The Theories and Behavior of

Gas

By Prof. Liwayway Memije-Cruz

Gas

Gas is one of the three

forms of matter. Every

known substance is either a

solid, liquid or a gas. These

forms differ in the way

they fill space and change

shape. A gas, such as air

has neither a fixed shape

nor a fixed volume and has

weight.

Properties of Gases

What makes a gas different from liquid and a

solid?

Most gases

exist as

molecules (in

case of inert

gases as

individual

atoms).

The molecules of gases are randomly

distributed and are far apart.

Gases can be easily

compressed, the

molecules can be

forced to be closed

together resulting to

lesser space between

them.

The volume or

space occupied by

the molecules

themselves is

negligible as

compared to the

total volume of the

container so that the

volume of the

container can be

taken as the volume

of the gas.

Gases have lower densities than

solids and liquids.

The attractive forces between molecules

(intermolecular) are negligible.

Most substances that are gaseous at normal

conditions have low molecular mass.

Measurable Properties of Gases

Note:

1 atm = 1 atmosphere = 760 torr = 760 mm = 76

m Hg

Temperature is always in Kelvin. At absolute zero

(0K) molecules stop moving entirely, the gas is as

cold as anything can get.

Standard Temperature and Pressure (STP) or

Standard Conditions (SC):

T = 0 0C = 273 0K

P = 1 atm or its equivalents

Kinetic Molecular Theory

1. All matter is made of constantly moving atoms or molecules.

Because of their mass and velocity, they possess kinetic

energy, (K.E. = 1/2mv). The molecules collide with one

another and with the sides of the container.

2. There is no kinetic energy lost during collisions inspite of the

transfer of energy from one molecule to another. At any given

instant, the molecule do not have the same kinetic energy.

3. The average kinetic energy of the molecule is directly

proportional to the absolute temperature. At any given

temperature, the average kinetic energy is the same for the

molecules of all gases.

Boyle’s Law

Boyles Law

• At a given temperature, the volume occupied by a

gas is inversely proportional to the pressure.

Equation: P = k 1/v

Where:

P = pressure of a gas sample

V = volume of a gas sample

k = a constant

Therefore: PV = k

At a given temperature, the product of the pressure and

volume of a gas must be constant. If the pressure is

increased, the volume must decrease to maintain the

constant product. For a given gas sample to be studied

under different pressures, the following expressions

must hold:

P1V1 = P2V2

Where:

P1 = original pressure of a gas sample

V1 = original volume of the sample

P2 = new pressure of a gas sample

V2 = new volume of the sample

Example:

A sample of a gas entrapped in a cylinder with

a movable piston occupies a volume of 720 ml

under a pressure of 0.375 atm. What volume

will the gas occupy under a pressure of 1.000

atm when the temperature remains constant?

V1 = 720 ml P1 = 0.375 atm

V2 = ? P2 = 1.000 atm

V2 = 0.375 atm/1.000 atm

V2 = 270 ml

Boyle's Law states that at a given temperature, the

volume occupied by a gas is inversely proportional

to the pressure.

Exercise:

• A gas has a volume of 500 milliliters when

a pressure equivalent to 760 millimeters of

mercury is exerted upon it. Calculate the

volume if the pressure is reduced to 730

millimeters.

Charles Law

At a given pressure, the volume occupied by a gas is

directly proportional to the absolute temperature of the

gas.

Equation:

V = K T

Where:

V = volume of the gas sample

T = absolute temperature of the gas sample

K = a constant

Therefore: V/T = k

For a given sample, if the temperature is changed, this

ratio must remain constant, so the volume must change in

order to maintain the constant ratio. The ratio at a new

temperature must be the same as the ratio at the original

temperature, so:

V1 = V2 /T1 = T2

V1T2 = V2T1

Where:

V1 = original volume of sample of gas

T1 = original absolute temperature

V2 = new volume of the sample

T2 = new absolute temperature of the sample

Example:

A given mass of gas has a volume of 150 ml

at 25 0C. What volume will the sample of gas

occupy at 45 0C, when the pressure is held

constant?

V1 = 150 ml T1 = 25 + 273 = 298 0K

V2 = ? T2= 45 + 273 = 318 0K

V2 = 150 ml x 318 0K/2980K

V2 = 160 ml

Gay-Lussac’s LawStates that the pressure of a certain mass of gas is directly

proportional to its absolute temperature at constant volume.

P1 /T1 = P2/T2

Example:

An LPG tank registers a pressure of 120 atm at a temperature

of 27 0C. If the tank is placed in an air conditioned

compartment and cooled to 10 0C, what will be the new

pressure inside the tank?

• P1 = 120 atm T1 = 27 + 273 = 300 0K

• P2 = ? T2 = 10 + 273 = 283 0K

• P2 = 120 atm x 283 0K /2990K

• P2 = 113.6 atm

Combined Gas Law

States that the volume of a certain mass of gas is

inversely proportional to its pressure and directly

proportional to its absolute temperature.

A gas sample occupies 250mm at 27 0C, and 780

mm pressure. Find its volume at 0 0C and 760mm

pressure.

T1 = 270C + 273 = 300 0A

T2 = 00C + 273 = 273 0A

V2 = 250 mm x 2730A/3000A x 780 mm/760 mm

V2 = 234 mm

Ideal Gas Law

Follows the gas law perfectly. Such a gas is non-

existent, for no known gas obeys the gas laws at all

possible temperatures. There are two principal reasons

why real gases do not behave as ideal gases:

* The molecules of a real gas has mass, or weight, and

the matter thus contained in them cannot be destroyed.

* The molecules of a real gas occupy space, and thus

can be compressed only so far. Once the limit of

compression has been reached, neither increased

pressure nor cooling can further reduce the volume of

gas.