Page 136 - Physical chemistry understanding our chemical world

ENTHALPY 103

Justification Box 3.1

We saw above how the work w performed by a gas is pV. Because performing work
will decrease the internal energy, we say

w =−pV (3.14)

Substitution of this simple relationship into the definition of internal energy in Equation
(3.5) yields
U = q − pV (3.15)

and rearranging Equation (3.15) yields q = U + pV .
This combination of variables occurs so often in phys- We often call a col-
ical chemistry, that we give it a name: we call it the lection of variables a
enthalpy, and give it the symbol H. Accordingly, we ‘compound variable’.
rewrite Equation (3.15) as:
H = U + pV (3.16)

The change in enthalpy H during a thermodynamic process is defined in terms of
internal energy and pressure–volume work by

H = U + (pV ) (3.17)
Because it is usual to perform a chemical experiment with the top of the beaker
open to the open air, the pressure p during most chemical reactions and thermodynamic
O
processes is the atmospheric pressure p . Furthermore, this pressure will not vary. In
other words, we usually simplify (pV ) saying p V because only the volume changes.
Accordingly, Equation (3.17) becomes

H = U + p V (3.18)
The equation in the form of Equation (3.18) is the usual form we use. Changes in U
are not equal to the energy supplied as heat (at constant pressure p) because the system
employs some of its energy to push back the surroundings as they expand. The pV term
for work is, therefore, a correction for the loss of energy as work. Because many, if
not most, physicochemical measurements occur under conditions of constant pressure,
changes in enthalpy are vitally important because it automatically corrects for the loss
of energy to the surroundings.

Aside

One of the most common mistakes we make during calculations of this kind is forgetting
the way ‘k’ stands for ‘1000’. Think of it this way: a job advertisement offers a salary
of £14 k. We would be very upset if, at the end of the first year, we were given just
£14 and the employer said he ‘forgot’ the ‘k’ in his advert!