Ideal Gas Laws

In the normal range of temperature and pressure, water vapor can be generally be
considered as an ideal gas. By definition, an ideal gas follows the following laws:

Boyle's Law: this law states that at constant temperature, the product of the volume
and pressure of a given amount of gas is a constant.

P x V = constant

The value of the constant depends on how much gas is in the volume.

Charles's Law: this law states that at constant pressure, the volume of a given
quantity of gas is proportional to absolute temperature (° K).

V = q x T

where q is a proportionality constant that depends on the quantity of gas.

Charles's law can be stated in another form: at constant volume, the pressure of
a given quantity of gas is proportional to absolute temperature.

P = j x T

where j is a proportionality constant that depends on the particular sample of gas
and its volume.

note: to convert temperature in ° C into absolute temperature in ° K, add the constant 273.16.

Dalton's Law of Partial Pressures: this law states that that the total pressure of
a mixture of gases is equal to the sum of the pressures that each gas would exert
if it were present alone.

Pt= P1+ P2+ P3+ ...

where P1, P2, etc., are the partial pressures of gases 1, 2, etc.

Avogadro's Hypothesis: this hypothesis states that equal volumes of gases at
the same temperature and pressure contain equal numbers of molecules.
For instance, one liter of any ideal gas at a temperature of 0°C and a pressure
of 1013 hPa, contains 2.688 x 1022 molecules.

note: the temperature of 0°C and pressure of 1013 hPa is the standard
temperature and pressure condition or STP.

Volume of a Mole of Gas at STP:

A mole of any element is defined as the amount of that element that contains
the same number of molecules (or atoms in the case of a mono atomic element)
as exactly 12 g of ¹²C (Carbon 12).

It has been experimentally determined that the number of atoms in this quantity
of ¹²C is 6.022 x 1023. This number is called Avogadro's number.

As one liter of gas, at STP, contains 2.688 x 1022 molecules (or atoms in the
case of a mono atomic gas), it follows that a mole of gas (6.022 x 1023 molecules)
occupies a volume of

22.4 liter at STP.

Ideal Gas Law: this law states that the product of volume and pressure of a given
amount of gas is proportional to absolute temperature.

P x V = n x R x T

where n is the number of moles of gas and R the molar gas constant.

The constant R is equal to:

0.08206 atm x liter/°K x mole.

8.30928 Pa x m3/°K x mole

Mole Fractions and Partial Pressure: the composition of one mole of a gas mixture
can be expressed in terms of the mole fractions of its components. The mole fraction
of a particular component is defined as the total number of moles of the component
divided by the total number of moles of all the components. From this definition,
it follows that the sum of all mole fractions is equal to one. Taking dry air near sea level
as an example, the mole fractions of the three main components are as follows:

Nitrogen : 0.78084
Oxygen : 0.20948
Carbon Dioxide : 0.00954

If Pb is the barometric (or total) pressure of a gas mixture and n1, n2, etc. the mole
fractions of its components, it follows that: Pb = Pb x (n1+ n2 + ...) and
Pb = Pb x n1+ Pb x n2 + ...

where Pb x n1, Pb x n2, etc. are the partial pressures of components 1, 2, etc.

The above equation is another form of Dalton's law.