Gas Laws

THE GAS LAWS

Made by – VIKASH PRASAD

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?

These are all examples of gases at work!

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Important Characteristics of Gases

1) Gases are highly compressible An external force compresses the gas sample and decreases its volume, removing the external force allows the gas volume to increase.2) Gases are thermally expandable When a gas sample is heated, its volume increases, and when it is cooled its volume decreases.3) Gases have high viscosity Gases flow much easier than liquids or solids.4) Most Gases have low densities Gas densities are on the order of grams per liter whereas liquids and solids are grams per cubic cm, 1000 times greater.5) Gases are infinitely miscible

Gases mix in any proportion such as in air, a mixture of many gases.

Properties of Gases

We can predict the behavior of gases based on the following properties:


Pressure

Volume

Amount (moles)

Temperature

Units of Pressure

1 pascal (Pa) = 1 N/m2

1 atm = 760 mmHg = 760 torr

1 atm = 101,325 Pa

Barometer

Pressure = ForceArea

Volume

Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the liter, l.

Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…)


Amount (moles)Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas.

By definition, one mole of a substance contains approximately 6.022 x 1023 particles of the substance. You can understand why we use mass and moles!


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.

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:

when one goes up, the othercomes down.


pressure

volum

e

Boyle’s Law at Work…

Doubling the pressure reduces the volume by half. Conversely, when the volume doubles, the pressure decreases by half.


Application of Boyle’s Law

Boyle’s Law can be used to predict the interaction of pressure and volume.

p1 * V1 = p2 * V2

p1 = initial pressure

V1 = initial volume

p2 = final pressure

V2 = final volume


Boyle’s Law

• Hyperbolic Relation Between Pressure and Volume

p

V

p – V Diagramp – V Diagram

isotherms

T1 T2 T3 T3 >T2>T1

(courtesy F. Remer)

Boyle’s Law: Summary

Pressure * Volume = Constant p1 * V1 = p2 * V2

With constant temperature and amount of gas, you can use these relationships to predict changes in pressure and volume.


Charles’ Law

This law is named for Jacques Charles, who studied the relationship volume, V, and temperature, T, around the turn of the 19th 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.


volum

e

temp

erature

Charles’ Law

• Linear Relation Between Temperature and Pressure

P

T (K)0 100 200 300

P – T DiagramP – T Diagram

isochorsisochorsV1 V2

V3

V1 <V2 <V3

(courtesy F. Remer)

Charles’ Law

Real data must be obtained above liquefaction temperature.Experimental curves for different gasses, different masses, different pressures all extrapolate to a common zero.

Partial Pressure

Partial Pressure Pressure each gas in a mixture would exert if it

were the only gas in the container

Dalton's Law of Partial PressuresThe total pressure exerted by a gas mixture is

the sum of the partial pressures of the gases in that mixture.

PT = P1 + P2 + P3 + .....

Charles’ Law at Work…

As the temperature increases, the volume increases. Conversely, when the temperature decreases, volume decreases.


Application of Charles’ Law

Charles’ Law can be used to predict the interaction of temperature and volume.

V1 / T1 = V2 / T2

V1 = initial volume

T1 = initial temperature

V2 = final volume

T2 = final temperature


Charles’ Law: Summary

Volume / Temperature = Constant V1 / T1 = V2 / T2

With constant pressure and amount of gas, you can use these relationships to predict changes in temperature and volume.


Avogadro’s Law

V number of moles (n)

V = constant x n

V1/n1 = V2/n2

Constant temperatureConstant pressure

Ideal Gas Equation

Charles’ law: V T(at constant n and P)

Avogadro’s law: V n(at constant P and T)

Boyle’s law: V (at constant n and T)1P

V nT

P

V = constant x = RnT

P

nT

PR is the gas constant

PV = nRT

Dalton’s Law of Partial Pressures

V and T are

constant

P1 P2 Ptotal = P1 + P2

Kinetic Molecular Theory• The Kinetic Molecular Theory is a single set of descriptive

characteristics of a substance known as the Ideal Gas. • All real gases require their own unique sets of descriptive

characteristics. Considering the large number of known gases in the World, the task of trying to describe each one of them individually would be an awesome task.

• In order to simplify this task, the scientific community has decided to create an imaginary gas that approximates the behavior of all real gases. In other words, the Ideal Gas is a substance that does not exist.

• The Kinetic Molecular Theory describes that gas. While the use of the Ideal Gas in describing all real gases means that the descriptions of all real gases will be wrong, the reality is that the descriptions of real gases will be close enough to correct that any errors can be overlooked.

The Nature of Gases

Three basic assumptions of the kinetic theory as it applies to gases: 1. Gas is composed of particles- usually molecules or atoms

–Small, hard spheres– Insignificant volume; relatively far apart

from each other–No attraction or repulsion between

particles

The Nature of Gases

2. Particles in a gas move rapidly in constant random motion

–Move in straight paths, changing direction only when colliding with one another or other objects

–Average speed of O2 in air at 20 oC is an amazing 1660 km/h! (1.6km=1mile)

The Nature of Gases 3. Collisions are perfectly elastic- meaning kinetic energy is transferred without loss from one particle to another- the total kinetic energy remains constantNewtonian Cradle-Where the collisions between the balls elastic?Yes, because kinetic energy was transferred with each collision

THE KINETIC THEORY OF GASES

• Gas consists of large number of particles (atoms or molecules)

• Particles make elastic collisions with each other and with walls of container

• There exist no external forces (density constant)• Particles, on average, separated by distances

large compared to their diameters• No forces between particles except when they

collide

Remember the assumptions

Ideal Gas Model Kinetic Molecular Theory (KMT) for an ideal gas

states that all gas particles: • are in random, constant, straight-line motion. • are separated by great distances relative to their

size; the volume of the gas particles is considered negligible.

• have no attractive forces between them. • have collisions that may result in the transfer of

energy between gas particles, but the total energy of the system remains constant.

Deviations from ideal behaviour

• A real gas is most like an ideal gas when the real gas is at low pressure and high temperature.

• At high pressures gas particles are close therefore the volume of the gas particles is considered.

• At low temperatures gas particles have low kinetic energy therefore particles have some attractive force

• Example• Dry ice, liquid oxygen and nitrogen

Compression and expansion of adiabatically isolated gas is accompanied by its heating

and cooling.

Gas Laws

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