SME
Grade 10 Science · Problem type
Dalton’s law of partial pressures
Use this for a mixture of gases: the total pressure from each gas’s partial pressure, and one gas’s mole fraction.
Diagram
Dalton’s law: P = 2 + 0.5 + 1.5 = 4 atm.
Each gas’s share of the particles is its share of the pressure: 24 drawn, 12 He, 3 O₂, 9 N₂.
He’s mole fraction = 2/4 = 0.5.
This is an example. Type your own values to start a new problem.
P (atm)
=
P₁ (atm)
+
P₂ (atm)
+
P₃ (atm)
x₁
Mole fraction of helium
calculated
Formulas
P
=
P₁
+
P₂
+
P₃
4 = 2 + 0.5 + 1.5
x₁
=
P₁
P
0.5
=
2
4
Assumptions
•
A tank holds helium, oxygen and nitrogen, all ideal and at one temperature.
•
Each gas pushes as if it were alone, so the total pressure is the sum of the partial pressures.
•
A gas’s share of the pressure is its share of the particles: its mole fraction.
Step-by-step
WE KNOW
P₁ = 2 atm, P₂ = 0.5 atm, P₃ = 1.5 atm
FIND
total pressure (P), mole fraction of helium (x₁)
Step 1 · Find total pressure (P)
Use P = P₁ + P₂ + P₃
Each gas adds its own push to the total.
P
=
2
+
0.5
+
1.5
P
=
4
atm
Step 2 · Find mole fraction of helium (x₁)
Use x₁ = P₁/P
Helium’s share of the pressure is its share of the particles.
x₁
=
2
4
x₁
=
0.5
Check
Put the numbers back in. Both sides should match.
4 = 2 + 0.5 + 1.5 ✓
0.5
=
2
4
✓
← Previous lesson
Effusion: Graham’s law
Next lesson →
Phase changes, vapor pressure and colligative properties
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Gases and the gas laws (PV = nRT)
Main lesson
Boyle’s law: squeezing a gas
Use this for a gas squeezed or let out at one temperature: “6 L at 1 atm is pressed into 3 L. What is the pressure?”
Charles’s law: heating a gas
Use this for a gas warmed or cooled at one pressure: “2.00 L at 300 K is heated to 450 K. What is its volume?”
Gay-Lussac’s law: a sealed, rigid container
Use this for a gas heated in a rigid container: “A tire at 2.00 atm and 280 K warms to 308 K. What is the pressure?”
The combined gas law
Use this when pressure, volume and temperature all change: “5.00 L at 1.00 atm and 300 K goes to 2.00 atm and 360 K. What is the volume?”
Effusion: Graham’s law
Use this for “Helium (4.00 g/mol) and argon (39.95 g/mol) leak from one tank. Which escapes faster, and how many times as fast?”