Page 167 - Physical chemistry understanding our chemical world

134 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

Worked Example 4.1 Show mathematically how the entropy of a gas is higher than
the entropy of its respective liquid.

If S (final state) is S (g) and S (initial state) is S (l) ,then S = S (g) − S (l) . Because the volatilizing
of the compound is spontaneous, the sign of S must be positive.
The only way to make S positive is when S (g) >S (l) .

Why do damp clothes become dry when hung outside?

Reaction spontaneity by inspection

Everyone knows damp clothes become dry when hung outside on the washing line.
Any residual water is lost by evaporation from the cloth. In fact, moisture evap-
orates even if the damp clothes hang limp in the absence of a breeze. The water
spontaneously leaves the fabric to effect the physicochemical process H 2 O (l) →
H 2 O (g) .
The loss of water occurs during drying in order to increase the
We obtain the energy overall amount of entropy, because molecules of gaseous water
for evaporating the have a greater energy than do molecules of liquid, merely as a
water by lowering the result of being gas and liquid respectively. In summary, we could
internal energy of the have employed our working definition of entropy (above), which
garment fibres, so the leads to a prediction of the clothes becoming dry, given time,
clothes feel cool to the as a result of the requirement to increase the entropy. Inspection
touch when dry.
alone allows us a shrewd guess at whether a process will occur
spontaneously or not.

Worked Example 4.2 By inspection alone, decide whether the sublimation of iodine
(Equation (4.3)) will occur spontaneously or not:

(4.3)
I 2(s) −−−→ I 2(g)
Molecules in the gas phase have more entropy than molecules in the liquid phase; and
molecules in the liquid phase have more entropy than molecules in the solid state. As an
excellent generalization, the relative order of the entropies is given by

This argument says S (g) S (l) >S (s) (4.4)
nothing about the rate
of sublimation. In fact, The product of sublimation is a gas, and the precursor is a solid.
we do not see subli- Clearly, the product has greater entropy than the starting material,
mation occurring sig- so S increases during sublimation. The process is spontaneous
nificantly at room tem- because S is positive.
perature because it is
so slow.
In a bottle of iodine, the space above the solid I 2 always shows
a slight purple hue, indicating the presence of iodine vapour.