Kinetic MolecularTheory

is based on the idea that particles of matter are always in constant motion. The theory applies to all states of matter and can be used to explain the properties of solid, liquids, and gases.

Ideal GasesDo not really exist but is a close

approximation.Assumptions of the Kinetic

Theory• Particles of gases are always

in constant motion.

Ideal Gases

• Gases consist of a number of particles that are far apart

• Particles have elastic collisions (no energy lost)

• Particles have no volume

Ideal Gases• No attractive forces between

particles

• Kinetic Energy of particles is directly proportional to absolute temperature

K.E. = ½ mv2

Why real gases do not behave like ideal gases.

• Real gases have attractive forces (They can form solids and liquids)

• Real gases occupy space (have volume)

Deviations from Deviations from Ideal Gas LawIdeal Gas Law

• Real molecules have volume.The ideal gas consumes the entire

amount of available volume. It does not account for the volume of the molecules themselves.

• There are intermolecular forces.

An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions.

– Otherwise a gas could not condense to become a liquid.

What are attractive forces?

Attractive forces are called intermolecular forces

(IMFs). They exist between covalent compounds.

They areLondon Dispersion (LD)

Dipole-Dipole (DD)Hydrogen Bonding (HB)

IMFs in polar molecules -weak London dispersion forces-dipole forces -maybe hydrogen bonding

IMFs in non-polar molecules-weak London dispersion-maybe hydrogen bonding

Hydrogen Bonding occurs whenhydrogen bonds to fluorine, nitrogen,or oxygen.

Remember:As molar mass increases thenumber of electrons increaseand the London Dispersion forces become stronger.

Molecular substances existas solids, liquids, or gases atroom temperature due to intermolecular forces.

The weaker the intermolecular forces the more likely a molecular substance exist as a liquid or gas at room temperature.

Most Ideal

Gas

Least IdealGas

•Nonpolar monatomic (noble gases)

•Nonpolar diatomic

•Nonpolar

•Polar

•Polar w/hydrogen bonding(remember there are always exceptions)

The stronger the intermolecular forces the less ideal a gas will be.

Which of the following wouldbe the least ideal? The most ideal? Explain your answer.

HCl NH3 H2O Ne I2

How can you make a real gas behave like an ideal

gas?• Use high temperature and low

pressure.• Why does this work?Weakens the effect of the IMFs.

How can you condense a gas?

Increase the pressure and lower the temperature.

THREE STATES OF THREE STATES OF MATTERMATTER

THREE STATES OF THREE STATES OF MATTERMATTER

General Properties of General Properties of GasesGases

• There is a lot of “free” space There is a lot of “free” space in a gas.in a gas.

• Gases can be expanded Gases can be expanded infinitely.infinitely.

• Gases fill containers uniformly Gases fill containers uniformly and completely.and completely.

• Gases diffuse/effuse and mix Gases diffuse/effuse and mix rapidly.rapidly.

Effusion is a process where a gas passes through an opening.

Diffusion is the random spreading out of a gas

PressurePressurePressure of air is Pressure of air is

measured with ameasured with a BAROMETERBAROMETER (developed by (developed by Torricelli in 1643)Torricelli in 1643)

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

P of Hg pushing down related to P of Hg pushing down related to • Hg densityHg density• column heightcolumn height

Manometers are used tomeasure the pressure inside a container.

Pressure = Force/Area Newton/cm2 (unit) Pascal (SI unit)How is pressure related toforce? Area?

PressurePressureColumn height measures Column height measures

Pressure of atmospherePressure of atmosphere• 1 standard atmosphere 1 standard atmosphere

(atm) *(atm) *= 760 mm Hg (or torr) *= 760 mm Hg (or torr) *= 29.92 inches Hg *= 29.92 inches Hg *= 14.7 pounds/in= 14.7 pounds/in2 2 (psi)(psi)

= 101.3 kPa (SI unit is PASCAL) = 101.3 kPa (SI unit is PASCAL)

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

* Memorize these!* Memorize these!

Pressure Conversions

A. What is 475 mm Hg expressed in atm?

1 atm 760 mm Hg

B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?

