23 Gas Laws

Gas Laws: Pressure, Volume,

and Hot Air

 Investigate the relationships among the pressure,

volume, and temperature of a gas

 Describe how knowledge of gases has helped to

advance technology, and how such technological advances have led to a better understanding of

environmental phenomena and issues.

Opening thoughts…

Have you ever:

Seen a hot air balloon?

Had a soda bottle spray all over you?

Baked (or eaten) a nice, fluffy cake?

Gases are important in:



Respiration



Photosynthesis



Combustion



Air bags



Protection from UV

radiation



Water cycle



Weather



Diving



Medicine



Food processing



Global warming



Bombs



Aurora Borealis

States of Matter: Solids

•

Crystal lattice

structure

•

Fixed volume

•

Vibrational motion

•

Strong attractive

forces

Liquids



Fixed volume



Particles can move past

each other ( flow)



Vibrational and

rotational motion



Attractive forces are

weaker than in solids



E.g. Dipole-dipole

forces (polar molecules)

GASES



No fixed volume



Particles are very far

apart



Vibrational,

rotational, and

translational motion



High kinetic energy

Weak attractive

forces



Generally non polar

Kinetic Molecular Theory of

Gases



The volume of an individual gas molecule is

negligible compared to the volume of the

container



There are no attractive or repulsive forces

between gas molecules



Gas molecules move randomly in all directions

in straight lines



All gas molecule collisions are perfectly elastic

The average kinetic energy of gas molecules is

Kinetic Molecular Theory

Think!

Ideal vs Real gases

In real gases:



There are attractive forces between

molecules



Collisions are not completely elastic

Gas particles have some volume

Properties of Gases

You can predict the behavior of gases

based on the following properties:

Pressure

Volume

Amount (moles)

Temperature

Pressure

Volume

Amount (moles)

Temperature

Pressure

Pressure

is defined as the force the gas

exerts on a given area of the container in

which it is contained. The SI unit for

pressure is the Pascal, Pa.

• If you’ve ever inflated a tire, you’ve probably made a

pressure measurement in

Gases and Pressure

Gas pressure is created by the particles of the gas hitting the container

Pressure is the force exerted over a certain area Pressure (P) is measured in

a) Millimetres of mercury (mm Hg) b) Pascals (Pa) or kPa

c) Atmospheres ( atm)

d) Pounds per square inch (psi)

Converting Units of Pressure

101.3 kPa = 1 atm = 760 torr = 760 mm Hg = 14.7 psi

Pressure

Volume

Amount (moles)

Temperature

Volume

Volume

is the three-dimensional space inside

the container holding the gas.

The SI unit for volume is the cubic metre, m

.

A more common and convenient unit is the litre,

L. One cubic metre is 1000 litres.

Think of a 2-litre bottle of soda to get an idea of how big a litre is.

Pressure

Volume

Amount (moles)

Temperature

Amount (moles)

Amount of substance is tricky. As we’ve already

Pressure

Volume

Amount (moles)

Temperature

Temperature

Temperature is the measurement with which you’re probably most familiar (and the most complex to

describe completely). For these lessons, we will be using temperature measurements in Kelvin, K.

The Kelvin scale starts at Absolute 0,

which is -273.15°C. To convert Celsius to Kelvin, add 273.15.

Conversions

760 mm Hg = 760 torr = 14.7 psi = 1 atm = 101.3 kPa

0 K = -273 °C

STP (standard temperature and pressure:

0°C and 101.3 kPa

How do they all relate?

Some relationships of gases may be

easy to predict. Some are more subtle.

Now that we understand the factors that

affect the behavior of gases, we will

How do they all relate?

Some relationships of gases may be

easy to predict. Some are more subtle.

Now that we understand the factors that

affect the behavior of gases, we will

study how those factors interact.

Boyle’s Law

Boyle’s Law describes the

Boyle’s Law



This law is named for Charles Boyle, who

studied the relationship between

pressure

,

p, and

volume

, V, in the mid-1600s.



Boyle determined that for the same

amount

of a gas at constant

temperature,

p * V = constant



This defines an inverse relationship:

Boyle’s Law



This law is named for Charles Boyle, who

studied the relationship between

pressure

,

p, and

volume

, V, in the mid-1600s.



