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CHAPTER 10

- GASES AND KINETIC-MOLECULAR THEORY

CHAPTER GOALS

- Comparison of Solids, Liquids, and Gases
- Composition of the Atmosphere and Some Common

Properties of Gases - Pressure
- Boyles Law The Volume-Pressure Relationship
- Charles Law The Volume-Temperature

Relationship The Absolute Temperature Scale - Standard Temperature and Pressure
- The Combined Gas Law Equation
- Avogadros Law and the Standard Molar Volume

CHAPTER GOALS

- Summary of Gas Laws The Ideal Gas Equation
- Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances - Daltons Law of Partial Pressures
- Mass-Volume Relationships in Reactions Involving

Gases - The Kinetic-Molecular Theory
- Diffusion and Effusion of Gases
- Real Gases Deviations from Ideality

Comparison of Solids, Liquids, and Gases

- The density of gases is much less than that of

solids or liquids.

Densities (g/mL) Solid Liquid Gas

H2O 0.917 0.998 0.000588

CCl4 1.70 1.59 0.00503

- Gas molecules must be very far apart compared to

liquids and solids.

Composition of the Atmosphere and Some Common

Properties of Gases

Composition of Dry Air

Gas by Volume

N2 78.09

O2 20.94

Ar 0.93

CO2 0.03

He, Ne, Kr, Xe 0.002

CH4 0.00015

H2 0.00005

Pressure

- Pressure is force per unit area.
- lb/in2
- N/m2
- Gas pressure as most people think of it.

Pressure

- Atmospheric pressure is measured using a

barometer. - Definitions of standard pressure
- 76 cm Hg
- 760 mm Hg
- 760 torr
- 1 atmosphere
- 101.3 kPa

Hg density 13.6 g/mL

Boyles Law The Volume-Pressure Relationship

- V ? 1/P or
- V k (1/P) or PV k
- P1V1 k1 for one sample of a gas.
- P2V2 k2 for a second sample of a gas.
- k1 k2 for the same sample of a gas at the same

T. - Thus we can write Boyles Law mathematically as

P1V1 P2V2

Boyles Law The Volume-Pressure Relationship

- Example 12-1 At 25oC a sample of He has a volume

of 4.00 x 102 mL under a pressure of 7.60 x 102

torr. What volume would it occupy under a

pressure of 2.00 atm at the same T?

Boyles Law The Volume-Pressure Relationship

- Notice that in Boyles law we can use any

pressure or volume units as long as we

consistently use the same units for both P1 and

P2 or V1 and V2. - Use your intuition to help you decide if the

volume will go up or down as the pressure is

changed and vice versa.

Charles Law The Volume-Temperature

Relationship The Absolute Temperature Scale

absolute zero -273.15 0C

Charles Law The Volume-Temperature

Relationship The Absolute Temperature Scale

- Charless law states that the volume of a gas is

directly proportional to the absolute temperature

at constant pressure. - Gas laws must use the Kelvin scale to be correct.
- Relationship between Kelvin and centigrade.

Charles Law The Volume-Temperature

Relationship The Absolute Temperature Scale

- Mathematical form of Charles law.

Charles Law The Volume-Temperature

Relationship The Absolute Temperature Scale

- Example 12-2 A sample of hydrogen, H2, occupies

1.00 x 102 mL at 25.0oC and 1.00 atm. What

volume would it occupy at 50.0oC under the same

pressure? - T1 25 273 298
- T2 50 273 323

Standard Temperature and Pressure

- Standard temperature and pressure is given the

symbol STP. - It is a reference point for some gas

calculations. - Standard P ? 1.00000 atm or 101.3 kPa
- Standard T ? 273.15 K or 0.00oC

The Combined Gas Law Equation

- Boyles and Charles Laws combined into one

statement is called the combined gas law

equation. - Useful when the V, T, and P of a gas are changing.

The Combined Gas Law Equation

- Example 12-3 A sample of nitrogen gas, N2,

occupies 7.50 x 102 mL at 75.00C under a pressure

of 8.10 x 102 torr. What volume would it occupy

at STP?

The Combined Gas Law Equation

- Example 12-4 A sample of methane, CH4, occupies

2.60 x 102 mL at 32oC under a pressure of 0.500

atm. At what temperature would it occupy 5.00 x

102 mL under a pressure of 1.20 x 103 torr? - You do it!

The Combined Gas Law Equation

Avogadros Law and the Standard Molar Volume

Avogadros Law and the Standard Molar Volume

- Avogadros Law states that at the same

temperature and pressure, equal volumes of two

gases contain the same number of molecules (or

moles) of gas. - If we set the temperature and pressure for any

gas to be STP, then one mole of that gas has a

volume called the standard molar volume. - The standard molar volume is 22.4 L at STP.
- This is another way to measure moles.
- For gases, the volume is proportional to the

number of moles. - 11.2 L of a gas at STP 0.500 mole
- 44.8 L ? moles

Avogadros Law and the Standard Molar Volume

- Example 12-5 One mole of a gas occupies 36.5 L

and its density is 1.36 g/L at a given

temperature and pressure. (a) What is its molar

mass? (b) What is its density at STP?

