Carbon Cycle - Biology

1. Fundamental Concepts

Definition: The carbon cycle is a biogeochemical cycle that describes the movement of carbon as it is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of Earth.
Key Processes: Photosynthesis, Respiration, Decomposition, Combustion, and Carbon Sequestration
Carbon Reservoirs: Atmosphere, Oceans, Terrestrial Ecosystems, Sediments, and Fossil Fuels

2. Key Concepts

Photosynthesis Equation: $$6 \text{{CO}}_2 + 6 \text{{H}}_2\text{{O}} \rightarrow \text{{C}}_6\text{{H}}_{12}\text{{O}}_6 + 6 \text{{O}}_2$$

Respiration Equation: $$\text{{C}}_6\text{{H}}_{12}\text{{O}}_6 + 6 \text{{O}}_2 \rightarrow 6 \text{{CO}}_2 + 6 \text{{H}}_2\text{{O}} + \text{{Energy}}$$

Carbon Sequestration: Processes that remove carbon dioxide from the atmosphere and store it in plants, soils, or geological formations.

3. Examples

Example 1 (Basic)

Problem: Calculate the amount of oxygen produced if 6 moles of carbon dioxide are used in photosynthesis.

Step-by-Step Solution:

From the photosynthesis equation: $$6 \text{{CO}}_2 + 6 \text{{H}}_2\text{{O}} \rightarrow \text{{C}}_6\text{{H}}_{12}\text{{O}}_6 + 6 \text{{O}}_2$$
If 6 moles of $$\text{{CO}}_2$$ are used, then 6 moles of $$\text{{O}}_2$$ will be produced.

Validation: According to the stoichiometry of the reaction, for every mole of $$\text{{CO}}_2$$ used, one mole of $$\text{{O}}_2$$ is produced. Therefore, 6 moles of $$\text{{O}}_2$$ are correctly produced.

Example 2 (Intermediate)

Problem: If a forest absorbs 100 tons of carbon annually through photosynthesis, how much oxygen is released?

Step-by-Step Solution:

From the photosynthesis equation: $$6 \text{{CO}}_2 + 6 \text{{H}}_2\text{{O}} \rightarrow \text{{C}}_6\text{{H}}_{12}\text{{O}}_6 + 6 \text{{O}}_2$$
For every 12 grams of carbon absorbed, 32 grams of oxygen are released.
Calculate the total oxygen released: $$\frac{32}{12} \times 100 \text{{ tons}} = 266.67 \text{{ tons}}$$

Validation: Using the molar ratio from the photosynthesis equation, the calculation confirms that approximately 266.67 tons of oxygen are released.

4. Problem-Solving Techniques

Stoichiometry Application: Use balanced chemical equations to determine the relationships between reactants and products.
Unit Conversion: Ensure all units are consistent before performing calculations.
Graphical Representation: Use graphs to visualize the flow of carbon through different reservoirs over time.