He determined that for the same

amount

of

a gas at constant

temperature,

p * V = constant



This defines an inverse relationship:

Pressure and

Volume



Robert Boyle determined the

relationship between P and V



Boyle’s law : for the same

amount of gas at a constant

temperature the volume of a

gas is inversely proportional

to the pressure.

P * V = constant

Or

V = 1/P * constant

What does Boyle’s Law mean?

p * V = constant

Suppose you have a cylinder with a piston in the

top so you can change the

volume

. The cylinder

has a gauge to measure

pressure

, is contained so

the

amount

of gas is constant, and can be

maintained at a constant

temperature

.

A decrease in volume will result in increased

pressure.

Boyle’s Law at Work…

Application of Boyle’s Law



Boyle’s Law can be used to predict the interaction

of pressure and volume.



If you know the initial pressure and volume, and

have a target value for one of those variables, you

can predict what the other will be for the same

amount of gas under constant temperature.

Application of Boyle’s Law

p

* V

= p

* V

p

= initial pressure

V

= initial volume

p

= final pressure

V

= final volume

Application of Boyle’s Law

p₁ * V₁ = p₂ * V₂ p₁ = 1 KPa

V₁ = 4 liters p₂ = 2 KPa V₂ = ?

Solving for V₂, the final volume equals 2 liters.

Boyle’s Law: Summary



Pressure * Volume = Constant



p

* V

= p

* V



With constant temperature and amount

of gas, you can use these relationships

to predict changes in pressure and

Charles’ Law

Charles’ Law



This law is named for Jacques Charles, who

studied the relationship

volume

, V, and

temperature

, T, around the turn of the 19

century.



He determined that for the same

amount

of

a gas at constant

pressure,

V / T = constant



This defines a direct relationship:

an increase in one results in an

increase in the other.

What does Charles’ Law mean?

V / T = constant

Suppose you have that same cylinder with a piston

in the top allowing

volume

to change, and a

heating/cooling element allowing for changing

temperature

. The force on the piston head is

constant to maintain

pressure

, and the cylinder is

contained so the

amount

of gas is constant.

An increase in

temperature

results in increased

volume

.

Charles’ Law at Work…

Application of Charles’ Law



Charles’ Law can be used to predict the

interaction of temperature and volume.



If you know the initial temperature and

volume, and have a target value for one of

those variables, you can predict what the

other will be for the same amount of gas

under constant pressure.

Application of Charles’ Law

V

/ T

= V

/ T

V

= initial volume

T

= initial temperature

V

= final volume

T

= final temperature

Application of Charles’ Law

V

/ T

= V

/ T

V

= 2.5 liters

T

= 250 K

V

= 4.5 liters

T

= ?

Solving for T

the final temperature equals 450 K.

Charles’ Law: Summary



Volume / Temperature = Constant



V

/ T

= V

/ T



With constant pressure and amount of

gas, you can use these relationships to

predict changes in temperature and

Gay Lussac’s Law



Gay-Lussac investigated the relationship

between the pressure of a gas and its

temperature.



At a constant volume and amount of gas,

the pressure of a gas sample is directly

proportional to the Kelvin Temperature.

Gay Lussac’s Law



P

Gay-Lussac’s Law



P

1

/ T

= P

/ T



A gas cylinder containing explosive

hydrogen gas has a pressure of 50 atm at a

temperature of 300 K. The cylinder can

withstand a pressure of 500 atm before it

bursts, causing a building-flattening

explosion. What is the maximum

Thermometers

 Glass bulb thermometers- how do they work?  These thermometers have a glass bulb attached

to a sealed glass tube. A very thin opening,

Combined Gas Law



Combines Boyle, Charles’ and Gay-Lussac’s Law



Shows relationship between P, V, T



P

V

/T

= P

V

/T



STP- standard temp and pressure :

101.325kPa, 273.15K



SATP- standard ambient temp and pressure:

Dalton’s law of Partial

Pressures



Total Pressure of a gas

mixture is the sum of the

Partial Pressure of each gas.

Dalton’s law of Partial

Pressures



The gas acts as if there is only one gas in

the container, because:



There is an enormous amount of space

between the gas molecules



Gas molecules do not affect other molecules

Only true if there is lots of space between

How Much Pressure?

