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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 103
E4B.7(b) �e Clausius–Clapeyron equation [4B.9–133] is d ln p/dT = ∆vapH/RT2.�is
equation is rearranged for ∆vapH, and the expression for ln p is di�erentiated.
It does not matter that the pressure is given in units of Torr because only the
slope of ln p is required.
∆vapH = RT2 d ln p
dT
= RT2 d
dT
(18.361 − 3036.8K
T
) = RT2 (3036.8K
T2
)
= (3036.8K)R = (3036.8K) × (8.3145 JK−1mol−1) = 25.249 kJmol−1
E4B.8(b) (i) �e Clausius–Clapeyron equation [4B.9–133] is d ln p/dT = ∆vapH/RT2.
�is equation is rearranged for ∆vapH, and the expression for ln p is dif-
ferentiated, noting from inside the front cover that ln x = (ln 10) log x. It
does not matter that the pressure is given in units of Torr because only
the slope of ln p is required.
∆vapH = RT2 d ln p
dT
= RT2 ln 10d log p
dT
= RT2 ln 10 d
dT
(8.750 − 1625K
T
)
= RT2 ln 10(1625K
T2
) = (1625K)R ln 10
= (1625K) × (8.3145 JK−1mol−1) × ln 10 = 31.11 kJmol−1
(ii) �e normal boiling point refers to the temperature at which the vapour
pressure is 1 atm which is 760 Torr.�e given expression, log(p/Torr) =
8.750 − (1625K)/T is rearranged for T and a pressure of 760 Torr is
substituted into it to give
T = 1625K
8.750 − log(p/Torr)
= 1625K
8.750 − log 760
= 276.9 K or 3.720 ○C
Note that this temperature lies outside the range 15 ○C to 35 ○C for which
the expression for log(p/Torr) is known to be valid, and is therefore an
estimate.
E4B.9(b) �e relationship betweenpressure and temperature along the solid–liquid bound-
ary is given by [4B.7–132], p = p∗ + (∆fusH/T∗∆fusV)(T − T∗).�e value of
∆fusV is found using Vm = M/ρ where M is the molar mass and ρ is the mass
density:
∆fusV = Vm(l) − Vm(s) =
M
ρ(l)
− M
ρ(s)
= 46.1 gmol−1
0.789 × 106 gm−3 −
46.1 gmol−1
0.801 × 106 gm−3 = 8.75... × 10
−7m3mol−1
[4B.7–132] is then rearranged for T and the values substituted in to give
T = T∗ + (p − p∗)T
∗∆fusV
∆fusH
= ([−3.65 + 273.15]K) + ([100 × 106 − 1 × 105]Pa)
× ([−3.65 + 273.15]K) × (8.75... × 10−7m3)
8.68 × 103 Jmol−1
= 272K or −0.935 ○C