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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 157
of NH4Cl than S1 so it corresponds to a saturated solution in the presence
of solid NH4Cl; S3 corresponds to yet more solid being present.
Adding (NH4)2SO4 to each of these solutions corresponds to travers-
ing the dashed lines from S i to the lower right-hand vertex which cor-
responds to pure (NH4)2SO4. Starting from S1 the system �rst traverses
a one-phase region, meaning that both salts are entirely dissolved, before
moving into a two phase region which implies that one of the salts will
precipitate out.�e tie lines are not given, but presumably as the amount
of (NH4)2SO4 increases the composition of the aqueous solution moves
along the curve to the point where the four lines meet. At this point the
last drop of solution vanishes.
Starting from S2 the system �rst traverses a two-phase region, meaning
that the (NH4)2SO4 is going into solution. Eventually the system moves
into a one-phase region, which implies that addition of (NH4)2SO4 has
caused the excess solid NH4Cl to dissolve. As with the path starting from
S1, this path eventually crosses into a two-phase region where the be-
haviour is as has already been described.
Starting from S3 the system �rst traverses a two-phase region but in con-
trast to S1 and S2 it never enters a one-phase region.
(ii) It is �rst necessary to convert the given masses to mole fractions, using
MNH4Cl = 53.49 gmol
−1 and M(NH4)2SO4 = 132.14 gmol
−1. �e mole
fraction of NH4Cl is
xNH4Cl =
(25 g)/(53.49 gmol−1)
(25 g)/(53.49 gmol−1) + (75 g)/(132.14 gmol−1)
= 0.45
and hence x(NH4)2SO4 = 1− xNH4Cl = 0.55; this point is shown in Fig. 5.30
as S4. Adding water to such a mixture involves traversing the dotted line
from S4 to the apex of the diagram, which corresponds to pure H2O.
To start with the system is entirely solid, but when the line between the
three-phase to two-phase region is crossed the two phases in question
are some kind of solid and an aqueous solution, which appears for the
�rst time. As the two-phase region is traversed the composition of this
aqueous solution traverses the gray line until point S5 where it meets the
dotted line. A�er this, the system moves into a one-phase region: all the
solids are dissolved.
Solutions to problems
P5E.2 (a) �e given points are shown by �lled dots in the phase diagram shown
in Fig. 5.31. �e fact that CO2 and nitroethane have a two-phase region
between xnitroethane = 0.08 and 0.84, and that there is a plait point at
xCO2 = 0.18, xnitroethane = 0.53 establishes some limits on the two-phase
region, the outline of which is indicated by a plausible line. Similarly, the
CO2/DEC two-phase region is established by the given data.
(b) Mixtures with nitroethane and CO2 in a �xed ratio, but with increasing
amounts of DEC, fall on a straight line from some point on the right-hand