SME
Grade 10 Science · Problem type
The limiting reactant
Use this to find which reactant runs out first, how much product forms and what is left over.
Diagram
3
1
=
3
runs
of
N₂;
6
3
=
2
runs
of
H₂.
H₂ runs out first (the limiting reactant): 2 whole runs.
Made: 4 NH₃ (2 × 2).
Left over (ringed): 3 − 1 × 2 = 1 N₂.
This is an example. Type your own values to start a new problem.
a
N₂ molecules at the start
example
b
H₂ molecules at the start
example
r
Times the reaction happens
worked out (not typed)
m₁
NH₃ molecules made
worked out (not typed)
x
N₂ molecules left over
worked out (not typed)
y
H₂ molecules left over
worked out (not typed)
Formulas
r
=
smaller
of
a
1
and
b
3,
rounded
down
2
=
smaller
of
3
1
and
6
3,
rounded
down
m₁
=
2
×
r
4 = 2 × 2
x
=
a
−
r
1 = 3 − 2
y
=
b
−
3
×
r
0 = 6 − 3 × 2
Assumptions
•
The equation is balanced: N₂ + 3H₂ → 2NH₃.
•
Divide each amount by its coefficient: the smaller answer is the limiting reactant.
•
The reactant with fewer molecules is not always the one that runs out.
Step-by-step
WE KNOW
a = 3, b = 6
FIND
times the reaction happens (r), NH₃ molecules made (m₁), N₂ molecules left over (x), H₂ molecules left over (y)
Step 1 · Find times the reaction happens (r)
Use r = smaller of a ÷ 1 and b ÷ 3, rounded down
Each reactant allows its amount divided by its coefficient runs; the smaller number is how many can happen.
r
=
smaller
of
3
1
and
6
3,
rounded
down
3
1
=
3
for
N₂,
6
3
=
2
for
H₂:
H₂
is
the
limiting
reactant
r
=
2
Step 2 · Find NH₃ molecules made (m₁)
Use m₁ = 2 × r
Each run makes 2 NH₃.
m₁
=
2
×
2
m₁
=
4
Step 3 · Find N₂ molecules left over (x)
Use x = a − r
Each run uses 1 N₂; the rest is left over.
x
=
3
−
2
x
=
1
Step 4 · Find H₂ molecules left over (y)
Use y = b − 3 × r
Each run uses 3 H₂; the rest is left over.
y
=
6
−
3
×
2
y
=
6
−
6
y
=
0
Check
Put the numbers back in. Both sides should match.
2
=
smaller
of
3
1
and
6
3,
rounded
down
✓
4 = 2 × 2 ✓
1 = 3 − 2 ✓
0 = 6 − 3 × 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.