Ideal Gas Law: Equation of State for a Gas
An equation of state can relate the pressure, volume and temperature of a material, over a wide range of conditions. The ideal gas equation or ideal gas law is the equation of state that all gases are found to follow, approximately. It can be assumed that, for most purposes, whether considered individually or as a mixture, atmospheric gases obey the ideal gas law exactly. The first form of the ideal gas law can be written as follows:
pV = mRT
(1)
where p, V, m, T are the pressure (pa), volume (m^3), mass (kg) and absolute temperature (K) of the gas respectively. K = degrees C +273.15. R, the gas constant, is constant for 1kg of gas. It's value is dependant on the articular gas being considered.
m/V = p, where p is the density of the gas, the ideal gas law can also be written in a second form:
This can be rewritten again, for a unit mass (1kg) of gas m = 1, therefore (1) becomes:
where = 1/p = V/m is the specific volume of the gas. That is, the volume occupied by 1kg of gas at pressure, p, and temperature T.
Where temperature is constant (1) reduces to Boyles Law. Charles' two laws are also implicit in (1).
The first law states that: For a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature.
The second law states that: For a fixed mass of gas held within a fixed volume, the pressure of the gas is proportional to its absolute temperature.
The gram-molecular weight or mole (mol) of any substance is defined as the molecular weight, M, of the substance expressed in grams. As an example, the molecular weight of water is 18.015: therefore 1 mol of water is 18.015g of water. The number of moles n in mass m (in grams) of a substance is given by:
n = m/M
Because the masses contained in 1 mol of different substances bear the same ratio's to each other as the molecular weights of the substances, 1 mol of any substance must contain the same number of molecules as 1 mol of any other substance. Therefore, the number of molecules in 1 mol of any substance is a universal constant called Avogadro's Number (NsubA).
Avogadro's hypothesis states that: Equal volumes of gases under contanct temperature and pressure contain the same number of molecules, independant of the gas.
Provided the same number of molecules are taken for any gas, the constant R in (1) will be the same. However, as 1 mol of any gas contains the same number of molecules as 1 mol of any other gas, the constant R, for 1 mol, is th same for all gases. It is known as the universal gas constant (R*).
The value of R* = 8.3145 J K^-1 mol^-1.
The ideal gas law can now be rewritten for 1 mol of any gas:
