Gases: Properties and

Behaviour

Gas Laws

Partial Pressures

Kinetic Theory and Ideal Gases

Real Gases

Diffusion and Effusion

Learning objectives

Describe properties of gases and define ideal gas

Describe the physical basis for pressure

Identify units of pressure and convert between

units

Describe and apply the main gas laws

Apply gas laws to stoichiometric problems

Describe and apply law of partial pressures

Features of gases

Gases are always miscible

Gases are compressible

Gases exert pressure

Gases are mostly nothing: less than 0.1 % of the

volume is occupied by molecules (contrast 70 %

for solids and liquids)

The ideal gas law assumes molecules occupy

zero percent

Molecular interactions

Strength of interactions

between molecules

determines the state

Strong attractions make

for high melting point

(ionic solids)

Weaker interactions

between molecules

occur in liquids

(covalent molecules)

Molecular interactions in gases are

negligible

Air is more than one removed

from nothing

Gases are mostly empty space:

molecules occupy <0.1 %

volume

1,000 times less dense than

solids and liquids

Emptiness allows complete

mixing

The Ideal gas

The ideal gas is defined as follows

Interactions between molecules are nonexistent

Volume occupied by molecules is zero

Collisions

There are two types of

collision

Between the

molecules and the

container

Between molecules

In the ideal gas these

collisions are perfectly

elastic (no energy loss)

Collisions between billiard

balls mirrors the collisions

between the molecules of an

ideal gas

Origins of pressure

Pressure is force per unit area: F/A

Force is rate of change of momentum: F = ma = d(mv)/dt

Molecules colliding with the walls of the container

exchange momentum

Units of pressure

The S.I. unit of pressure is the pascal (Pa)

1 Pa = 1 N/m2, where N is the S.I. unit of force

1 N = 1 kgm/s2

The weight of the air exerts pressure –

atmospheric pressure

This pressure is about 100,000 Pa

Older is better

101 kPa is an inconvenient way of measuring pressure

Traditional units are still used in preference to the SI system

Atmospheres, cm (or mm) of Hg and torr are the most common

Bar is becoming more widespread (1 bar = 100 kPa)

How do I measure the atmosphere?

Let me count the ways

1 atmosphere =

760 mm Hg = 76.0 cm Hg

14.70 psi

760 torr

1.013 bar

29.9 in Hg

101.3 kPa

Standard temperature and pressure

(STP)

Standard conditions allow direct comparison of

properties of different substances

Standard temperature is 273 K (0ºC)

Standard pressure is 760 mm Hg

At STP, 1 mole of any ideal gas occupies 22.414 L

Balancing act

Weight of air supports equal weight of mercury (or other liquid)

Mercury being dense, column is 76 cm equivalent to same weight of atmosphere (several miles high)

76 cm (760 mm) Hg = 1 atm

Manometers measure pressure in a

container (A) If pressure inside bulb < atmospheric,

atmosphere pushes down more.

(B) If pressure inside bulb > atmospheric, column

is pushed towards open end.

Gas Laws

Physical properties of gases were among the first experiments performed in the “modern” scientific era, beginning in the 17th century

All gases exhibit similar physical properties even if their chemical properties differ widely

Properties can be summarized in a few simple laws

Variables are pressure, volume, temperature and quantity. Keep one (or two) constant and vary the others

Gas laws: experience in math form

The properties of gases can be described by a number of simple laws

The laws establish quantitative relationships between different variables

They are largely intuitively obvious and familiar

The four variables

Pressure (P)

Volume (V)

Temperature (T in Kelvin)

Number of molecules (n in moles)

Variables and constants

In the elementary gas laws two of the four

variables are kept constant

Each law describes how one variable reacts to

changes in another variable

All the simple laws can be integrated into one

combined gas law

The first experimental gas law

Pressure increases, volume

decreases (T, n constant)

Boyle’s law

1P

V

Mathematical form

The volume of a fixed amount of an ideal gas varies inversely with pressure at constant temperature

PV = constant

P α 1/V

0

20

40

60

80

100

120

0 1 2 3 4 5

Pre

ssu

re (a

tm)

1/Volume (1/L)

P vs 1/V

Getting some exercise An exercise ball at pressure (Pa) = 1000 mm Hg

has volume (Va) = 60 L

When sat on, new volume (Vb) = 40 L. What is

new pressure?

