SME
Physical Chemistry I: Thermodynamics & Kinetics · Problem type
Degree of dissociation from Kp
Use this for “Kp = 0.148 for N₂O₄ ⇌ 2NO₂ at 25 °C. At a total pressure of 1.00 bar, what fraction of the N₂O₄ dissociates, and what are the partial pressures?”
Diagram
Dalton’s law: P = 0.6822 + 0.3178 = 1 bar.
Each gas’s share of the particles is its share of the pressure: 24 drawn, 16 N₂O₄, 8 NO₂ (rounded).
This is an example. Type your own values to start a new problem.
Kp
=
4
×
α
2
×
P (bar)
1
−
α
2
p(N₂O₄)
Partial pressure of N₂O₄
calculated · bar
p(NO₂)
Partial pressure of NO₂
calculated · bar
Formulas
Kp
=
4
×
α
2
×
P
1 −
α
2
0.148
=
4
×
0.189
2
×
1
1 −
0.189
2
p(N₂O₄)
=
P
×
1 −
α
1 +
α
0.682
=
1
×
1 − 0.189
1 + 0.189
p(NO₂)
=
2
×
α
×
P
1 +
α
0.318
=
2
×
0.189
×
1
1 + 0.189
Assumptions
•
The gas starts as pure N₂O₄. A fraction α of it splits, leaving 1 − α of N₂O₄ and making 2α of NO₂, so 1 + α moles in all.
•
Each partial pressure is its mole fraction times the total pressure P, and Kp = p(NO₂)² ÷ p(N₂O₄) with pressures in bar.
•
Both gases are ideal. Raising P lowers α: the mixture shifts to the side with fewer moles of gas.
Step-by-step
WE KNOW
Kp = 0.148, P = 1 bar
FIND
degree of dissociation (α), partial pressure of N₂O₄ (p(N₂O₄)), partial pressure of NO₂ (p(NO₂))
Step 1 · Find degree of dissociation (α)
Use Kp = 4 × α² × P ÷ (1 − α²)
Kp(1
−
α
2
)
=
4
α
²
P
,
so
α
2
=
Kp
Kp + 4
P
.
Take
the
positive
root.
α
=
√(
Kp
Kp + 4 ×
P
)
α
=
√(
0.148
0.148 + 4 × 1
)
α
=
√(
0.148
4.148
)
α
=
√
0.03568
α
=
0.189
Step 2 · Find partial pressure of N₂O₄ (p(N₂O₄))
Use p(N₂O₄) = P × (1 − α) ÷ (1 + α)
N₂O₄
is
1
−
α
of
the
1
+
α
moles:
its
share
of
the
total
pressure.
p(N₂O₄)
=
1
×
1 − 0.189
1 + 0.189
p(N₂O₄)
=
0.811
1.189
p(N₂O₄) = 0.682 bar
Step 3 · Find partial pressure of NO₂ (p(NO₂))
Use p(NO₂) = 2 × α × P ÷ (1 + α)
NO₂
is
2
α
of
the
1
+
α
moles:
its
share
of
the
total
pressure.
p(NO₂)
=
2
×
0.189
×
1
1 + 0.189
p(NO₂)
=
2
×
0.189
1.189
p(NO₂)
=
0.378
1.189
p(NO₂) = 0.318 bar
Check
Put the numbers back in. Both sides should match.
0.148
=
4
×
0.189
2
×
1
1 −
0.189
2
✓
0.682
=
1
×
1 − 0.189
1 + 0.189
✓
0.318
=
2
×
0.189
×
1
1 + 0.189
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.