The Foundations of Chemistry

products). The surroundings exert a constant pressure of one atmosphere and do work on
the system by compressing it. The internal energy of the system increases by an amount
equal to the amount of work done on it.
The work done on or by a system depends on the externalpressure and the volume.
When the external pressure is constant during a change, the amount of work done is equal
to this pressure times the change in volume. The work done ona system equals P
V
or P(V 2 V 1 ).

V 2 is the final volume, and V 1 is the

initial volume.

15-10 Changes in Internal Energy, E 615

Compression (volume decreases) Expansion (volume increases)

Work is done bythe surroundings on Work is done bythe system onthe
the system, so the sign of wis surroundings, so the sign of wis
positive negative
V 2 is less than V 1 , so
V(V 2 V 1 ) is V 2 is greater than V 1 , so
V(V 2 V 1 )
negative is positive

wP
Vis positive wP
Vis negative

()()() ()()()

Can be due to a decreasein number of Can be due to an increasein number of
moles of gas (
nnegative) moles of gas (
npositive)

We substitute P
Vfor win the equation
Eqwto obtain

EqP
V

In constant-volume reactions, no P
Vwork is done. Volume does not change, so
nothing “moves through a distance,” and d0 and fd0. The change in internal energy
of the system is just the amount of heat absorbed or released at constant volume, qv.

Eqv

Figure 15-8 shows the same phase change process as in Figure 15-6, but at constant volume
condition, so no work is done.
Solids and liquids do not expand or contract significantly when the pressure changes
(
V0). In reactions in which equal numbers of moles of gases are produced and
consumed at constant temperature and pressure, essentially no work is done. By the ideal
gas law, P
V(
n)RTand
n0, where
nequals the number of moles of gaseous
products minus the number of moles of gaseous reactants. Thus, the work term whas a
significant value at constant pressure only when there are different numbers of moles of
gaseous products and reactants so that the volume of the system changes.

EXAMPLE 15-13 Predicting the Sign of Work

For each of the following chemical reactions carried out at constant temperature and constant
pressure, predict the sign of wand tell whether work is done onor bythe system. Consider the
reaction mixture to be the system.
(a) Ammonium nitrate, commonly used as a fertilizer, decomposes explosively.

2NH 4 NO 3 (s)88n2N 2 (g)4H 2 O(g)O 2 (g)

This reaction was responsible for an explosion in 1947 that destroyed nearly the entire port of
Texas City, Texas, and killed 576 people.

(b) Hydrogen and chlorine combine to form hydrogen chloride gas.

H 2 (g)Cl 2 (g)88n2HCl(g)

Do not make the error of setting work

equal to V
P.

A subscript v indicates a constant-

volume process; a subscript p indicates

a constant-pressure process.

Figure 15-8 A system that absorbs

heat at constant volume. Some dry

ice [CO 2 (s)] is placed into a rigid

flask, which is then sealed. As the

dry ice absorbs heat from the

surroundings, some CO 2 (s) sublimes

to form CO 2 (g). In contrast to the

case in Figure 15-6, this system

cannot expand (
V0), so no work

is done, and the pressure in the flask

increases. Thus, the heat absorbed at

constant volume, qv, is equal to 
E

for the process.