prove that ∆H=∆v+∆ngRT
Answers
Answer:
Explanation:
Let H1 ,U1 ,P1 ,V1 and H2 ,U2 ,P2 ,V2 represent enthalpies, internal energies, pressures and volumes in the initial and final states respectively.
For a reaction involving n1 moles of gaseous reactants in initial state and n2 moles of gaseous products at final state,
n1 X(g) → n2 Y(g)
If H1 and H2 are the enthalpies in initial and final states respectively, then the heat of reaction is given by enthalpy change as
ΔH= H2 − H1
Mathematical definition of 'H' is H=U+PV
Thus, H1 = U1 + P1 V1 and H2 = U2 + P2 V2,
∴ΔH = U2 + P2 + P2 V2 − (U1 + P1V1 )
∴ΔH = U2 + P2 V2 −U1 − P1 V1
∴ΔH = U2 − U1 + P2 V2 − P1 V1
Now, ΔU = U2 − U1
Since, PV=nRT
For initial state, P1 V1 = n1 RT
For final state, P2 V2 = n2 RT
P2 V2 − P1 V1 = n2 RT−n1 RT
=(n2 −n1 )RT
=ΔnRT
where, Δn= [No. of moles of gaseous products] - [No. of moles of gaseous reactants]
∴ΔH=ΔU+ΔnRT
In an isochoric process, the volume remains constant i.e., ΔV=0
Therefore,
ΔH=ΔU