Biology · Introductory biology · Worked example

Find the CO₂ a crop takes in for its sugar

A field of wheat stores $900 g$ of glucose on a sunny day. How much ${CO}_{2}$ did it take from the air, and how much $O_{2}$ did it give off? Use molar masses rounded to $180 g / mol$ for glucose, $44.0$ for ${CO}_{2}$ , $32.0$ for $O_{2}$ and $18.0$ for water.

Write the balanced equation

One glucose needs $6 {CO}_{2}$ and $6 H_{2} O$ and releases $6 O_{2}$ . Every count below follows from these mole ratios.

6 {CO}_{2} + 6 H_{2} O \to C_{6} H_{12} O_{6} + 6 O_{2}

\begin{array}{c} 6 {CO}_{2} + 6 H_{2} O \\ \to C_{6} H_{12} O_{6} + 6 O_{2} \end{array}

Convert the glucose to moles

Divide the mass by the molar mass, $180 g$ per mole.

\frac{900}{180} = 5

Moles of ${CO}_{2}$

Why times six? Each glucose holds six carbons, and each came from one ${CO}_{2}$ .

6 (5) = 30

Mass of ${CO}_{2}$

Multiply the moles by $44.0 g$ per mole. That is $1.32 kg$ of ${CO}_{2}$ taken from the air.

30 (44.0) = 1320

Mass of $O_{2}$

Six $O_{2}$ leave for every glucose, so $30 mol$ leave, at $32.0 g$ per mole.

30 (32.0) = 960

Check that the masses balance

The ${CO}_{2}$ and the $30 mol$ of water taken in must weigh what the glucose and $O_{2}$ weigh. Both sides come to $1, 860 g$ .

1320 + 30 (18.0) = 900 + 960

Result

The crop made $5 mol$ of glucose from $30 mol$ of ${CO}_{2}$ , $1, 320 g$ taken from the air. It gave off $30 mol$ of $O_{2}$ , $960 g$ . The masses balance at $1, 860 g$ on each side.

Your turn

1. One like the example

A young tree stores $3.6 kg$ of glucose in a season. How much ${CO}_{2}$ did it fix? Use $180 g / mol$ for glucose and $44.0$ for ${CO}_{2}$ .

Show the answer and explanation

$120 mol$ of ${CO}_{2}$ , $5, 280 g$ or $5.28 kg$ .

$3600 / 180 = 20 mol$ of glucose, and $6 (20) = 120 mol$ of ${CO}_{2}$ . Then $120 \times 44.0 = 5280 g$ . The tree took more mass of ${CO}_{2}$ from the air than the sugar it stored.

\begin{array}{l} \frac{3600}{180} = 20 \\ 6 (20) = 120 \\ 120 (44.0) = 5280 \end{array}

2. A variation

The algae in a pond release $96 g$ of $O_{2}$ in an afternoon. How much glucose did they make? Use $32.0 g / mol$ for $O_{2}$ and $180$ for glucose.

Show the answer and explanation

$0.5 mol$ of glucose, $90 g$ .

$96 / 32.0 = 3 mol$ of $O_{2}$ . Six $O_{2}$ come with each glucose, so $3 / 6 = 0.5 mol$ , and $0.5 \times 180 = 90 g$ . This time the ratio divides, because the count runs from $O_{2}$ back to sugar.

\begin{array}{l} \frac{96}{32.0} = 3 \\ \frac{3}{6} = 0.5 \\ 0.5 (180) = 90 \end{array}

3. Somewhere new

Plants are given water whose oxygen atoms are the heavy isotope ¹⁸O, with ordinary ${CO}_{2}$ . Where does the heavy oxygen turn up? Where would it turn up if the ${CO}_{2}$ carried it instead?

Show the answer and explanation

With heavy water, the heavy oxygen turns up in the $O_{2}$ given off. With heavy ${CO}_{2}$ , it turns up in the sugar and in water the plant makes, not in the $O_{2}$ .

Photosystem II splits water and releases its oxygen as $O_{2}$ . The oxygen of ${CO}_{2}$ is fixed by rubisco and stays in the sugar, apart from some that leaves as water. That is how the source of the $O_{2}$ is known.

Keep exploring

Find the masses in Math starts from $900 / 180 = 5$ . Write $6 (5) = 30$ under it, and each row is checked.

Return to the concept →

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

After reading

Study it, then try it

Practice the key terms as flashcards, then open the example in its tool, change a value and keep a useful result on your board.

Study the 9 key terms Open the Calvin cycle Find the masses in Math Open worked example on a board Molecular cycles in Biology Reference

Your existing work stays on this device. Examples open as editable copies.

Write the balanced equation

Convert the glucose to moles

Moles of CO2CO2​

Mass of CO2CO2​

Mass of O2O2​

Check that the masses balance

Result

Your turn

1. One like the example

120 mol120 mol of CO2CO2​, 5,280 g5,280 g or 5.28 kg5.28 kg.

2. A variation

0.5 mol0.5 mol of glucose, 90 g90 g.

3. Somewhere new

With heavy water, the heavy oxygen turns up in the O2O2​ given off. With heavy CO2CO2​, it turns up in the sugar and in water the plant makes, not in the O2O2​.

Keep exploring

Study it, then try it

Moles of ${CO}_{2}$

Mass of ${CO}_{2}$

Mass of $O_{2}$

$120 mol$ of ${CO}_{2}$ , $5, 280 g$ or $5.28 kg$ .

$0.5 mol$ of glucose, $90 g$ .

With heavy water, the heavy oxygen turns up in the $O_{2}$ given off. With heavy ${CO}_{2}$ , it turns up in the sugar and in water the plant makes, not in the $O_{2}$ .