SME
Grade 10 Science · Problem type
Vapor pressure of a solution
Use this for “0.5 mol of glucose is dissolved in 9.5 mol of water at 25 °C. How much does the vapor pressure drop?”
Chart
9.5 + 0.5 = 10 mol.
This is an example. Type your own values to start a new problem.
n₁
Moles of water
example · mol
n₂
Moles of solute particles
example · mol
n
Moles in all
calculated · mol
x
Mole fraction of water
calculated
P°
Vapor pressure of pure water
example · mmHg
P
Vapor pressure of the solution
calculated · mmHg
ΔP
Drop in vapor pressure
calculated · mmHg
Formulas
n
=
n₁
+
n₂
10 = 9.5 + 0.5
x
=
n₁
n
0.95 = 9.5/10
P
=
x
×
P
°
22.61 = 0.95 × 23.8
ΔP
=
n₂
n
×
P
°
1.19 = 0.5/10 × 23.8
ΔP
=
P
°
−
P
1.19 = 23.8 − 22.61
Assumptions
•
The solute does not evaporate, so only water molecules at the surface escape (Raoult’s law).
•
The vapor pressure is the pure water’s times water’s mole fraction; at 25 °C pure water’s is 23.8 mmHg.
•
Count particles: a salt that splits into ions counts each ion.
•
The solution is dilute and ideal: mostly water.
Step-by-step
WE KNOW
n₁ = 9.5 mol, n₂ = 0.5 mol, P° = 23.8 mmHg
FIND
moles in all (n), mole fraction of water (x), vapor pressure of the solution (P), drop in vapor pressure (ΔP)
Step 1 · Find moles in all (n)
Use n = n₁ + n₂
Add the water’s moles and the solute particles’.
n
=
9.5
+
0.5
n
=
10
mol
Step 2 · Find mole fraction of water (x)
Use x = n₁/n
Water’s share of all the particles.
x
=
9.5/10
x
=
0.95
Step 3 · Find vapor pressure of the solution (P)
Use P = x × P°
Only the water’s share of the surface escapes, so the pressure drops by that share.
P
=
0.95
×
23.8
P
=
22.61
mmHg
Step 4 · Find drop in vapor pressure (ΔP)
Use ΔP = n₂/n × P°
The pressure drops by the solute’s share of the particles.
ΔP = 0.5/10 × 23.8
ΔP = 0.05 × 23.8
ΔP = 1.19 mmHg
Check
Put the numbers back in. Both sides should match.
10 = 9.5 + 0.5 ✓
0.95 = 9.5/10 ✓
22.61 = 0.95 × 23.8 ✓
1.19 = 0.5/10 × 23.8 ✓
1.19 = 23.8 − 22.61 ✓
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Phase changes, vapor pressure and colligative properties
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What moves the boiling point?
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