Question

what is the balanced chemical equation for cellular respiration?
photosynthesis: how do plants get matter and energy?
model ideas
matter:

• plants take in low energy molecules (co₂ + h₂o) and use energy from the sun to rearrange them into high energy molecules, glucose (c₆h₁₂o₆ - food!) and o₂. the reactions involved are collectively called photosynthesis.
• over a 24 hour period, the rate of photosynthesis in a plant is greater than the rate of cellular respiration. as a result:
• plants use more co₂ than they give off.
• plants produce more o₂ than they use.
• this means that a plant produces more glucose than it uses for energy.
• glucose not used for energy is used to build biomass.

energy:

• plants take in low energy molecules (co₂ + h₂o) and use energy from the sun to rearrange them into high energy molecules, glucose (c₆h₁₂o₆ - food!) and o₂. the reactions involved are collectively called photosynthesis.

Explanation:

Cellular respiration is a process in biology where glucose and oxygen are used to produce carbon dioxide, water, and energy (ATP). The balanced chemical equation for aerobic cellular respiration (the most common type) is derived from the reverse of photosynthesis in terms of reactants and products, but with the energy source being glucose's chemical energy. The reactants are glucose ($\ce{C6H12O6}$) and oxygen ($\ce{O2}$), and the products are carbon dioxide ($\ce{CO2}$), water ($\ce{H2O}$), and energy (usually represented as ATP, but not shown in the simple equation for balancing). To balance the equation:

1. Start with the unbalanced equation: $\ce{C6H12O6 + O2 -> CO2 + H2O}$
2. Balance the carbon atoms first. There are 6 carbon atoms in glucose, so we need 6 $\ce{CO2}$ molecules: $\ce{C6H12O6 + O2 -> 6CO2 + H2O}$
3. Balance the hydrogen atoms. There are 12 hydrogen atoms in glucose, so we need 6 $\ce{H2O}$ molecules (since each $\ce{H2O}$ has 2 hydrogen atoms): $\ce{C6H12O6 + O2 -> 6CO2 + 6H2O}$
4. Balance the oxygen atoms. On the right side, we have 62 (from $\ce{CO2}$) + 61 (from $\ce{H2O}$) = 12 + 6 = 18 oxygen atoms. On the left side, glucose has 6 oxygen atoms, so the $\ce{O2}$ must provide 12 oxygen atoms (since 18 - 6 = 12), which means we need 6 $\ce{O2}$ molecules (since each $\ce{O2}$ has 2 oxygen atoms): $\ce{C6H12O6 + 6O2 -> 6CO2 + 6H2O}$

Answer:

The balanced chemical equation for cellular respiration is $\boldsymbol{\ce{C6H12O6 + 6O2 -> 6CO2 + 6H2O}}$ (glucose + oxygen → carbon dioxide + water + energy, where energy is in the form of ATP, not shown in the equation for simplicity).