gas. Here T is the temperature in kelvin or (absolute) scale. K is a constant for the given sample but varies with the volume of the gas. If we now bring in the idea of atoms or molecules, then K is proportional to the number of molecules, (say) N in the sample.
We can write K = N k . Observation tells us that this k is same for all gases. It is called Boltzmann constant and is denoted by k B . As P V P V N T N T = constant = k B ( .
) if P , V and T are same, then N is also same for all gases. This is Avogadro’s hypothesis, that the number of molecules per unit volume is the same for all gases at a fixed temperature and pressure. The number in . litres of any gas is .
× . This is known as Avogadro number and is denoted by N A . The mass of . litres of any gas is equal to its molecular weight in grams at S.T.P (standard temperature K and pressure atm).
This amount of substance is called a mole (see Chapter for a more precise definition). Avogadro had guessed the equality of numbers in equal volumes of gas at a fixed temperature and pressure from chemical reactions. Kinetic theory justifies this hypothesis. The perfect gas equation can be written as PV = µ RT ( .
) where µ is the number of moles and R = N A k B is a universal constant. The temperature T is absolute temperature. Choosing kelvin scale for absolute temperature, R = . J mol – K – .
Here µ = ( . ) where M is the mass of the gas containing N molecules, M is the molar mass and N A the Avogadro’s number. Using Eqs. ( .
) and ( . ) can also be written as PV = k B NT or P = k B nT P (atm) Fig. . Real gases approach ideal gas behaviour at low pressures and high temperatures.