Turning light into food: the photosynthesis equations
By the end of this lesson you will be able to
- State the word equation and the balanced symbol equation for photosynthesis, and describe it as the transformation of light energy into chemical energy.
- Explain the role of chlorophyll and chloroplasts, and why the reaction happens only in green cells in the light.
- Describe how a leaf is tested for starch and interpret the variegated-leaf and covered-leaf experiments as evidence.
- Outline how van Helmont, Priestley and Ingenhousz each changed what people believed a plant does.
- Analyse pondweed bubble counts against lamp distance and identify the limiting-factor plateau.
The puzzle
A mopane tree in the Tuli Block weighs several tonnes. Dig around its roots and the soil is still there — it has not been eaten away into a tree-shaped hole. The tree did not come from the soil. It did not come from the water alone either: water is hydrogen and oxygen, and wood is mostly carbon. So where did the tonnes of carbon come from? The answer is invisible, weighs almost nothing, and you are breathing it out right now.
A seedling with a mass of 2 g is planted in a pot holding exactly 1000 g of dry soil, watered for a year, and grows to 120 g. Predict the mass of the dry soil at the end: about 1000 g, about 900 g, or about 880 g? Then predict where the extra 118 g of plant came from.
Compare your answer
The soil still has a mass of about 1000 g — it loses a few grams of minerals at most. The 118 g came almost entirely from the air and the water: carbon dioxide from the air supplies the carbon, water supplies the hydrogen, and the plant assembles them into sugar, then into cellulose and everything else. A tree is mostly air, rearranged. Jan Baptist van Helmont did this exact experiment with a willow in the 1640s and got the right result and the wrong conclusion, which is the story at the end of this lesson.
The science — structured notes
1.1 The equations
Photosynthesis is the process by which green plants (and algae and some bacteria) make their own food. It takes two simple, low-energy substances — carbon dioxide and water — and, using the energy of light, builds them into glucose, a high-energy sugar, releasing oxygen as a by-product.
carbon dioxide + water → glucose + oxygen
(in the presence of light and chlorophyll)
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Read the symbol equation slowly. Six molecules of carbon dioxide supply six carbon atoms — exactly the six carbons in one glucose molecule. Six molecules of water supply twelve hydrogen atoms — exactly the twelve in glucose. Count the oxygen atoms: 12 + 6 = 18 on the left; 6 in glucose + 12 in six O₂ = 18 on the right. The equation is balanced: no atom is created or destroyed, only rearranged into new molecules. That is why the tree is not made “from nothing” — it is made from atoms that arrived as gas and liquid.
| Substance | Formula | Where the plant gets it or puts it | Role |
|---|---|---|---|
| Carbon dioxide | CO₂ | Diffuses in from the air through stomata (Lesson 2.2); dissolved in water for pondweed | Reactant — supplies carbon and oxygen |
| Water | H₂O | Absorbed by roots, carried up the xylem | Reactant — supplies hydrogen (and the oxygen given off) |
| Glucose | C₆H₁₂O₆ | Made in chloroplasts; used, stored as starch, or turned into cellulose, fats, proteins | Product — the chemical energy store |
| Oxygen | O₂ | Diffuses out through stomata; bubbles from pondweed | Product — a by-product the plant does not need for this reaction |
| Light | — | Absorbed by chlorophyll | Energy input — written above the arrow, never as a reactant |
| Chlorophyll | — | In chloroplasts | Pigment that captures the light; not used up, so it is not a reactant |
1.2 An energy transformation — the heart of the unit
Carbon dioxide and water are what you get when fuel has burnt: the ash-and-smoke end of chemistry, with very little energy left in them. Glucose is a fuel — a gram of it releases about 16 kJ when it is respired or burnt. Photosynthesis therefore runs “uphill”: it needs a large input of energy, and that input is light. The light energy absorbed by chlorophyll is transformed into chemical energy stored in the bonds of glucose. Every joule in a bowl of bogobe, a litre of petrol or a log on the fire was once a joule of sunlight caught by a leaf. This is the unit’s statement of inquiry in one sentence: photosynthesis stores the energy, respiration (Lesson 2.5) releases it, and between them they form a system that humans have learnt to manipulate.
