SME
Physical Chemistry I: Thermodynamics & Kinetics · Problem type
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.”
Diagram
Pxy diagram of A–B: the bubble curve runs from P₂ˢᵃᵗ = 28.4 to P₁ˢᵃᵗ = 95.1 torr, the dew curve under it; between them liquid and vapor coexist.
P = x₁P₁ˢᵃᵗ + (1 − x₁)P₂ˢᵃᵗ = 0.6 × 95.1 + 0.4 × 28.4 = 68.42 torr.
y₁
=
x₁P₁
ˢᵃᵗ
P
=
0.834:
the
vapor
is
richer
in
A,
the
more
volatile.
This is an example. Type your own values to start a new problem.
P (torr)
=
xA
×
PA° (torr)
+
(1
−
xA
)
×
PB° (torr)
The picture numbers the liquids, 1 for A and 2 for B, so its x₁, P₁ˢᵃᵗ and P₂ˢᵃᵗ are xA, PA° and PB°.
yA
Mole fraction of A in the vapor
calculated
Formulas
P
=
xA
×
PA°
+
(1
−
xA)
×
PB°
68.42 = 0.6 × 95.1 + (1 − 0.6) × 28.4
yA
=
xA
×
PA°
÷
P
0.834
=
0.6
×
95.1
68.42
Assumptions
•
An ideal solution: each liquid’s partial pressure is its mole fraction times its own vapor pressure, PA = xAP_A° (Raoult’s law).
•
The vapor is an ideal gas, so each liquid’s share of the vapor is its partial pressure ÷ the total (Dalton’s law).
•
Both pure vapor pressures are at the mixture’s temperature; xB = 1 − xA.
Step-by-step
WE KNOW
xA = 0.6, PA° = 95.1 torr, PB° = 28.4 torr
FIND
total vapor pressure (P), mole fraction of A in the vapor (yA)
Step 1 · Find total vapor pressure (P)
Use P = xA × PA° + (1 − xA) × PB°
Each liquid adds its mole fraction times its own vapor pressure; add the two partial pressures.
P
=
0.6
×
95.1
+
(1
−
0.6)
×
28.4
P
=
0.6
×
95.1
+
0.4
×
28.4
P
=
57.06
+
11.36
P
=
68.42
torr
Step 2 · Find mole fraction of A in the vapor (yA)
Use yA = xA × PA° ÷ P
A’s partial pressure over the total is its mole fraction in the vapor.
yA
=
0.6
×
95.1
68.42
yA
=
57.06
68.42
yA = 0.834 → yA > xA: the vapor is richer in A, the more volatile liquid.
Check
Put the numbers back in. Both sides should match.
68.42 = 0.6 × 95.1 + (1 − 0.6) × 28.4 ✓
0.834
=
0.6
×
95.1
68.42
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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