Question

prove that ∆H=∆v+∆ngRT​

Answer 1

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