Summary of Gas Laws The Ideal Gas Law

- Boyles Law - V ? 1/P (at constant T n)
- Charles Law V ? T (at constant P n)
- Avogadros Law V ? n (at constant T P)
- Combine these three laws into one statement
- V ? nT/P
- Convert the proportionality into an equality.
- V nRT/P
- This provides the Ideal Gas Law.
- PV nRT
- R is a proportionality constant called the

universal gas constant.

Summary of Gas Laws The Ideal Gas Law

- We must determine the value of R.
- Recognize that for one mole of a gas at 1.00 atm,

and 273 K (STP), the volume is 22.4 L. - Use these values in the ideal gas law.

Summary of Gas Laws The Ideal Gas Law

- R has other values if the units are changed.
- R 8.314 J/mol K
- Use this value in thermodynamics.
- R 8.314 kg m2/s2 K mol
- Use this later in this chapter for gas

velocities. - R 8.314 dm3 kPa/K mol
- This is R in all metric units.
- R 1.987 cal/K mol
- This the value of R in calories rather than J.

Summary of Gas Laws The Ideal Gas Law

- Example 12-6 What volume would 50.0 g of ethane,

C2H6, occupy at 1.40 x 102 oC under a pressure of

1.82 x 103 torr? - To use the ideal gas law correctly, it is very

important that all of your values be in the

correct units! - T 140 273 413 K
- P 1820 torr (1 atm/760 torr) 2.39 atm
- 50 g (1 mol/30 g) 1.67 mol

Summary of Gas Laws The Ideal Gas Law

Summary of Gas Laws The Ideal Gas Law

- Example 12-7 Calculate the number of moles in,

and the mass of, an 8.96 L sample of methane,

CH4, measured at standard conditions. - You do it!

Summary of Gas Laws The Ideal Gas Law

Summary of Gas Laws The Ideal Gas Law

- Example 12-8 Calculate the pressure exerted by

50.0 g of ethane, C2H6, in a 25.0 L container at

25.0oC. - You do it!

Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances

- Example 12-9 A compound that contains only

carbon and hydrogen is 80.0 carbon and 20.0

hydrogen by mass. At STP, 546 mL of the gas has

a mass of 0.732 g . What is the molecular (true)

formula for the compound? - 100 g of compound contains 80 g of C and 20 g of

H.

Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances

Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances

Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances

- Example 12-10 A 1.74 g sample of a compound that

contains only carbon and hydrogen contains 1.44 g

of carbon and 0.300 g of hydrogen. At STP 101 mL

of the gas has a mass of 0.262 gram. What is its

molecular formula? - You do it!

Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances

Determination of Molecular Weights and Molecular

Formulas of Gaseous Substances

Daltons Law of Partial Pressures

- Daltons law states that the pressure exerted by

a mixture of gases is the sum of the partial

pressures of the individual gases. - Ptotal PA PB PC .....

Daltons Law of Partial Pressures

- Example 12-11 If 1.00 x 102 mL of hydrogen,

measured at 25.0 oC and 3.00 atm pressure, and

1.00 x 102 mL of oxygen, measured at 25.0 oC and

2.00 atm pressure, were forced into one of the

containers at 25.0 oC, what would be the pressure

of the mixture of gases?

Daltons Law of Partial Pressures

- Vapor Pressure is the pressure exerted by a

substances vapor over the substances liquid at

equilibrium.

Daltons Law of Partial Pressures

- Example 12-12 A sample of hydrogen was collected

by displacement of water at 25.0 oC. The

atmospheric pressure was 748 torr. What pressure

would the dry hydrogen exert in the same

container?

Daltons Law of Partial Pressures

- Example 12-13 A sample of oxygen was collected

by displacement of water. The oxygen occupied

742 mL at 27.0 oC. The barometric pressure was

753 torr. What volume would the dry oxygen

occupy at STP? - You do it!

Daltons Law of Partial Pressures

Mass-Volume Relationships in Reactions Involving

Gases

Mass-Volume Relationships in Reactions Involving

Gases

- In this section we are looking at reaction

stoichiometry, like in Chapter 3, just including

gases in the calculations.

- 2 mol KClO3 yields 2 mol KCl and 3 mol O2
- 2(122.6g) yields 2 (74.6g) and 3

(32.0g) - Those 3 moles of O2 can also be thought of as
- 3(22.4L) or 67.2 L at STP

Mass-Volume Relationships in Reactions Involving

Gases

- Example 12-14 What volume of oxygen measured at

STP, can be produced by the thermal decomposition

of 120.0 g of KClO3? - You do it!

Mass-Volume Relationships in Reactions Involving

Gases

The Kinetic-Molecular Theory

- The basic assumptions of kinetic-molecular theory

are - Postulate 1
- Gases consist of discrete molecules that are

relatively far apart. - Gases have few intermolecular attractions.
- The volume of individual molecules is very small

compared to the gass volume. - Proof - Gases are easily compressible.

