Relation Between ΔH AND ΔE

When a system changes from initial to final state,

                            DH  =  H₂  –  H₁

            Where H₂ and H₁ are enthalpies of final and initial state respectively.

                            But,   H      =      E  +  PV.

                            DH    =     (E₂ + P₂V₂) – (E₁ + P₁V₁)

                            DH    =     E₂ + P₂V₂ – E₁ – P₁V₁

                            DH    =     E₂ – E₁ + P₂V₂ – P₁V₁                         

                            DH    =     DE  +  P₂V₂ – P₁V₁ 

                            But,   PV     =     nRT.

                            \                  P₁V_­1  =     n₁RT

                            &                   P₂V₂  =     n₂RT, at constant temperature.

                                                  DH     =    DE   +   n₂RT – n₁RT

                                                  DH     =    DE   +   RT (n₂ – n₁)   

                                                  DH     =    DE   +   DnRT                                                  

                            Where n₂ – n₁ is change in moles.