SME
Grade 10 Science · Problem type
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?”
Diagram
Before and after, P₁V₁/T₁ = P₂V₂/T₂: 1 × 5/300 = 2 × 3/360.
At
360
K
the
particles
move
√
360
300
≈
1.1
times
as
fast.
This is an example. Type your own values to start a new problem.
P₁ (atm)
×
V₁ (L)
T₁ (K)
=
P₂ (atm)
×
V₂ (L)
T₂ (K)
Formulas
(
P₁
×
V₁
)/
T₁
=
(
P₂
×
V₂
)/
T₂
(1 × 5)/300 = (2 × 3)/360
Assumptions
•
The gas is ideal: its particles take up no room and do not attract each other.
•
Temperatures are in kelvins: add 273 to °C. Pressures are in atm.
•
The amount of gas stays the same.
Step-by-step
WE KNOW
P₁ = 1 atm, V₁ = 5 L, T₁ = 300 K, P₂ = 2 atm, T₂ = 360 K
FIND
volume after (V₂)
Step 1 · Find volume after (V₂)
Use (P₁ × V₁)/T₁ = (P₂ × V₂)/T₂
Multiply
both
sides
by
T₂
and
divide
by
P₂
.
V₂
=
(
P₁
×
V₁
×
T₂
)/(
T₁
×
P₂
)
V₂
=
(1
×
5
×
360)/(300
×
2)
V₂
=
1,800
600
V₂
=
3
L
Check
Put the numbers back in. Both sides should match.
(1 × 5)/300 = (2 × 3)/360 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Related lessons
Gases and the gas laws (PV = nRT)
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