760 mm Hg 14.7 psi

= 1.52 x 103 mm Hg

= 0.625 atm475 mm Hg x

29.4 psi x

Pressure Conversions

A. What is 2 atm expressed in torr?

B. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa?

Properties of GasesProperties of Gases(Four measurable (Four measurable

quantities)quantities)• V V = volume of the gas = volume of the gas • T T = temperature (K)= temperature (K)

–ALL temperatures in the ALL temperatures in the entire chapter MUST be entire chapter MUST be in Kelvin!!! No in Kelvin!!! No Exceptions!Exceptions!

• nn = amount (moles) = amount (moles)• PP = pressure = pressure

To convert Celsius to Kelvin

K = C + 273

Boyle’s LawBoyle’s LawP P αα 1/V 1/VThis 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.

PP11VV11 = P = P22 V V22 Robert Boyle Robert Boyle (1627-1691). (1627-1691). Son of Early of Son of Early of Cork, Ireland.Cork, Ireland.

Boyle’s Law and Kinetic Boyle’s Law and Kinetic Molecular TheoryMolecular Theory

Boyle’s Law and Kinetic Boyle’s Law and Kinetic Molecular TheoryMolecular Theory

Pressure and volume are indirectly Pressure and volume are indirectly related.related.

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

Practice problems textbook.p. 370 #2

Practice problems textbook.p. 372 #2

Charles’s Charles’s LawLaw

If n and P are constant, If n and P are constant, then V then V αα T T

V and T are directly V and T are directly proportional.proportional.

VV11 VV2 2

TT11 = T = T22

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

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

Charles’s LawCharles’s LawGraphGraph

Textbook problems page 372 #1

Textbook page 372 # 2

Gay-Lussac’s LawGay-Lussac’s LawIf n and V are constant, If n and V are constant,

then P then P αα T TP and T are directly P and T are directly

proportional.proportional.PP11 P P22

==

TT11 T T22

• If one temperature If one temperature

goes up, the pressure goes up, the pressure goes up!goes up!

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

Gay-Lussac’s LawGay-Lussac’s LawGraphGraph

Textbook Page 374 #1

Textbook page 374 # 2

Textbook page 374 # 3

Combined Gas Law

P1 V1 P2 V2

= T1 T2

Textbook page 375 # 1

Textbook page 375 #2

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 = ??

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?

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?

Dalton’s Dalton’s LawLaw

John DaltonJohn Dalton1766-18441766-1844

Ptotal = P1 + P2 + P3…The total pressure is equal to the sum of the partial pressures.

Gases in the AirThe % of gases in air Partial pressure (STP)

78.08% N2 593.4 mm Hg

20.95% O2 159.2 mm Hg

0.94% Ar 7.1 mm Hg

0.03% CO2 0.2 mm Hg

PAIR = PN + PO + PAr + PCO = 760 mm Hg 2 2 2

Total Pressure 760 mm Hg

Collecting a gas “over water”

• Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected “over water”, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial Pressures becomes useful.

Solve This!

A student collects some hydrogen gas over water at 20 degrees C and 768 torr. What is the pressure of the gas?

768 torr – 17.5 torr = 750.5 torr

Table of Vapor Pressures for Water

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 Pressure

The volume of a gas depends ontwo variables

Temperature and Pressure

Two scientist can do the same experiments at different temperatures and pressures and get two different volumes.

Colorado and Alaska

To solve this problem scientist implemented STP

Standard Temperature andPressure (STP)

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 degree C (273 K)

A sample of gas was collected by water displacement at 25 C, 270 mm Hg, and occupies a volume of 35.0 L. What is the volume at STP?

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?

Standard Molar Volume of a Gas

1 mole of a gas at standardtemperature and pressure is equal to 22.4 L

1mole of a gas @ STP = 22.4 L

Example:

Convert 2.00 L of hydrogengas to grams of hydrogen

Avogadro’s Principle

Equal volumes of a gas atthe same temperature andpressure contain the same

number of molecules

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

P have the same number of molecules.P have the same number of molecules.

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

twice as many twice as many moleculesmolecules

Avogadro’s Hypothesis and Kinetic Avogadro’s Hypothesis and Kinetic Molecular TheoryMolecular Theory

Avogadro’s Hypothesis and Kinetic Avogadro’s Hypothesis and Kinetic Molecular TheoryMolecular Theory

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.

