Question

3
chlorophyll in plants
what is needed for photosynthesis? how can you use the amount of chlorophyll in
a lake to determine the level of biological productivity?
photosynthesis is the process by which plants acquire energy from the sun. sunlight,
carbon dioxide, and water are used by a plant to produce glucose and dioxygen.
before:
6 carbon dioxide + 6 water
after:
glucose + 6 dioxygen

1. you want to make models of the molecules

involved in photosynthesis for a science
fair project. the table shows the number
of each element used for each molecule.
let x, y, and z represent the costs of a model
carbon atom, model hydrogen atom, and
model oxygen atom.
a. write and simplify an expression to find
the cost of the model atoms you use to
represent the molecules used by a plant
for photosynthesis.
b. write and simplify an expression to find the cost of the model atoms you use
to represent the molecules produced by photosynthesis.
c. what do you notice about the expressions in part (a) and part (b)? explain.
d. you spend $0.50 on each model carbon atom, $0.25 on each model hydrogen
atom, and $0.75 on each model oxygen atom. write and evaluate an expression to
find the total cost of your science fair project.

molecule	number of atoms
carbon dioxide	1	0	2
water	0	2	1
glucose	6	12	6
dioxygen	0	0	2

big ideas math: modeling real life grade 7 4

Explanation:

Step1: Analyze Reactants (Used Molecules)

For photosynthesis, reactants are 6 Carbon Dioxide ($\ce{CO_2}$) and 6 Water ($\ce{H_2O}$).

• Carbon Dioxide: 1 C, 0 H, 2 O per molecule. For 6 molecules: $6\times(1x + 0y + 2z)=6x + 12z$.
• Water: 0 C, 2 H, 1 O per molecule. For 6 molecules: $6\times(0x + 2y + 1z)=12y + 6z$.

Total for reactants: $(6x + 12z)+(12y + 6z)=6x + 12y + 18z$.

Step2: Analyze Products (Produced Molecules)

Products are 1 Glucose ($\ce{C_6H_{12}O_6}$) and 6 Dioxygen ($\ce{O_2}$).

• Glucose: 6 C, 12 H, 6 O per molecule: $6x + 12y + 6z$.
• Dioxygen: 0 C, 0 H, 2 O per molecule. For 6 molecules: $6\times(0x + 0y + 2z)=12z$.

Total for products: $(6x + 12y + 6z)+12z=6x + 12y + 18z$.

Step3: Notice the Expressions (Part c)

The expressions from part (a) (reactants) and part (b) (products) are identical: $6x + 12y + 18z$. This reflects the Law of Conservation of Mass—atoms are neither created nor destroyed in a chemical reaction, so the total cost (based on atom counts) for reactants and products must be equal.

Step4: Evaluate Total Cost (Part d)

Given $x = 0.50$, $y = 0.25$, $z = 0.75$. Substitute into $6x + 12y + 18z$:
$6(0.50) + 12(0.25) + 18(0.75)$
$= 3 + 3 + 13.5$
$= 19.5$.

Answer:

s (Key Parts):
a. Cost expression (simplified): $\boldsymbol{6x + 12y + 18z}$
b. Cost expression (simplified): $\boldsymbol{6x + 12y + 18z}$
c. The expressions are equal (due to conservation of atoms/mass).
d. Total cost: $\boldsymbol{\$19.50}$