SME
Grade 9 Science · Problem type
The photosynthesis equation
Use this for “How many CO₂ molecules make 2 glucose molecules, and are the atoms conserved?”
Diagram
6 CO₂ + 6 H₂O → C₆H₁₂O₆ + 6 O₂
Carbon: 6 × 1 = 6 before, 1 × 6 = 6 after
Hydrogen: 6 × 2 = 12 before, 1 × 12 = 12 after
Oxygen: 6 × 2 + 6 × 1 = 18 before, 1 × 6 + 6 × 2 = 18 after
Balanced: the same atoms on both sides, only rearranged.
This is an example. Choose your own values to start a new problem.
c
CO₂
+
w
H₂O
→
g
C₆H₁₂O₆
+
o
O₂
C₁
Carbon atoms before
worked out (not typed)
C₂
Carbon atoms after
worked out (not typed)
H₁
Hydrogen atoms before
worked out (not typed)
H₂
Hydrogen atoms after
worked out (not typed)
O₁
Oxygen atoms before
worked out (not typed)
O₂
Oxygen atoms after
worked out (not typed)
Formulas
c
=
6
×
g
6 = 6 × 1
w
=
6
×
g
6 = 6 × 1
o
=
6
×
g
6 = 6 × 1
C₁
=
c
6 = 6
C₂
=
6
×
g
6 = 6 × 1
H₁
=
2
×
w
12 = 2 × 6
H₂
=
12
×
g
12 = 12 × 1
O₁
=
2
×
c
+
w
18 = 2 × 6 + 6
O₂
=
6
×
g
+
2
×
o
18 = 6 × 1 + 2 × 6
Assumptions
•
Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. Respiration is the same equation read backward.
•
Atoms are rearranged, never made or lost: each element has as many atoms after as before.
Step-by-step
WE KNOW
g = 1
FIND
CO₂ molecules (c), H₂O molecules (w), O₂ molecules (o), carbon atoms before (C₁), carbon atoms after (C₂), hydrogen atoms before (H₁), hydrogen atoms after (H₂), oxygen atoms before (O₁), oxygen atoms after (O₂)
Step 1 · Find CO₂ molecules (c)
Use c = 6 × g
Each glucose takes 6 CO₂.
c
=
6
×
1
c
=
6
Step 2 · Find H₂O molecules (w)
Use w = 6 × g
Each glucose takes 6 H₂O.
w
=
6
×
1
w
=
6
Step 3 · Find O₂ molecules (o)
Use o = 6 × g
Each glucose gives off 6 O₂.
o
=
6
×
1
o
=
6
Step 4 · Find carbon atoms before (C₁)
Use C₁ = c
One carbon in each CO₂.
C₁
=
6
Step 5 · Find carbon atoms after (C₂)
Use C₂ = 6 × g
Six carbons in each glucose.
C₂
=
6
×
1
C₂
=
6
Step 6 · Find hydrogen atoms before (H₁)
Use H₁ = 2 × w
Two hydrogens in each H₂O.
H₁
=
2
×
6
H₁
=
12
Step 7 · Find hydrogen atoms after (H₂)
Use H₂ = 12 × g
Twelve hydrogens in each glucose.
H₂
=
12
×
1
H₂
=
12
Step 8 · Find oxygen atoms before (O₁)
Use O₁ = 2 × c + w
Two oxygens in each CO₂ and one in each H₂O.
O₁
=
2
×
6
+
6
O₁
=
12
+
6
O₁
=
18
Step 9 · Find oxygen atoms after (O₂)
Use O₂ = 6 × g + 2 × o
Six
oxygens
in
each
glucose
and
two
in
each
O₂
.
O₂
=
6
×
1
+
2
×
6
O₂
=
6
+
12
O₂
=
18
Check
Put the numbers back in. Both sides should match.
6 = 6 × 1 ✓
6 = 6 × 1 ✓
6 = 6 × 1 ✓
6 = 6 ✓
6 = 6 × 1 ✓
12 = 2 × 6 ✓
12 = 12 × 1 ✓
18 = 2 × 6 + 6 ✓
18 = 6 × 1 + 2 × 6 ✓
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