics, Physics, Amsterdam. Amsterdam. Nobel Prize 1910.Nobel Prize 1910.

nRTV - nbV2

n2aP + ----- )(

Deviations from Ideal Gas Deviations from Ideal Gas LawLawDeviations from Ideal Gas Deviations from Ideal Gas LawLaw

ClCl22 gas has gas has aa = 6.49, = 6.49, bb = 0.0562 = 0.0562

For 8.0 mol ClFor 8.0 mol Cl22 in a 4.0 L tank at 27 in a 4.0 L tank at 27 ooC.C.

P (ideal) = nRT/V = 49.3 atmP (ideal) = nRT/V = 49.3 atm

P (van der Waals) = 29.5 atmP (van der Waals) = 29.5 atm

Measured V = V(ideal)Measured P

intermol. forces

vol. correction

nRTV - nbV2

n2aP + -----