derive the relation between change in internal energy and change in enthalpy for a system in which the reactants and products are gases

Dear student
Please find the solution to the asked query:

From First law of Thermodynamics we have:
ΔU = q +w

ΔU is the change in internal energy,  q  is the heat transfered, w is the work done

If a change is brought about at constant pressure , in that case volume changes . Let volume change from VA to VB at constant pressure P. The work done by the system is given by:
w = -P (VB- VA)

Substituting this value in the above equation:
ΔU = q  - P (VB- VA)
or UB -UA =   q  - P (VB- VA)
(UB  +PVB) - (U A +PVA)  =q

The quantity , U +PV is called the enthalpy of the system and is denoted by H
Thus [ HB -HA =  ΔH = q] and
H = U +PV

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