Check: P increases as V decreases

Note: doesn’t matter what units provided they are

consistent

a a b bPV PV

(1000 )(60 )1500

40

a a

b

b

PV mmHg LP mmHg

V L

Example

Charles’ Law

Pressure and amount constant

As temperature increases, the volume increases

Mathematical form The volume of a fixed amount of an ideal gas varies

directly with absolute temperature at constant pressure

V α T

V/T = constant

NOTE: Temperature must be in Kelvin (ºC + 273)

At absolute zero there is no motion and the residual volume is that of the atoms – which is assumed to be zero

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Vo

lum

e (L

)

Temperature (K)

V vs T

Example

Avogadro’s Law Pressure and temperature constant

Increase the amount, the volume increases

Summary of gas laws

Mathematical form

The volume of an ideal gas varies directly with its

molar amount at constant T and P

V α n

V/n = constant

Same volume of any gas contains same number

of moles at constant T,P

The standard molar volume at 273 K and 1 atm is

22.414 L

Comparison with reality Standard molar volume of 22.41 L compares with

experimental values of common real gases

Agreement shows that these ideal gas laws can

be widely applied for real gases

Less ideal gases (NH3) agree better than some

more ideal gases (Ar)

Putting them together: the ideal gas

law PV = nRT

R is the gas constant = 0.0821 L-atm/mol-K

Note units of R. R also appears in thermodynamic calculations, but with different units and numerical value (8.315 J/K-mol). Use the one appropriate to the calculation

• Units of pressure – atm

• Units of temperature – K

• Units of volume – L

Standard temperature and pressure: T = 0 ºC and P = 1 atm

Example

The combined gas law

Allows us to calculate change in one variable for

changes in the three other variables

PVR

nT Combined

Gas Law

AvogadroAmonton

CharlesBoyle

Applications A system at initial conditions Xa changes to new

conditions Xb

If we know three of the variables in state b, the

fourth can be obtained

In most of these problems na = nb

a a b b

a a b b

PV PV

n T n T

a a b b

a b

P V PV

T T

The “simple” laws are derived from

the combined law

In case variable does not change its value, a = b

Example: if T and n are unchanged,

Boyle’s law is obtained:

a a b b

a a a a

PV PV

n T n T

PV k

Example

Stoichiometry and gas reactions:

Mole relationships in different states

Solids: mass and molar mass

Solutions: volume and molarity

Gases: volume and ideal gas law

Calculate volume of gas produced (product) or

consumed (reactant) in a reaction at given

conditions of P and T

Calculate molar mass or density of a gas using

ideal gas law

Example

Mixtures of gases: partial pressures

Dalton’s law states that, in a mixture of gases,

each gas behaves independently of the others and

exerts the same pressure that it would by itself

The total pressure exerted is the sum of the

individual (partial) pressures of the components of

the mixture

P = P1 + P2 + P3 +…

Example

Partial pressure and the ideal gas law

In a mixture of gases, pressure exerted by

component i

Where ni is number of moles of component i

Total pressure is then:

V

RTnP i

i

V

RTnnnPP

i

itot

...)( 321

Mole fraction and the ideal gas law

Mole fraction (Xi) is ratio of moles of component i to total

number of moles ntot

But n = PV/RT

tot

i

tot

i

iP

P

RT

VP

RT

VP

X

i

i

i

tot

iii

n

n

n

n

nnn

nX

...)( 321

i

itot nn

Mole fractions and partial pressures

The partial pressure exerted by any gas is equal to

its mole fraction times the total pressure

What is the partial pressure of each component in

this mixture if total pressure is 600 mm Hg?

totalii PXP

Visual summary of the gas laws