A maize plant makes 1.2 kg of glucose in a season. Roughly how much light energy did it store, and how does this compare with the sunlight that fell on it?
Glucose stores about 16 kJ per gram, so 1200 g × 16 kJ/g ≈ 19 000 kJ (19 MJ).
A square metre of ground in Botswana receives about 20 MJ of sunlight per day, roughly 3000 MJ over a 150-day season. If the plant occupies half a square metre, about 1500 MJ fell on it.
19 MJ stored out of 1500 MJ received is a little over 1 %. Crops typically convert 1–2 % of the sunlight they receive into stored chemical energy; the rest is reflected, passes through, or warms the leaf. That low figure is why the 2026 projects in Lesson 2.4 are trying to improve it.
1.3 Chlorophyll and chloroplasts — where and why
1.4 Testing a leaf for starch — the four steps and why each is there
| Step | What you do | Why |
|---|---|---|
| 1 | Drop the leaf in boiling water for about 30 s | Kills the cells and stops all reactions; breaks the cell membranes so iodine can enter later |
| 2 | Move it to a boiling tube of ethanol standing in the hot water (burner off) | Ethanol dissolves the chlorophyll, so the leaf turns white and the colour change can be seen; ethanol is flammable, so it is warmed in a water bath, never over a flame |
| 3 | Rinse in warm water | Ethanol makes the leaf brittle; water softens it so it can be spread flat |
| 4 | Spread on a white tile and add iodine solution | Iodine turns from orange-brown to blue-black where starch is present |
A geranium plant is kept in the dark for 48 hours (destarched), so any starch found afterwards must have been made during the experiment. Two leaves are then treated.
Variegated leaf (green with white patches, no chlorophyll in the white). After 6 hours in sunlight and the starch test: green parts blue-black, white parts stay orange-brown. Conclusion: chlorophyll is needed for photosynthesis — the only thing that differs between the two regions.
Covered leaf. A strip of black foil is clipped across the middle of a green leaf for the same 6 hours. Result: uncovered parts blue-black, the strip’s shadow orange-brown. Conclusion: light is needed — the covered part had chlorophyll, water and carbon dioxide, and still made no starch.
Why destarch first? Without it, starch left over from yesterday would turn every leaf blue-black, and the experiment would show nothing. The 48 hours in darkness is what makes the result a fair test of what happened today.
A student skips the ethanol step and adds iodine directly to a boiled green leaf. What will she see, and why is the result useless?
Reveal answer
The leaf stays dark green — iodine may darken it slightly, but the blue-black of the starch–iodine complex cannot be distinguished from the green of the chlorophyll. The result is useless because there is no visible contrast between “starch present” and “starch absent”; a positive and a negative leaf would look the same. The ethanol step removes the pigment precisely so that the colour change can be seen against a white leaf.
1.5 Pondweed and the lamp — measuring the rate
Starch tests give a yes or no. To measure how fast photosynthesis is happening you need a product you can count, and pondweed (Elodea or Cabomba) obliges: cut the stem and it releases a stream of oxygen bubbles that you can count per minute, or collect in a gas syringe as a volume. Move the lamp closer and the bubbles come faster. But light intensity is not proportional to how close the lamp is — it follows the inverse-square law:
light intensity ∝ 1d² so halving the distance gives four times the light
Another class, using a different shoot and a richer carbon dioxide supply, counted these bubbles per minute at 10, 20, 30, 40 and 60 cm: 58, 44, 25, 14, 6. Is the rate proportional to light intensity?
Convert distance to relative light intensity using 1d²: 1/100 = 0.0100, 1/400 = 0.0025, 1/900 = 0.0011, 1/1600 = 0.0006, 1/3600 = 0.0003 (per cm²).
From 60 cm to 30 cm the intensity rises four times (0.0003 → 0.0011) and the rate rises about four times (6 → 25): at low light, rate is roughly proportional to intensity — light is the limiting factor.
From 20 cm to 10 cm the intensity rises four times again (0.0025 → 0.0100) but the rate only from 44 to 58 — a 30 % rise. The curve is flattening: something else (carbon dioxide in the water, or the temperature) is now limiting. This plateau is the subject of Lesson 2.3.
