derivation of van der waals equation of state and critical constants


Van der waal force include all intermolecular forces that act between electrically neutral molecules. it is the negligible  force that hold molecules of gas at same place before any amount of energy ( increase in individual kinetic energy of molecules) disperse them. in liquid for example , it is the force that hold water molecules together before being dispersed into steam at boiling point.
 Certain assumption are made in the derivation of the ideal gas equation, PV=nRT, below are some of the assumption made and cannot be valid are according to van der waal
·         the volume of the gas cannot be negligible in respect to the volume of the containing vessel.
·         the force of attraction between the gaseous molecules cannot be negligible as postulated in the kinetic theory.
with real gases, the relation PV=nRT, fails at high pressure and low temperature, to account for the above observations , some correction are made to the ideal gas relations, PV=nRT  as follows.
 the correction for the volume of the gas molecules is taken into account  by changing the volume
 V →v-b, where b is the volume of the gas molecules.
the correction for the attractive force is accounted for by adding a/v2 to the pressure , where a is a constant, therefore the van der waal equation for  real gases becomes
( p + a/v2 )(v-b)=RT
( p + a/v2 )(v-b)=nRT  for n moles of gases

No comments:

Post a Comment