Concise Physical Chemistry

c03 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

ENERGY AND ENTHALPY 45

It would be very convenient here to have a thermodynamic function that plays the

same role for constant pressure transformations that energy plays for constant volume

transformations. We can define such a property. It is called theenthalpy, and it is

the heat produced or absorbed under the usual constant pressure conditions that

characterize the reactions we carry out in the lab. The enthalpy has the analogous

definition

Cp≡

(

∂q

∂T

)

p

=

(

∂H

∂T

)

p

Now the volume is not constant but may vary in such a way as to do work on

the surroundings or for the surroundings to do work on the system, sodU=dq+

pdVand

Cp=

(

∂q

∂T

)

p

≡

(

∂H

∂T

)

p

=

(

∂U−pdV

∂T

)

p

We have in effectconstructeda new thermodynamic variable by specifying the path

H≡U−pV

dH=dU−pdV−Vdp

whereVdpis zero over the stipulated path becausep=constant. ThepdVwork over

a stipulated path is conserved; that is, it sums to zero over a circular path. Enthalpy

is thus the sum of a thermodynamic function and a conserved function, and therefore

it must be conserved.

Enthalpy is a thermodynamic state variable.

Enthalpy is the constant pressure analog of energy in processes like chemical

reactions. It can be handled mathematically in the same way that energy is han-

dled and should be thought of almost as its twin. In many semiquantitative dis-

cussions the distinction between energy and enthalpy is ignored but it should be

borne in mind, because it is important in rigorous treatments like the correction of

quantum mechanical values for the energy of a molecule at 0 K to the enthalpy

at 298 K.

The difference between enthalpy and energy is thepVwork done on or by the

system. For ordinary chemical reactions this is often negligible but if a gas is taken

up or produced during a chemical reaction,UandHwill be different because pro-

duction of a gas represents an expansion against the atmosphere and consump-

tion of a gaseous reactant is a contraction of the system driven by pressure of the

surroundings.