For each observation, state which part of the photosynthesis equation it is evidence for.
(a) A sealed jar of pondweed in sunlight: the water’s dissolved carbon dioxide falls during the day.
(b) Bubbles from pondweed relight a glowing splint.
(c) A geranium leaf kept in a bag of air with all the CO₂ removed by soda lime makes no starch, even in bright light.
Reveal answer
(a) Carbon dioxide is a reactant — it is used up, so its concentration falls while the plant photosynthesises.
(b) Oxygen is a product — relighting a glowing splint is the test for oxygen, so the gas released is O₂.
(c) Carbon dioxide is essential — with light, water and chlorophyll all present but CO₂ absent, no glucose (and so no starch) is made. The soda-lime bag is the control that isolates one reactant.
“Plants get their food from the soil through their roots.”
Reveal answer
False. Plants make their food — glucose — in their leaves from carbon dioxide and water, using light. The roots absorb water and small quantities of mineral ions (nitrates for proteins, magnesium for chlorophyll), which are not food in the energy sense. Van Helmont’s willow gained 74 kg while the soil lost 57 g; the soil is a source of water and minerals, not of the plant’s mass or energy.
What if a plant were kept in bright light, with plenty of water and CO₂, but at 2 °C? Predict the starch test result and explain.
Reveal answer
Little or no starch. Photosynthesis is a chain of enzyme-controlled reactions inside the chloroplast; at 2 °C the molecules move so slowly that the enzymes work at a tiny fraction of their rate at 25 °C, so almost no glucose is made even though every reactant and the light are present. Temperature is the third factor that can limit the rate (Lesson 2.3), and it is why a greenhouse is heated as well as lit.
Try it — pondweed, the lamp and the inverse-square law
Count the oxygen bubbles from a pondweed shoot for one minute at six lamp distances. Then convert each distance into a light intensity using 1/d² and plot rate against intensity: is it a straight line, or does it bend? Then change the sodium hydrogencarbonate (the CO₂ supply) and the water temperature, and see how far each one moves the whole curve.
Suppose your means were: 60 cm → 13, 50 → 16, 40 → 21, 30 → 27, 20 → 34, 10 → 40 bubbles per minute.
(a) Describe the relationship between lamp distance and rate, quoting values.
(b) Use the 1/d² values to decide whether the rate is proportional to light intensity across the whole range.
(c) Explain why counting bubbles is a less precise measure of the rate than collecting the gas in a syringe.
Reveal answer
(a) As the lamp distance decreases from 60 cm to 10 cm, the rate increases from 13 to 40 bubbles per minute — roughly three times — and the rise is gradual rather than sudden: +8 bubbles for the 20 cm from 60 to 40, and +6 for the last 10 cm from 20 to 10. The relationship is a curve, not a straight line, because equal steps in distance are not equal steps in light: intensity rises with 1/d².
(b) 1/d² × 10 000: 2.8, 4.0, 6.3, 11.1, 25, 100. From 60 cm to 30 cm the intensity rises 4.0 times but the rate rises only 2.1 times (13 → 27); from 20 cm to 10 cm the intensity rises 4.0 times again and the rate rises only 1.2 times (34 → 40). So the rate is not proportional to intensity anywhere in this range, and it is furthest from proportional near the lamp. Even at 60 cm the chloroplasts already have more light than they can use at 1 % sodium hydrogencarbonate, so carbon dioxide is sharing the role of limiting factor from the start. To see a proportional region you would have to work at far lower intensities than a 60 cm lamp gives.
(c) Bubbles vary in size — a large bubble and a small one each count as one, so the count measures the number of bubbles, not the volume of oxygen; and at high rates bubbles merge or come too fast to count reliably. A gas syringe or an inverted measuring cylinder measures the volume of oxygen in cm³ per minute directly, which is the quantity that is actually proportional to the rate. Counting is a random error that scatters points; using volume removes it.
Common mistakes to avoid
- Light as a reactant — light is energy, not a substance; write it above the arrow with chlorophyll.
