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100 4 PHYSICAL TRANSFORMATIONS OF PURE SUBSTANCES
E4A.2(b) �e change in Gibbs energy when an in�nitesimal amount dn of substance is
moved from location 1 to location 2 is given by (Section 4A.1(c) on page 121)
dG = (µ2 − µ1)dn
Assuming that 0.15 mmol is a su�ciently small amount to be regarded as in-
�nitesimal, the Gibbs energy change in this case is
∆G = (µ2 − µ1)∆n = (−8.3 × 103 Jmol−1) × (0.15 × 10−3 mol) = −1.2 J
E4A.3(b) Use the phase rule [4A.1–124], F = C−P+2, with C = 4 (for four components).
Rearranging for the number of phases gives
P = C − F + 2 = 4 − F + 2 = 6 − F
�e number of variables that can be changed arbitrarily, F, cannot be smaller
than zero so the maximum number of phases in this case is 6 .
E4A.4(b) Use the phase rule [4A.1–124], F = C − P + 2, with C = 1 (one component).
Inserting P = 2 gives F = 1−2+2 = 1.�e condition P = 2 therefore represents
a line . A line has F = 1 because a variation in pressure determines the required
variation in the temperature needed to stay on the line. P = 2 indicates that two
phases are present, so this result con�rms that a situation in which two phases
are in equilibrium is represented by a line in a phase diagram.
E4A.5(b) (i) 100 K and 1 atm lies in the Ice I region of the phase diagram, so only
one phase (Ice I) will be present.
(ii) 300 K and 10 atm lies in the liquid region, so only one phase (liquid) will
be present.
(iii) 273.16K and611 Pa corresponds to the triple point ofwater. So three phases
(Ice I, liquid water, and gas) will be present.
Solutions to problems
P4A.2 (a) At 200 K and 0.1 atm, the phase diagram indicates that CO2 is a gas. On
increasing the pressure, a point will be reached at which gas and solid are
in equilibrium. Above this pressure only the solid form will exist.
(b) 310 K is above the critical temperature so distinct liquid and gas phases
do not exist. A single phase (a supercritical �uid) therefore exists at all
pressures (except perhaps at extremely high pressures when a solid might
be formed).
(c) 216.8 K corresponds to the triple point of CO2. Below 5.11 atm (the pres-
sure corresponding to the triple point) CO2 will exist as a gas. At 5.11 atm
solid, liquid and gas phases will all be present in equilibrium. Above
this pressure, the phase diagram shows that only the solid phase will be
present.
P4A.4 A schematic phase diagram is shown in Fig 4.1. Note that in reality the phase
boundaries may be curved rather than straight.�ere is one triple point which
is marked with a dot.