SME
Grade 10 Science · Problem type
Balancing the combustion of an alkene
Use this to balance an alkene burning, such as “C₅H₁₀ + O₂ → CO₂ + H₂O”: with an odd number of carbons the fuel’s coefficient is 2.
Diagram
2 C₅H₁₀ + 15 O₂ → 10 CO₂ + 10 H₂O
Carbon: 2 × 5 = 10 before, 10 × 1 = 10 after
Hydrogen: 2 × 10 = 20 before, 10 × 2 = 20 after
Oxygen: 15 × 2 = 30 before, 10 × 2 + 10 × 1 = 30 after
Balanced: the same atoms on both sides, only rearranged.
This is an example. Type your own values to start a new problem.
a
C
H
+
b
O₂
→
c
CO₂
+
d
H₂O
Formulas
y
=
2
×
x
10 = 2 × 5
a
=
1
if
y
is
a
multiple
of
4,
else
2
2 = 1 if 10 is a multiple of 4, else 2
c
=
a
×
x
10 = 2 × 5
d
=
a
×
y
2
10
=
2
×
10
2
b
=
c
+
d
2
15
=
10
+
10
2
Assumptions
•
A hydrocarbon burns in oxygen to make carbon dioxide and water; coefficients count molecules, subscripts never change.
•
An alkene has 2x hydrogen atoms for x carbon atoms.
•
Balance carbon first, then hydrogen, and oxygen last, since O₂ appears alone.
•
When the hydrogens are not a multiple of 4, the O₂ would come out as a half: double the fuel.
Step-by-step
WE KNOW
x = 5
FIND
hydrogen atoms in the fuel (y), fuel molecules (a), carbon dioxide molecules (c), water molecules (d), oxygen molecules (b)
Step 1 · Find hydrogen atoms in the fuel (y)
Use y = 2 × x
Each carbon holds 2 hydrogens and the ends 2 more; the double bond takes 2 away.
y
=
2
×
5
y
=
10
Step 2 · Find fuel molecules (a)
Use a = 1 if y is a multiple of 4, else 2
Each O₂ brings 2 oxygen atoms. With one fuel molecule the water’s oxygen would leave half an O₂ unless the hydrogens are a multiple of 4.
a
=
1
if
10
is
a
multiple
of
4,
else
2
a
=
2
Step 3 · Find carbon dioxide molecules (c)
Use c = a × x
Carbon first: one CO₂ for each carbon atom in the fuel.
c
=
2
×
5
c
=
10
Step 4 · Find water molecules (d)
Use d = a × y/2
Hydrogen next: each H₂O takes 2 of the fuel’s hydrogen atoms.
d
=
2
×
10
2
d
=
10
Step 5 · Find oxygen molecules (b)
Use b = c + d/2
Oxygen last: 2 atoms in each CO₂ and 1 in each H₂O, halved because each O₂ brings 2.
b
=
10
+
10
2
20 + 10 = 30 oxygen atoms on the right, so 15 O₂ on the left
b
=
15
Check
Put the numbers back in. Both sides should match.
10 = 2 × 5 ✓
2 = 1 if 10 is a multiple of 4, else 2 ✓
10 = 2 × 5 ✓
10
=
2
×
10
2
✓
15
=
10
+
10
2
✓
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Balancing the combustion of an alkane
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