Gases are defined by:◦The particles are free to move (fluid).◦The particles are far apart.◦The particles move very fast.◦The particles have no attraction nor

repulsion for each other.◦The fact that they have no definite shape

or volume – they take the shape of the container.

◦The fact that they are compressible.

Ch. 5 Gases

Gases have four measurable variables.1. Pressure (P) of a gas.

◦ Measured in a variety of units like mmHg, atm, Pascals, torr, bars, and psi.

2. Volume (V) of a gas,◦ Measured in mL or L.

3. Temperature (T) of a gas.◦ Measured in Celsius or Kelvin.◦ For all formulas, Kelvin temperatures must be used.

4. Quantity of a gas.◦ Measured in grams or moles (n).◦ Formulas will require moles.

Variables

Pressure

Pressure is the force per unit area. As the molecules of a gas collide with the walls,

they exert a force.

ForcePressure =

Area

The column of air above us exerts a force due to the gravitational force.

Atmospheric pressure has two main variables. What are they?

Atmospheric Pressure

A barometer is used to measure pressure.

A dish is filled with liquid mercury.

A glass tube that has been evacuated of all air molecules is then placed into the pool of mercury.

Atmospheric Pressure

The height of the mercury in the tube over the pool of mercury is measured with a ruler.

In weather, it is reported as inches of mercury – inHg.

We will measure ours in millimeters of mercury – mmHg.

On an average day, at sea level – the column would measure 760mmHg = 1 atmosphere (atm).

Atmospheric Pressure

As altitude increases, the pressure decreases.

Denver, CO Death Valley, CA

Atmospheric Pressure

Look at the relationship between two of the four variables.

Boyle’s, Charles’, and Gay-Lussac’s Laws. Direct (linear) relationship – as one variable

increase, so does the other. Inverse relationship – as one variable

increase, the other decreases.

Empirical Gas Laws

Allows P and V to vary, while n and T are constant.

Boyle found that as P , the V and vice versa.

What type of relationship – Direct or Inverse?

P x V = constant Formula: P1V1 = P2V2

LEP #1

Boyle’s Law

Pressure vs. Volume

0.00

1.00

2.00

3.00

4.00

5.00

0.00 10.00 20.00 30.00

Volume, mL

Pre

ssu

re,

atm

Graph

Charles’ Law

Allows V and T to vary, while n and P are constant.

Charles’ found that as V , the T . What type of relationship – Direct or Inverse?

Formula:

LEP #2

V = constant, when T is in Kelvin

T

1 2

1 2

V V =

T T

GraphVolume vs. Temperature

0

200

400

600

0 100 200 300 400

Temperature (K)

Vo

lum

e (m

l)

Allows P and T to vary, while n and V are constant.

Gay-Lussac found that as P , the T . Direct or Inverse? Formula? LEP #3

Gay-Lussac’s Law

Combined Gas Law

All three empirical gas laws can be merged into a single formula.

This means that two of the three variables can be changed.

LEP #4

1 1 2 2

1 2

P V P V =

T T

The quantity of a gas (moles) and volume are proportional.

STP = standard temperature (0oC) and pressure (1 atm).

At STP, one mole of any gas will occupy 22.4L.

LEP #5

Avogadro’s Relationship

The relationship between ALL four variables is found in the ideal gas law.

Formula: PV = nRT. R is called the gas law constant and equals

0.08206 L atm / mol K. Because of the units, each of the variables

must be in the same units! LEP #6

Ideal Gas Law

Other derived versions of the ideal gas law can be useful.

Since moles = grams (g) / molar mass (MW),

Ideal Gas Law

PV

gRT MW

Density is grams / volume, so we can include this in our formula as well.

LEP #7 LEP #8

Ideal Gas Law

P

DRT MW

Many reactions generate a gas as a product. Grams of solid or liquid must be converted

to moles of gas. Ex) 2 KClO3(s) 2 KCl(s) + 3 O2(g)

In this example, when 2 moles of KClO3 decompose, 3 moles of O2 gas are generated.

LEP #8

Stoichiometry and Gases

Explosives like dynamite, TNT, nitroglycerin, etc. are compounds that produce mostly gases when allowed to react.

Unlike hydrocarbons, most explosives _________ rather than burn.

A ____________ is a very rapid chemical reaction using oxygen that is contained in the material rather than in the air.

Explosives

Explosives

2 C7H5N3O6 → 3 N2 + 5 H2O + 7 CO + 7 C

TNT

CH3

O2N

NO2

NO2

Ammonium nitrate / fuel oil is commonly used in mining.

It was also used in the bombing of the Murrah building in Oklahoma City.

LEP #10

ANFO

Many gases we encounter are mixtures of two or more substances.

The total pressure exerted by a mixture is equal to the partial pressures of each of the gases.

Ptotal = Pa + Pb + Pc + … The partial pressure of a gas is proportional

to its mole fraction. Pa = Ptotal ca. LEP #11, #12

Dalton’s Law

In the study of gases, five postulates describing them were published by Rudolf Clausius in 1857.

1. Gases consist of large numbers of molecules that are in continuous, random motion.

◦ Pressure is uniform on any surface.

Kinetic Molecular Theory

2. The volume occupied by the molecules is negligible when compared to the volume of the container.

◦ A 5.0L container is assumed to be the volume even though the gas molecules must occupy some of that space.

3. Attractive and repulsive forces between gas molecules are negligible.

Kinetic Molecular Theory

4. Collisions of gas molecules are elastic. Energy can be transferred between molecules, but cannot be lost.

5. The average kinetic energy of a gas is proportional to the temperature of the gas.

Kinetic Molecular Theory

KE of a Gas

This is an approximation of the average speed of a gas molecule.

LEP #13

Root-mean-square Velocity

mM

3RT u

All gases deviate from “ideal” behavior under different conditions.

At higher pressures, gas molecules do occupy a portion of the volume.

Real Gases

At low temperatures, gas molecules can have attractive forces for each other.

Both of these factors can be corrected for in the van der Waals equation.

Real Gases

nRT nb - VV

an P

2

2

Real Gases