Gas Stoichiometry

H2 + Cl2 → 2HCl

1 mole 1 mole 2 mole

1 volume 1volume 2 volume(1 Liter) (1 Liter) (2 Liter)

H2 + Cl2 → 2HCl

Convert 2.00 L of hydrogen to Liter of HCl

3H2 + N2 → 2 NH3

If 3.00 L of ammonia is produced, how many L of hydrogen was required?

IDEAL GAS LAWIDEAL GAS LAW

Brings together gas Brings together gas properties.properties.

Can be derived from Can be derived from experiment and theory.experiment and theory.

BE SURE YOU KNOW THIS BE SURE YOU KNOW THIS EQUATION!EQUATION!

P V = n R TP V = n R T

Using PV = nRTUsing PV = nRTP = Pressure (atm)P = Pressure (atm)V = Volume (L)V = Volume (L)T = Temperature (K)T = Temperature (K)N = number of moles (moles)N = number of moles (moles)

***** Make V and N the same compound.***** Make V and N the same compound.***** Adjust pressure if gas was collected by***** Adjust pressure if gas was collected by water displacement.water displacement.R is a constant, called the R is a constant, called the Ideal Gas ConstantIdeal Gas Constant

R = 0.0821 atm L/mol KR = 0.0821 atm L/mol K

How did scientist come up with0.0821 atm●L/mol●K for R (the

ideal gas constant)?

Molar volume of a gas1 mole of any gas @STP = 22.4L

Page 385 # 6

Twenty-five (25.0 g) of oxygen is collected by water displacement at a temperature of 25○C and pressure of 730 mm Hg. Determine the volume in liters.

3H2 + N2 → 2 NH3If 35.0 ml of hydrogen is at 25 C and 780 mm Hg, what mass of ammonia will be produced?

3 F2 + 3 H2O→ 6 HF + O3

What volume of HF will be producedat 30○C and 105 KPa if 3.00 grams offluorine were used? The gas was collected by water displacement.

Learning Check

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mm Hg) in the tank in the dentist office?

A. What is the volume at STP of 4.00 g of CH4?

B. How many grams of He are present in 8.0 L of gas at STP?

Learning Check

A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?

Gas Stoichiometry: Practice!

2 H2O ― 2 H2 + O2

How many liters of water will be needed

to

Produce 2.00 ml of hydrogen

***Remember a liter to liter is just like

a mole to mole conversion.

Gases and StoichiometryGases and Stoichiometry

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

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a volume of in a flask with a volume of 2.50 L. What is the volume of O2.50 L. What is the volume of O22 at STP? at STP?

Bombardier beetle Bombardier beetle uses decomposition uses decomposition of hydrogen peroxide of hydrogen peroxide to defend itself.to defend itself.

GAS DENSITYGAS DENSITYGAS DENSITYGAS DENSITY

HighHigh densitydensity

Low Low densitydensity

22.4 L of ANY gas AT STP = 1 mole

Using PV=nRT to determinedensity.

Determine the density of CO2 if the pressure is 750 mm Hg and the temperature is 30○C.

Using PV=nRT to determinethe molar mass of a gas.

Determine the molar mass of a Gas if the 2.00 grams occupies a volume of 3.00 liters at a pressure of 760 mm Hg and a temperature of 25○C.

GAS DIFFUSION AND EFFUSIONGAS DIFFUSION AND EFFUSION

• diffusiondiffusion is the gradual is the gradual mixing of molecules of mixing of molecules of different gases.different gases.

• effusioneffusion is the is the movement of movement of molecules through a molecules through a small hole into an small hole into an empty container.empty container.

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

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

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Molecules effuse thru holes in a Molecules effuse thru holes in a rubber balloon, for example, at a rubber balloon, for example, at a rate (= moles/time) that israte (= moles/time) that is

• proportional to Tproportional to T• inversely proportional to M.inversely proportional to M.Therefore, He effuses more rapidly Therefore, He effuses more rapidly

than Othan O22 at same T. at same T.

HeHe

Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion

Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

Health NoteWhen a scuba diver is several hundred feet under water, the high pressures cause N2 from the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N2 will form bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O2 in scuba tanks used for deep descents.