iii. Isochoric process : Substitution of
W = -Pext ∆V into Eq. (4.12)
∆U = Q - Pext ∆V (4.16)
As the reaction is carried out in a closed
container, volume of the system is constant or
∆V = 0 and
∆U = Qv (4.17)
Equation (4.17) shows a change in
internal energy of the system is due to heat
transfer at constant volume. The subscript ‘V’
indicates that heat is transferred at the constant
volume. Further U being a state function, Qv is
also a state function.
iv. Isobaric process : Usually chemical
reactions are carried out in the open containers
under constant atmospheric pressure. In such
reactions, ∆V ≠ 0
Replacing Q by Qp and ∆U by Qp - Pext ∆V in
equation (4.16) gives
Qp = ∆U + Pext ∆V (4.18)
The reactions carried out in open
containers under constant atmospheric
pressure are common in chemistry, a special
symbol ∆H, the enthalpy change, is given to
indicate heat changes occurring at constant
pressure.
From Eq. (4.19), we write
H 1 = U 1 + P 1 V 1 and H 2 = U 2 + P 2 V 2
With these
∆H = U 2 + P 2 V 2 - U 1 + P 1 V 1
= (U 2 - U 1 ) + (P 2 V 2 - P 1 V 1 )
= ∆U + ∆(PV) (4.21)
For constant pressure, P 1 = P 2 = P and
∆H = ∆U + P∆V (4.22)
If the pressure inside and outside is the same or
Pext = P, Eq. (4.18) gives
Qp = ∆U + P ∆V (4.23)
From equations (4.22) and (4.23)
∆H = Qp (4.24)
Thus change in enthalpy of a system is
equal to heat transferred from it at the constant
pressure. H and Qp are state functions.
4.8.1 Relationship between ∆H and ∆U for
chemical reactions : At constant pressure, ∆H
and ∆U are related as
∆H = ∆U + P∆V
i. For reactions involving solids and liquids, ∆V
usually is very small (solids or liquids do not
show volume change with change of pressure)
and ∆H = ∆U
ii. For reactions involving gases, ∆V cannot be
neglected and
∆H = ∆U + P∆V
= ∆H + P(V 2 - V 1 )
∆H = ∆U + PV 2 - PV 1 (4.25)
where V 1 is the volume of gas phase reactants
and V 2 that of the gaseous products.
We assume reactant and product behave
ideally. Applying ideal gas equation PV = nRT.
When n 1 moles of gaseous reactants produce
n 2 moles of gaseous products. The ideal gas
equation give,
PV 1 = n 1 RT and PV 2 = n 2 RT (4.26)Remember...
q is not a state function.
Whereas Qv and Qp are state
functions.4.8 Enthalpy (H) : Enthalpy of a system is
sum of internal energy of a system and the
energy equivalent to PV work.
H = U + PV (4.19)
Change in enthalpy, ∆H, is also state
function given by
∆H = H 2 - H 1 (4.20)
where H 1 and H 2 are the enthalpies of initial
and final states, respectively.