The Kinetic-Molecular Theory

- Postulate 2
- Gas molecules are in constant, random, straight

line motion with varying velocities. - Proof - Brownian motion displays molecular motion.

The Kinetic-Molecular Theory

- Postulate 3
- Gas molecules have elastic collisions with

themselves and the container. - Total energy is conserved during a collision.
- Proof - A sealed, confined gas exhibits no

pressure drop over time.

The Kinetic-Molecular Theory

- Postulate 4
- The kinetic energy of the molecules is

proportional to the absolute temperature. - The average kinetic energies of molecules of

different gases are equal at a given temperature. - Proof - Brownian motion increases as temperature

increases.

The Kinetic-Molecular Theory

- The kinetic energy of the molecules is

proportional to the absolute temperature. The

kinetic energy of the molecules is proportional

to the absolute temperature. - Displayed in a Maxwellian distribution.

The Kinetic-Molecular Theory

- The gas laws that we have looked at earlier in

this chapter are proofs that kinetic-molecular

theory is the basis of gaseous behavior. - Boyles Law
- P ? 1/V
- As the V increases the molecular collisions with

container walls decrease and the P decreases. - Daltons Law
- Ptotal PA PB PC .....
- Because gases have few intermolecular

attractions, their pressures are independent of

other gases in the container. - Charles Law
- V ? T
- An increase in temperature raises the molecular

velocities, thus the V increases to keep the P

constant.

The Kinetic-Molecular Theory

The Kinetic-Molecular Theory

- The root-mean square velocity of gases is a very

close approximation to the average gas velocity. - Calculating the root-mean square velocity is

simple

- To calculate this correctly
- The value of R 8.314 kg m2/s2 K mol
- And M must be in kg/mol.

The Kinetic-Molecular Theory

- Example 12-17 What is the root mean square

velocity of N2 molecules at room T, 25.0oC?

The Kinetic-Molecular Theory

- Example 12-18 What is the root mean square

velocity of He atoms at room T, 25.0oC? - You do it!

The Kinetic-Molecular Theory

- Can you think of a physical situation that proves

He molecules have a velocity that is so much

greater than N2 molecules? - What happens to your voice when you breathe He?

Diffusion and Effusion of Gases

- Diffusion is the intermingling of gases.
- Effusion is the escape of gases through tiny

holes.

Diffusion and Effusion of Gases

- This is a demonstration of diffusion.

Diffusion and Effusion of Gases

- The rate of effusion is inversely proportional to

the square roots of the molecular weights or

densities.

Diffusion and Effusion of Gases

- Example 12-15 Calculate the ratio of the rate of

effusion of He to that of sulfur dioxide, SO2, at

the same temperature and pressure.

Diffusion and Effusion of Gases

- Example 12-16 A sample of hydrogen, H2, was

found to effuse through a pinhole 5.2 times as

rapidly as the same volume of unknown gas (at the

same temperature and pressure). What is the

molecular weight of the unknown gas? - You do it!

Real Gases Deviations from Ideality

- Real gases behave ideally at ordinary

temperatures and pressures. - At low temperatures and high pressures real gases

do not behave ideally. - The reasons for the deviations from ideality are
- The molecules are very close to one another, thus

their volume is important. - The molecular interactions also become important.

Real Gases Deviations from Ideality

- van der Waals equation accounts for the behavior

of real gases at low temperatures and high

pressures.

- The van der Waals constants a and b take into

account two things - a accounts for intermolecular attraction
- b accounts for volume of gas molecules
- At large volumes a and b are relatively small and

van der Waals equation reduces to ideal gas law

at high temperatures and low pressures.

Real Gases Deviations from Ideality

- What are the intermolecular forces in gases that

cause them to deviate from ideality? - For nonpolar gases the attractive forces are

London Forces - For polar gases the attractive forces are

dipole-dipole attractions or hydrogen bonds.

Real Gases Deviations from Ideality

- Example 12-19 Calculate the pressure exerted by

84.0 g of ammonia, NH3, in a 5.00 L container at

200. oC using the ideal gas law. - You do it!

Real Gases Deviations from Ideality

- Example 12-20 Solve Example 12-19 using the van

der Waals equation.

Real Gases Deviations from Ideality

Synthesis Question

- The lethal dose for hydrogen sulfide is 6.0 ppm.

In other words, if in 1 million molecules of air

there are six hydrogen sulfide molecules then

that air would be deadly to breathe. How many

hydrogen sulfide molecules would be required to

reach the lethal dose in a room that is 77 feet

long, 62 feet wide and 50. feet tall at 1.0 atm

and 25.0 oC?

Synthesis Question

Synthesis Question

Group Question

- Tires on a car are typically filled to a pressure

of 35 psi at 3.00 x 102 K. A tire is 16 inches

in radius and 8.0 inches in thickness. The wheel

that the tire is mounted on is 6.0 inches in

radius. What is the mass of the air in the tire?

End of Chapter 12

- Gases are the simplest state of matter.
- Liquids and solids are more complex.
- They are the subject of Chapter 13.