- “Plants make oxygen for us” — oxygen is a by-product; the plant’s product is glucose.
- Unbalanced symbol equation — 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂; count 6 C, 12 H, 18 O on each side.
- “Plants photosynthesise, animals respire” — plants respire too, all the time (Lesson 2.5); in the light they photosynthesise as well.
- Iodine test without removing the chlorophyll — you cannot see blue-black against green.
- Halving the distance doubles the light — it quadruples it: intensity ∝ 1/d².
How we found out — a willow, a mouse and a sprig of mint
In the 1640s the Flemish physician Jan Baptist van Helmont planted a willow shoot of mass 5 pounds in a tub of 200 pounds of dried soil, covered the soil against dust, and watered it with rainwater for five years. The tree grew to 169 pounds; the soil, dried and reweighed, had lost about 2 ounces. He concluded — reasonably, given what was known — that the 164 pounds of tree had come from water alone. He was wrong about the source but right about the method: he had shown by measurement that the soil is not where a plant’s substance comes from, and he had done it with a controlled experiment and a balance. His account was published in 1648, four years after his death. Nobody then knew that air was a mixture of gases, so the real answer was invisible to him.
In 1771 the English clergyman-chemist Joseph Priestley found that a candle burning in a sealed jar soon went out and that a mouse in the same “injured” air died — but that a sprig of mint growing in the jar for some days made the air good again: the candle relit and the mouse lived. Plants, he showed, restore something that burning and breathing remove. He had discovered oxygen without a name for it. The Dutch physician Jan Ingenhousz read Priestley’s work and in 1779 added the two missing conditions: submerged plants gave off the life-restoring gas only in light, and only from their green parts; in the dark they did the opposite, spoiling the air a little as animals do. In 1782 the Swiss pastor Jean Senebier showed that the “fixed air” (carbon dioxide) was the source of the plant’s carbon, and in 1804 Nicolas-Théodore de Saussure weighed everything and proved that water contributed to the mass too — van Helmont’s willow finally explained, 160 years on. Each step was a controlled experiment that tested one variable the previous person had not.
Van Helmont measured correctly and concluded wrongly. Explain what was missing from his experiment, and why his work is still counted as good science.
Reveal answer
He controlled the soil (covered, dried and weighed) and the water (rainwater only), but he did not consider the air — he could not, because nobody knew air contained a gas a plant could take in. So his conclusion “the tree came from water” was the only explanation his data allowed for the variables he could see. It is good science because he asked a measurable question, controlled what he could, weighed the inputs and outputs, and published his numbers so that others could re-test his conclusion — which they did, and corrected it. A wrong conclusion drawn honestly from measured data moves science forward; a right conclusion with no measurement does not.
Where it is used now
- Every meal in Botswana. Sorghum for bogobe, maize for paleche, beans, watermelon, the beef from cattle that ate grass — every calorie was assembled by photosynthesis from CO₂ and water, in a field near Pandamatenga or a pasture in the Kalahari.
- Fuel. Firewood and charcoal are stored sunlight from the last few decades; coal from Morupule is stored sunlight from 250 million years ago. Burning either reverses photosynthesis: C₆H₁₂O₆ (or its descendants) + O₂ → CO₂ + H₂O + energy.
- Oxygen. About half the oxygen in the atmosphere is made by microscopic algae in the oceans, the other half by land plants; the Okavango Delta’s reed beds and the miombo woodland to the north are part of the planet’s oxygen supply.
- Carbon accounting. Countries measure how much CO₂ their forests and grasslands absorb by photosynthesis to set climate targets; Botswana’s savanna is a carbon store that is measured from satellites (Lesson 2.4).
- Horticulture. Glen Valley on the edge of Gaborone grows vegetables under shade netting and in greenhouses, adjusting exactly the variables in the equation — light, water, CO₂ — to raise yield.
