Chapter 13 “Gases”

What are the properties of gases?

Chapt. 13 OBJECTIVESDescribe gas behavior & explain how the Kinetic-Molecular (K-M) Theory accounts for it.Explain what ‘gas pressure’ means & describe

how it is measured.State the “Gas Laws” and use them to solve

problems.Understand the significance of the “Ideal Gas

Law.”Compare ideal & real gases.Relate gas density to temperature and molar

mass.

What are the Physical Properties of Gases?

Gases have mass.It is easy to compress gases.Gases fill their containers completely.Different gases quickly move through each

other. (This mixing is called diffusion.)Gases exert pressure.The pressure of a gas depends on its

temperature.

How do we explain gas behavior?

Gas properties are explained by a model, called the kinetic-molecular model, that describes the behavior of the subatomic particles that make up a gas.

This is known as “The Kinetic Molecular Theory” or “K-M” Theory.

The Kinetic-Molecular (K-M) Theory Gases are composed of very small particles (atoms or

molecules) having mass. Gas particles have low volume, but are spaced widely,

with lots of empty space between them, making gases easy to compress.

There is no attraction or repulsion among the gas particles.

Gas particles move in constant, rapid, random motion, so a gas has no definite shape, but it fills its container completely.

The gas particles travel in short straight lines, with each particle moving independently.

When colliding with walls, other particles, etc., the gas particles rebound elastically, so the total kinetic energy (KE) is constant at a given temperature.

The average kinetic energy of the molecules of a gas is proportional to the temperature of the gas in kelvins.

13-2 Measuring GasesTo completely describe a gas sample and

to make predictions about its behavior under new conditions, we must deal with four variables: Amount of gas (n, in moles)

• n = mass/molar mass = m(g)/M(g/mol) Volume of gas (V, in liters)

• 1 L = 1000mL = 1000 cm3

Temperature (T, in kelvins)• T(K) = T(°C) + 273

Pressure (P, in atm, torr, kPa, etc.)

How to Measure PressurePressure is the force exerted by gas particles on

the walls of the container.Pressure = force/area (newtons/meter2 =

pascals)Atmospheric pressure results from the mass of

the air being attracted by the Earth’s gravity.

Conversions: 1 atmosphere (atm) = 101.3 kPa 1 atmosphere = 760 mm Hg (same as torr) 1 atmosphere = 14.70 lb/in2 (See Fig. 13-12, pg 426 for inter-conversions.)

Tools for Measuring PressureBarometer

Atmospheric pressure used to predict the weatherPressure gauge

Tire pressure gauges or gas cylinder regulatorsManometer

Laboratory tools for working with gases in closed space Examples: reading manometers

Do you remember STP? STP = Standard Temperature & Pressure STP = 273 K (0°C) & 1 atm (760 torr, etc.) It is important for measuring gas properties.

13-3 The Gas Laws (1)What happens when you put pressure on a gas?

Examples: Small balloon being squeezed, books piled on a small cylinder.

Robert Boyle (1600s) studied the effect of pressure (P) on the volume (V) of a gas.

Worksheet class activity What is the relationship between V and P?

Boyle’s Law: The pressure and volume of a sample of gas are inversely proportional to each other at constant temperature.

Boyle’s Law

Sample Data for Boyle's Law

0

20

40

60

0 50 100 150

Volume (cubic inches)

Pre

ssu

re (

inch

es

Hg

)

13-3 The Gas Laws (2)

What happens when you change the temperature of a gas? Examples: Hot air balloon inflating, automobile tires in

very cold weather.Jacques Charles (1700s) studied the effect of

temperature (T) on the volume (V) of a gas.Worksheet class activity

What is the relationship between V and T?

Charles’ Law: The volume of a sample of gas is directly proportional to the kelvin temperature at constant pressure.

Lab Activity: Predicting Absolute Zero

Charles’ Law

Data for Charles' Law

0

1

2

3

4

5

6

0 100 200 300 400 500 600 700

Temperature (kelvins)

Vo

lum

e (l

iter

s)

13-3 The Gas Laws (3)What happens to pressure of a fixed volume of

gas if you change the temperature? Example: “Empty” aerosol can thrown into an

incinerator. (Read the warning on the label!)Gay-Lussac (1700s) studied the effect of

pressure (P) and temperature (T) on a fixed volume (V) of gas.

Worksheet class activity What relationship do you see between P and T?

Gay-Lussac’s Law: The pressure and temperature of a fixed volume of gas are directly proportional to each other.

Gay-Lussac’s Law

Data for Gay-Lussac's Law

0

2

4

6

0 200 400 600 800

Temperature (kelvins)

Pre

ssu

re (

nn

Hg

)

13-3 The Gas Laws (4)How is the number of gas particles related to its

volume under constant conditions? Examples: Two balloons of different size.

