SME
Physical Chemistry I: Thermodynamics & Kinetics · Problem type
Degrees of freedom (phase rule)
Use this for “A mixture of ethanol and water boils, with liquid and vapor present. How many intensive variables can be changed on their own?”
Diagram
Water: the vapor curve runs from the triple point (273.2 K, 0.00604 atm) to the critical point (647.1 K, 217.7 atm); pressure on a log scale.
Between
neighbouring
points
ln
P
is
a
straight
line
in
1
T
:
Clausius–Clapeyron,
ln(
P₂
P₁
)
=
−(
ΔHᵥₐₚ
R
)(
1
T₂
−
1
T₁
),
with
ΔHᵥₐₚ
constant
on
each
piece.
The melting line leans left: dP/dT = −133 atm/K, so raising the pressure lowers the melting point.
F = C − P + 2 = 1 − 3 + 2 = 0: nothing can change; the point is fixed.
This is an example. Type your own values to start a new problem.
F
=
C
−
P
+
2
Formulas
F
=
C
−
P
+
2
0 = 1 − 3 + 2
Assumptions
•
F counts the intensive variables (T, P and the compositions) that can change while the same phases stay at equilibrium.
•
C is the number of components, the fewest species that can make every phase; P is the number of phases.
•
The picture is water’s diagram (C = 1): P = 3 sits at the triple point, P = 2 on the vapor curve, P = 1 in the liquid.
Step-by-step
WE KNOW
C = 1, P = 3
FIND
degrees of freedom (F)
Step 1 · Find degrees of freedom (F)
Use F = C − P + 2
T
and
P
give
2;
each
component
adds
a
composition
to
choose,
and
each
phase
past
the
first
ties
them
with
one
more
equation.
F
=
1
−
3
+
2
F
=
0
→
F
=
0:
a
single
point;
nothing
can
change
while
these
phases
coexist.
Check
Put the numbers back in. Both sides should match.
0 = 1 − 3 + 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Phase equilibria
Main lesson
Slope of a melting line (Clapeyron)
Use this for “Benzene melts at 278.7 K with ΔHfus = 9870 J/mol, and it grows by 10.3 cm³/mol as it melts. Find the slope dP/dT of its melting line.”
Vapor pressure of an ideal mixture (Raoult)
Use this for “Hexane (151 torr) and heptane (45.8 torr) are mixed at 25 °C with xₕₑₓₐₙₑ = 0.350. Find the total vapor pressure and the vapor’s mole fraction of hexane.”