Science now — and the scientist you need to be
What is happening in 2026
Photosynthesis is being redesigned. The natural process wastes energy at several steps — the enzyme that grabs CO₂ sometimes grabs oxygen by mistake, and leaves switch off their light-capture too slowly when a cloud passes. International research programmes have now gene-edited crops to bypass the mistake and speed the switch, and field trials of soybean and rice with these changes have reported yields up by a fifth. Artificial photosynthesis is closer too: laboratory devices that use sunlight to split water and combine the hydrogen with CO₂ into fuel, with no leaf involved, have reported solar-to-fuel efficiencies of the order of ten times a maize plant’s — though still at high cost and on a laboratory scale, and the best published figures are worth checking against the source rather than the press release. Meanwhile satellites measure the faint red glow that chlorophyll emits when it is working, mapping how much photosynthesis is happening across every continent every few days, so that a drought in the Kalahari or a good season in the Tuli Block is seen from orbit before the harvest is in. The equation you wrote today is one of the most closely watched reactions on the planet.
The mindshift
What you need to be able to do
Criterion A questions on photosynthesis ask for the word equation, the symbol equation with correct subscripts and balancing, and an explanation of each experiment as evidence for one condition. The examiner reports are blunt: “photosynthesis makes food” scores nothing; “light energy absorbed by chlorophyll is transformed into chemical energy stored in glucose, made from carbon dioxide and water” scores. Name the energy transformation, name the pigment, name the organelle. And when a question gives lamp distances, convert them to 1/d² before you say anything about proportion.
See an example
Leaf: a hibiscus leaf, foil strip across the middle for three days. After the test: both ends blue-black, the strip’s band pale orange — light is needed for starch. The uncovered edge next to the strip was patchy, probably where the foil lifted slightly in the wind, which is a reminder that the “covered” region must be fully dark. The AI wrote 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ and, asked to check, counted 6 C, 12 H and 18 O on each side — balanced.
Key terms
| Photosynthesis | The process in which green plants make glucose from carbon dioxide and water using light energy, releasing oxygen: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. |
| Chlorophyll | The green pigment in chloroplasts that absorbs light energy (mainly red and blue) for photosynthesis. |
| Chloroplast | The organelle in plant cells where photosynthesis takes place. |
| Glucose | A simple sugar, C₆H₁₂O₆, the product of photosynthesis and the plant’s store of chemical energy. |
| Starch | An insoluble store made by joining glucose molecules; detected with iodine, which turns blue-black. |
| Destarching | Keeping a plant in darkness for about 48 hours so it uses up its starch before an experiment. |
| Variegated leaf | A leaf with green and white regions; the white parts lack chlorophyll and make no starch. |
| Energy transformation | The change of light energy into chemical energy stored in glucose during photosynthesis. |
| Inverse-square law | Light intensity from a lamp is proportional to 1/d²: halving the distance quadruples the intensity. |
| Limiting factor | The one condition — light, CO₂ or temperature — in shortest supply, which sets the rate of photosynthesis. |
Think like a scientist
Criterion A A student sets up four test tubes of water, each with a sprig of pondweed, and adds a few drops of hydrogencarbonate indicator, which is red in normal air, turns yellow when the carbon dioxide concentration rises and purple when it falls. The tubes are treated as follows and left for 6 hours.
| Tube | Treatment | Colour after 6 h |
|---|---|---|
| 1 | Bright light | Purple |
| 2 | Wrapped in foil (dark) | Yellow |
| 3 | Bright light, pondweed boiled first | Red |
| 4 | Dim light | Red |
(a) Write the word equation and the balanced symbol equation for photosynthesis. [3]
(b) Explain the colour in tube 1, referring to the equation. [2]
(c) Explain the colour in tube 2. Your answer must name the process responsible. [2]
(d) State the purpose of tube 3 and explain its result. [2]
(e) Explain why tube 4 stayed red although the pondweed was alive and in the light. [2]
(f) Describe the energy transformation in tube 1 and name the pigment and organelle involved. [3]
Model answer
(a) carbon dioxide + water → glucose + oxygen (light energy, chlorophyll above the arrow) [1]; 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ [1 for formulae with correct subscripts, 1 for balancing coefficients].
(b) In bright light the pondweed photosynthesises faster than it respires, so it takes carbon dioxide out of the water faster than it puts it in [1]; the CO₂ concentration falls, so the indicator turns purple [1].
