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Chapter 8Gases

- The Gas Laws of Boyle, Charles and Avogadro
- The Ideal Gas Law
- Gas Stoichiometry
- Daltons Laws of Partial Pressure
- The Kinetic Molecular Theory of Gases
- Effusion and Diffusion
- Collisions of Gas Particles with the Container

Walls - Intermolecular Collisions
- Real Gases
- Chemistry in the Atmosphere

States of Matter

Solid Liquid Gas We start with gases because

they are simpler than the others.

Pressure (force/area, PaN/m2) A pressure of

101.325 kPa is need to raise the column of Hg 76

cm (760 mm). standard pressure 760 mm Hg 760

torr 1 atm 101.325 kPa

P1V1 P2V2 (fixed T,n)

Boyles Law

V x P const

1662

Charles Law

V1 / V2 T1 / T2 (fixed P,n)

V / T const

1787

V / n const

(fixed P,T)

Avogadro

1811

n number of moles

Boyles Law Pressure and Volume

The product of the pressure and volume, PV, of a

sample of gas is a constant at a constant

temperature PV k Constant (fixed T,n)

Boyles Law The Effect of Pressure on Gas Volume

Example The cylinder of a bicycle pump has a

volume of 1131 cm3 and is filled with air at a

pressure of 1.02 atm. The outlet valve is sealed

shut, and the pump handle is pushed down until

the volume of the air is 517 cm3. The

temperature of the air trapped inside does not

change. Compute the pressure inside the pump.

Charles Law T vs V

At constant pressure, the volume of a sample of

gas is a linear function of its temperature. V

bT

T(C) 273C(V/Vo)

When V0, T-273C

Charles Law T vs V

The Absolute Temperature Scale

Kelvin temperature scale

T (Kelvin) 273.15 t (Celsius)

Gas volume is proportional to Temp

Charles Law The Effect of Temperature on Gas

Volume

V vs T

V1 / V2 T1 / T2 (at a fixed pressure and for

a fixed amount of gas)

- Avogadros law (1811)
- V an
- n number of moles of gas
- a proportionality constant
- For a gas at constant temperature and pressure

the volume is directly proportional to the number

of moles of gas.

P1V1 P2V2 (at a fixed temperature)

Boyles Law

V kP -1

Charles Law

V1 / V2 T1 / T2 (at a fixed pressure)

V bT

(at a fixed pressure and temperature)

V an

Avogadro

n number of moles

PV nRT ideal gas law

an empirical law

V nRTP-1

Example At some point during its ascent, a sealed

weather balloon initially filled with helium at a

fixed volume of 1.0 x 104 L at 1.00 atm and 30oC

reaches an altitude at which the temperature is

-10oC yet the volume is unchanged. Calculate the

pressure at that altitude .

n1 n2

V1 V2

P2 P1T2/T1 (1 atm)(263K)/(303K)

STP (Standard Temperature and Pressure)

For 1 mole of a perfect gas at OC (273K) (i.e.,

32.0 g of O2 28.0 g N2 2.02 g H2)

nRT 22.4 L atm PV

At 1 atm, V 22.4 L

STP standard temperature and pressure 273 K

(0o C) and 1 atm

PV nRT

The Ideal Gas Law

What is R, universal gas constant?

the R is independent of the particular gas studied

PV nRT ideal gas law constants

Example What mass of Hydrogen gas is needed to

fill a weather balloon to a volume of 10,000 L,

1.00 atm and 30 C?

1) Use PV nRT nPV/RT. 2) Find the number of

moles. 3) Use the atomic weight to find the mass.

Example What mass of Hydrogen gas is needed to

fill a weather balloon to a volume of 10,000 L,

1.00 atm and 30 C?

n PV/RT (1 atm) (10,000 L) (293 K)-1 (0.082

L atm mol-1 K-1)-1 416 mol (416 mol)(1.0 g

mol-1) 416 g

Use volumes to determine stoichiometry.

Gas Stoichiometry

The volume of a gas is easier to measure than the

mass.

Gas Density and Molar Mass

Gas Density and Molar Mass

Example Calculate the density of gaseous hydrogen

at a pressure of 1.32 atm and a temperature of

-45oC.

Example Fluorocarbons are compounds containing

fluorine and carbon. A 45.6 g sample of a

gaseous fluorocarbon contains 7.94 g of carbon

and 37.7 g of fluorine and occupies 7.40 L at STP

(P 1.00 atm and T 273 K). Determine the

molecular weight of the fluorocarbon and give its

molecular formula.

Example Fluorocarbons are compounds of fluorine

and carbon. A 45.60 g sample of a gaseous

fluorocarbon contains 7.94 g of carbon and 37.66

g of fluorine and occupies 7.40 L at STP (P

1.00 atm and T 273.15 K). Determine the

approximate molar mass of the fluorocarbon and

give its molecular formula.

Mixtures of Gases

Daltons Law of Partial Pressures The total

pressure of a mixture of gases equals the sum of

the partial pressures of the individual gases.

Mole Fractions and Partial Pressures

The mole fraction of a component in a mixture is

define as the number of moles of the components

that are in the mixture divided by the total

number of moles present.