Q - A balloon is filled with pure oxygen. What is

the pressure of the oxygen in the balloon?

A - Atmospheric pressure. If it wasn’t, then the

balloon would expand or shrink.

Q - A windbag is blown up with exhaled air. What

is the pressure of oxygen in the bag?

A – Around 16 - 21% of atmospheric pressure (O

is 16% of exhaled air, 21% of atmosphere)

Q - A solid container is filled with pure oxygen.

What is the pressure in the container?

Vapor Pressure As a Partial

Pressure



P

is the sum of the

partial pressure of the

collected gas and the

partial pressure of the

gas phase of the liquid,

which is its vapor

pressure.



If the liquid is water,

then P

is :

Vapour Pressure Defined



Vapour pressure is the pressure exerted by a

vapour. E.g. the H

O(g) in a sealed container.

•

Yet, molecules both leave and join the surface,

so vapour pressure also pushes molecules up.

Eventually the air above the water is

filled with vapour pushing down. As

temperature



, more molecules fill the

air, and vapour pressure



.

•

To measure vapour pressure we can heat a

Measuring Vapour Pressure

•

When the vapour pressure is equal to the

atmospheric pressure (P

), the push out is enough

to overcome P

and boiling occurs.

Va

po

ur

p

re

ss

ur

e

Temperature

Vapour pressure for H

O

°C

kPa

°C

kPa

10

1.23

50 12.33

20

2.34

75 38.54

30

4.17 100

See pg. 596 for more

101.3

•

Thus, water will boil at a temperature below

Collecting gases over water



Many times gases are collected over H

O



Often we want to know the volume of dry gas

at STP (useful for stoichiometry).

For this we must make 3 corrections:

1.

The level of water inside and outside the tube

must be level (so pressure inside is equal to

the pressure outside).

2.

The water vapour pressure must be

subtracted from the total pressure (to get the

pressure of the dry gas).

Sample calculation

A gas was collected over 21°C H

O. After

equal-izing water levels, the volume was 325 mL. Give

the volume of dry gas at STP (P

=102.9 kPa).

Step 1: Determine vapour pressure (pg. 507)

At 21°C vapour pressure is 2.49 kPa

Step 2: Calculate the pressure of dry gas

P

= P

- P

= 102.9 - 2.49 = 100.41 kPa

Step 3: List all of the data

T

= 294 K, V

= 325 mL, P

= 100.41 kPa

Step 4: Convert to STP

(P

)(V

)(T

)

(P

)(T

)

V

=

(100.4 kPa)(325 mL)(273 K)

(101.325 kPa)(294 K)

=

Avogadro’s Law

 Equal volumes of a gas at the same temperature

and pressure contain the same number of molecules.

 One mole of any ideal gas at STP has a volume of

22.4L

 The volume of a real gas is slightly different than

22.4L at STP, but so close that 22.4L is an acceptable approximation

 Real gas deviations occur at high pressures or low

Molar Volume of Gases



n

/ V

= n

/V



Example 1: 5.00 L of a gas is known to

contain 0.965 mol. If the amount of gas is

Ideal Gas Law

P*V = n*R*T

This is one of the few equations in chemistry that you should commit to memory!

Ideal Gas Law

Combining Boyle’s, Charles’ and Avogadro’s laws

allows for developing a single equation and adds moles to the combined gas law:

P*V = n*R*T

P = pressure

V = volume in litres n = number of moles

T = temperature in Kelvin

R is the universal gas constant R= 8.3143510... kPa L mol-1 K-1

Question 1

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.

Question 1

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

Question 2

Based on Charles’ Law (V / T = constant) or the Ideal Gas

Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.

Question 2

Based on Charles’ Law (V / T = constant) or the Ideal Gas

Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are:

b. Directly proportional: if one goes up, the other goes up.

Increasing temperature

Question 3

Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most

effective way to increase the pressure in the tire?

a. Increase the force pressing on the outside of the tire.

b. Increase the temperature of the gas (air) in the tire.

Question 3

Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most

effective way to increase the pressure in the tire?

a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire.

c. Increase the amount (number of moles) of gas in the tire. When you inflate a tire with a pump, you are adding air, or

increasing the amount of air in the tire. This will often result in a slight increase in temperature because a tire is not a