(c) In the dark there is no light energy, so photosynthesis stops, but the pondweed cells are alive and continue to respire, releasing carbon dioxide [1]; the CO₂ concentration in the water rises, so the indicator turns yellow [1].
(d) Tube 3 is the control experiment: it shows that any colour change is caused by a living plant and not by the light acting on the indicator or the water [1]; boiling killed the cells, so neither photosynthesis nor respiration happens, the CO₂ concentration is unchanged and the indicator stays red [1].
(e) In dim light the rate of photosynthesis is low because light is the limiting factor, and it happens to equal the rate of respiration [1]; CO₂ is used by photosynthesis exactly as fast as it is released by respiration, so the concentration does not change and the indicator stays red — this is called the compensation point [1].
(f) Light energy is transformed into chemical energy stored in glucose [1]; the light is absorbed by chlorophyll [1] inside the chloroplasts of the pondweed cells [1].
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
Write the balanced symbol equation for photosynthesis and show that the oxygen atoms balance.
Reveal answer
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ [1 formulae, 1 coefficients]; oxygen: left 6 × 2 + 6 × 1 = 18; right 6 + 6 × 2 = 18 [1].
Explain why a variegated leaf gives a patchy result in the starch test.
Reveal answer
The white regions contain no chlorophyll, so they cannot absorb light energy and make no glucose or starch — they stay orange-brown with iodine [1]; the green regions have chlorophyll, photosynthesise, store starch and turn blue-black; since everything else (light, water, CO₂, temperature) is the same for both regions, chlorophyll is shown to be necessary [1].
A student writes: “Light + CO₂ + H₂O → C₆H₁₂O₆ + O₂. The chlorophyll is used up to make the glucose, which is why plants need sunlight to make more chlorophyll.” Identify three errors.
Reveal answer
Light is not a reactant and should be written above the arrow, not added as a substance [1]; the equation is unbalanced — it needs 6CO₂, 6H₂O and 6O₂ [1]; chlorophyll is not used up — it absorbs light and passes the energy on, and remains in the leaf; sunlight is needed as the energy source for the reaction, not to replace chlorophyll [1].
A lamp is moved from 40 cm to 20 cm from pondweed. State the factor by which the light intensity changes, and explain why the bubble rate might rise by less than this factor.
Reveal answer
Intensity ∝ 1/d², so halving the distance multiplies the intensity by 4 [1]; the rate rises only while light is the limiting factor [1]; at high intensity the carbon dioxide concentration or the temperature limits the rate, so extra light makes little difference and the rate rises by less than four times [1].
True or false, with a reason: “Priestley’s mint experiment showed that plants need light to restore the air.”
Reveal answer
False [1]: Priestley (1771) showed that a plant restores air that a candle or a mouse has spoiled, but he did not test light; it was Ingenhousz (1779) who showed the restoring gas is released only in the light and only by green parts [1].
A leaf is tested for starch at dawn and again at dusk on a sunny day. Predict the two results and explain the difference at the level of the cell.
Reveal answer
Dawn: little or no blue-black — during the night the leaf made no glucose and used up or exported its starch [1]; dusk: strong blue-black — through the day the chloroplasts absorbed light, made glucose from CO₂ and water faster than the cells used it [1]; the surplus glucose was joined into insoluble starch grains inside the chloroplasts, which is what the iodine detects [1].
Summary
- Photosynthesis: carbon dioxide + water → glucose + oxygen; 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, with light energy and chlorophyll above the arrow.
- It transforms light energy into chemical energy stored in glucose — the energy in every food and fuel started here.
- Chlorophyll in chloroplasts absorbs light; only green cells in the light photosynthesise; surplus glucose is stored as starch.
- The starch test (boil, ethanol, rinse, iodine) with destarched, variegated and covered leaves proves that light and chlorophyll are needed.
- Light intensity ∝ 1/d²; the rate rises with intensity until another factor limits it and the curve flattens.
- Van Helmont (1648), Priestley (1771), Ingenhousz (1779), Senebier (1782) and de Saussure (1804) each tested one more variable — that is how the equation was built.
Next time → The leaf as an organ: cuticle, palisade cells, air spaces, stomata, and why a leaf that opens its pores to feed must also lose water.