Example A solid hydrocarbon is burned in air in a

closed container, producing a mixture of gases

having a total pressure of 3.34 atm. Analysis of

the mixture shows it to contain 0.340 g of water

vapor, 0.792 g of carbon dioxide, 0.288 g of

oxygen, 3.790 g of nitrogen, and no other gases.

Calculate the mole fraction and partial pressure

of carbon dioxide in this mixture.

2NH4ClO4 (s) ? N2(g) Cl2 (g) 2O2 (g) 4 H2

(g)

The Kinetic Molecular Theory of Gases

- The Ideal Gas Law is an empirical relationship

based on experimental observations. - Boyle, Charles and Avogadro.
- Kinetic Molecular Theory is a simple model that

attempts to explain the behavior of gases.

The Kinetic Molecular Theory of Gases

1. A pure gas consists of a large number of

identical molecules separated by distances that

are large compared with their size. The volumes

of the individual particles can be assumed to be

negligible (zero).

2. The molecules of a gas are constantly moving

in random directions with a distribution of

speeds. The collisions of the particles with the

walls of the container are the cause of the

pressure exerted by the gas.

3. The molecules of a gas exert no forces on one

another except during collisions, so that between

collisions they move in straight lines with

constant velocities. The gases are assumed to

neither attract or repel each other. The

collisions of the molecules with each other and

with the walls of the container are elastic no

energy is lost during a collision.

4. The average kinetic energy of a collection of

gas particles is assumed to be directly

proportional to the Kelvin temperature of the gas.

Pressure and Molecular Motion

Pressure ? (impulse per collision) x (frequency

of collisions with the walls)

- frequency of collisions
- ? speed of molecules (u)

- impulse per collision
- ? momentum (m u)

- frequency of collisions
- ? number of molecules per unit

volume (N/V)

P ? (m u) (N/V) u

Pressure and Molecular Motion

P ? (m u) (N/V) u

PV ? Nmu2

Correction The molecules have a distribution of

speeds.

Mean-square speed of all molecules

Pressure and Molecular Motion

Make some substitutions

- 1/2m kinetic energy (KEave) of one

molecule. - KE is proportional to T (KEave RT)
- Divide by 3 (3 dimensions)
- N nNa (molecules moles x molecules/mole)

The Kinetic Molecular Theory of Gases

Speed Distribution

Temperature is a measure of the average kinetic

energy of gas molecules.

Velocity Distributions Distribution of Molecular

Speeds

ump uavg urms 1.000 1.128 1.225

Example

At a certain speed, the root-mean-square-speed

of the molecules of hydrogen in a sample of gas

is 1055 ms-1. Compute the root-mean square speed

of molecules of oxygen at the same temperature.

- Strategy
- Find T for the H2 gas with a urms 1055 ms-1

2. Find urms of O2 at the same temperature

H2 about 4 times velocity of O2

Gaseous Diffusion and Effusion

Diffusion mixing of Gases

e.g., NH3 and HCl

Effusion rate of passage of a gas through a tiny

orifice in a chamber.

Example A gas mixture contains equal numbers of

molecules of N2 and SF6. A small portion of it is

passed through a gaseous diffusion apparatus.

Calculate how many molecules of N2 are present in

the product of gas for every 100 molecules of SF6.

Real Gases

- Ideal Gas behavior is generally conditions of low

pressure and high temperature

Real Gases

- Kinetic Molecular Theory model
- assumed no interactions between gas particles and

- no volume for the gas particles
- 1873 Johannes van der Waals
- Correction for attractive forces in gases (and

liquids) - Correction for volume of the molecules

Pcorrected Vcorrected nRT

The Person Behind the Science

Johannes van der Waals (1837-1923)

- Highlights
- 1873 first to realize the necessity of taking

into account the volumes of molecules and - intermolecular forces (now generally called "van

der Waals forces") in establishing the

relationship between the pressure, volume and

temperature of gases and liquids. - Moments in a Life
- 1910 awarded Nobel Prize in Physics

- Significant Figures
- Zeros that follow the last non-zero digit

sometimes are counted. - E.g., for 700 g, the zeros may or not be

significant. - They may present solely to position the decimal

point - But also may be intended to convey the precision

of the measurement. - The uncertainty in the measurement is on the

order of /- 1 g or /- 10g or perhaps /- 100 g - It is impossible to tell which without further

information. - If you need 2 sig figs and want to write 40 use

either - Four zero decimal point 40. or
- 4.0 x 101

The Person Behind the Science

Lord Kelvin (William Thomson) 1824-1907

When you can measure what you are speaking

about and express it in numbers, you know

something about it but when you cannot measure

it, when you cannot express it in numbers, you

knowledge is of a meager and unsatisfactory kind

it may be the beginning of knowledge but you

have scarcely, in your thoughts advanced to the

stage of science, whatever the matter may be.

Lecture to the Institution of Civil

Engineers, 3 May 1883

The Person Behind the Science

Evangelista Torricelli (1608-1647)

- Highlights
- In 1641, moved to Florence to assist the

astronomer Galileo. - Designed first barometer
- It was Galileo that suggested Evangelista

Torricelli use mercury in his vacuum experiments.

- Torricelli filled a four-foot long glass tube

with mercury and inverted the tube into a dish. - Moments in a Life
- Succeed Galileo as professor of mathematics in

the University of Pisa. - Asteroid (7437) Torricelli named in his honor

Barometer P g x d x h