Amedeo Avogadro (1800s) studied different gases to determine the relationship between the number of gas particles and the volume at a given pressure (P) and temperature (T).

Worksheet class activity What is the relationship between V and n?

Avogadro’s Law: Equal volumes of gases at the same pressure and temperature contain an equal number of particles.

Avogadro’s Law

Equal volumes of different gases have the samenumber of particles under the same conditions.

13-3 The Gas Laws (Combined)These Gas Laws seem complicated, but fortunately we

can simplify things by combining the relationships into two

simple expressions, the one first being:

P1V1 =P2V2

T1 T2

This equation is used to solve “Combined Gas Law” problems, by simply“plugging in” the numbers!

Just remember two things:“Go Kelvin!” (Convert temperature to kelvins.)Be sure all units are consistent for P and V.

13-3 The Gas Laws (5) Another relationship about gases was proposed by John

Dalton. (Remember him? Why?) He proposed that gas particles in a mixture of gases act

independently to exert pressure on the container. Each gas in the mixture exerts the same pressure that it would if it

was alone in the container. This proposal was made before the Kinetic Molecular Theory was

developed, so he didn’t really have its ideas to help him.

Dalton’s Law of Partial Pressure: the sum of the partial pressures of all components of a gas mixture is equal to the total pressure of the gas mixture, or...

PT = P1 + P2 + P3 + .…. See sample problems.

13-4 The “Ideal Gas Law”

The second equation that may be derived from the various gas laws is the “Ideal Gas Equation” ---

PV = nRT

This describes the relationship among the four variables (P,V,n,T) of an ideal gas, where R is the gas constant. R = 0.0821 atm-L/mol-K R = 8.314 Pa-m3/mol-K R = 8.314 J/mol-K

Problems may be solved by simple substitution, but be careful to use consistent units.

But what is an “Idea Gas”?

Ideal Gas: one that is described by the postulates of the Kinetic-Molecular Theory.

No such gases exist! The gases we encounter are “real” – not “ideal”!

However, most gases behave like ideal gases under ordinary conditions of temperature and pressure. At low temperature and high pressure real

gases behave in non-ideal ways. (Why is this so? See the next slide!)

Deviations from Ideal Gas Behavior Occur Because:Kinetic-Molecular Theory makes two simplifying,

but WRONG, assumptions: Gas particles have no volume of their own. Gas particles have no attraction for each other.

But, as pressure increases… gas particles get closer together. At very high pressure, the volume of the gas particles

themselves become a significant part of the total volume, contrary to K-M Theory.

As temperature decreases… gas particles slow down. At very low temperature, attractive forces between

gas particles become significant, contrary to K-M Theory.

Nevertheless…

K-M Theory is valid for studying gas behavior under ordinary conditions.

We are safe to use the Ideal Gas Equation (PV = nRT) to solve problems for real gases, except at low temperature and high pressure conditions where gases start to behave in a non-ideal manner.

13-5 How Gases Work: Lift

Lifting Power This is the result of low density of a gas,

but the density must be lower than that of the air.

Low molar mass gases (H2, He, NH3, CH4) may be used to gain lift.

Or the gas, usually air, may be heated. Higher mass gases (CO2, Kr) are too

dense, so they sink in air.• Can have disastrous effects.

13-5 How Gases Work: Effusion

Effusion Related to ‘diffusion’ (one gas moving through

another). Effusion is the gas movement through a tiny hole

one particle at a time. Small, light gases have greater speeds than large,

heavy gases at a given temperature, so they effuse faster.

Graham’s Law of Effusion relates effusion to mass.

Graham’s Law of Effusion

Gases will effuse at a rate that is inversely proportional to the square root of the Molecular Masses, MMx, or:

rate1

rate2

= √MM2

MM1

See worksheet problems.

Did we meet the Chapt. 13 OBJECTIVES?Describe gas behavior & explain how the Kinetic-Molecular Theory accounts for it.Explain what ‘gas pressure’ means & describe

how it is measured.State the “Gas Laws” and use them to solve

problems.Understand the significance of the “Ideal Gas

Law.”Compare ideal & real gases.Relate gas density to temperature and molar

mass.

Gases are Fun!

The Kinetic-Molecular (K-M) Theory (A) A gas consists of very small particles having mass. The distances separating gas particles are very large

compared to the size of the particles. (The volume of the gas particles themselves are negligible compared with the total volume of gas.)

Gas particles exert no attractive force on each other. Gas particles are in constant, rapid, random motion. Collisions of gas particles with each other or the walls

of the container are perfectly elastic. The average kinetic energy of gas particles is

proportional to the kelvin temperature of the gas.