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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 151
T
e
m
p
e
ra
tu
re
, 
θ
/°
C
Mole fraction of B, x
B
 
0
0
0.2 0.4 0.6 0.8 1
500
400
300
T
1
T
2200
100
x
1
x
2
Figure 5.23
�is relationship is rearranged and terms in nc are collected on one side
and those in na on the other to give nax2 = nc(2 − 3x2). �e mole ratio
of compound to free A is given by
nc
na
= x2
2 − 3x2
= 0.41
2 − 3 × 0.41
= 0.53
Solutions to problems
P5D.2 �e mole fraction of sulfur, xS, corresponding to compound PnSm is computed
from the molar masses of sulfur and phosphorus,MS andMP, as
xS =
mMS
mMS + nMP
= m × (32.06 gmol−1)
m × (32.06 gmol−1) + n × (30.97 gmol−1)
Using this expression, mole fractions corresponding to the three compounds
are: (1) P4S3, 0.44; (2) P4S7, 0.64; (3) P4S10, 0.72.
�e phase diagram is a variation of that shown in Fig. 5D.4 on page 178 except
that instead of one compound being formed there are three.�e diagram there-
fore separates into four sections, as shown schematically in Fig. 5.24. Note that
no information is given on the temperature or composition of the eutectics, so
these have simply been selected arbitrarily.
�e diagram has four eutectics labelled e1, e2, e3, and e4; eight two-phase
liquid-solid regions, t1 through t8; and four two-phase solid regions, S1, S2,
S3, and S4.�e composition and physical state of the regions are as follows:
l: liquid S and P
S1: solid P and solid P4S3 S2: solid P4S3 and solid P4S7
S3: solid P4S7 and solid P4S10 S4: solid P4S10 and solid S
t1: liquid P and S and solid P t2: liquid P and S and solid P4S3
t3: liquid P and S and solid P4S3 t4: liquid P and S and solid P4S7
t5: liquid P and S and solid P4S7 t6: liquid P and S and solid P4S10
t7: liquid P and S and solid P4S10 t8: liquid P and S and solid S