Question

Plants convert carbon dioxide and water to glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) and oxygen in the process of photosynthesis. Write a balanced equation for this reaction, and determine how many moles of \(\mathrm{CO}_{2}\) are required to produce \(15.0 \mathrm{~mol}\) of glucose.

Short answer

90 moles of \(\text{CO}_2\) are required.

Step-by-step solution

Write the Chemical Equation

The general chemical equation for photosynthesis can be written as: \[ 6 ext{CO}_2 + 6 ext{H}_2 ext{O} ightarrow ext{C}_6 ext{H}_{12} ext{O}_6 + 6 ext{O}_2 \] This equation represents the conversion of carbon dioxide and water to glucose and oxygen.

Check the Balancing

Ensure that the number of atoms for each element is the same on both sides of the equation. Before balancing, we see 6 carbons, 12 hydrogens, and 18 oxygens on both sides. Therefore, this equation is balanced.

Moles of CO2 Calculated from Balanced Equation

According to the balanced chemical equation, 6 moles of \( ext{CO}_2\) are required to produce 1 mole of glucose (\( ext{C}_6 ext{H}_{12} ext{O}_6\)).

Calculate Required CO2 for Given Glucose

Given that you want to produce 15 moles of glucose, calculate the moles of \( ext{CO}_2\) needed using the mole ratio from the equation: \[ (15 ext{ mol of glucose}) \times \left( \frac{6 ext{ mol CO}_2}{1 ext{ mol glucose}} \right) = 90 ext{ mol CO}_2 \]

Conclude the Calculation

Therefore, you will need 90 moles of \( ext{CO}_2\) to produce 15 moles of glucose according to the balanced photosynthesis equation.

Key concepts

Chemical Equation Balancing

Balancing chemical equations is a critical skill in chemistry. It ensures that the matter is conserved, meaning the same number of atoms for each element is present on both sides of the equation. In photosynthesis, the equation is balanced when the number of carbon, hydrogen, and oxygen atoms are the same for both reactants and products. For instance, the photosynthesis reaction can be written as:

• Reactants: 6 molecules of carbon dioxide (\(\text{CO}_2\)) and 6 molecules of water (\(\text{H}_2\text{O}\)).
• Products: One molecule of glucose (\(\text{C}_6\text{H}_{12}\text{O}_6\)) and 6 molecules of oxygen (\(\text{O}_2\)).

To verify if an equation is balanced, count the atoms of each element present in the reactants and products. Both sides should have 6 carbon, 12 hydrogen, and 18 oxygen atoms. This balanced chemical equation not only tells us the substances involved but also allows us to calculate quantities, like how much of a reactant is required to get a certain amount of product.

Mole Calculations

Moles are used in chemistry as a way to count particles. A mole is defined as \(6.022 \times 10^{23}\) of anything, usually atoms or molecules. For photosynthesis, we use the balanced chemical equation to guide our mole calculations. According to the balanced reaction, 6 moles of \(\text{CO}_2\) are needed to produce 1 mole of glucose. This establishes a ratio of 6:1 for \(\text{CO}_2\) to glucose.

When tasked with determining the number of moles required for a reaction, we rely on these mole ratios. Suppose you want to produce 15 moles of glucose, then applying the ratio, it states that:

• \(15 \text{ moles of glucose} \times \left( \frac{6 \text{ moles } \text{CO}_2}{1 \text{ mole glucose}} \right) = 90 \text{ moles } \text{CO}_2\).

This tells us that 90 moles of carbon dioxide are necessary to produce the desired 15 moles of glucose.

Glucose Production

Glucose is a simple sugar and a fundamental energy source for plants and animals. In photosynthesis, plants convert light energy to chemical energy stored in glucose. The chemical formula for glucose is \(\text{C}_6\text{H}_{12}\text{O}_6\). Plants use this process to create food, releasing oxygen as a by-product.

From the balanced photosynthesis equation, we see that each glucose molecule produced requires 6 molecules of carbon dioxide and 6 molecules of water. Thus, understanding these inputs is crucial for comprehending glucose production energetically and stoichiometrically.

• Energy from sunlight drives these reactions within the plant cells' chloroplasts.
• Plants perform this work in order to produce glucose, which is then used for growth, reproduction, and other cellular processes.

In practical scenarios, calculating how much glucose plants can produce from available carbon dioxide helps comprehend the plant's efficiency in converting energy.

Carbon Dioxide

Carbon dioxide (\(\text{CO}_2\)) is a colorless gas, essential for photosynthesis. It's a key reactant, serving as the carbon source needed for building glucose. Without carbon dioxide, plants wouldn't be able to synthesize glucose, which is crucial for their survival.

During photosynthesis, plants absorb \(\text{CO}_2\) from the air through small openings in leaves called stomata. This absorbed \(\text{CO}_2\) is then combined with water, using sunlight energy, to create glucose.

• Photosynthesis helps reduce atmospheric \(\text{CO}_2\) levels, playing a significant role in Earth's carbon cycle.
• Understanding the volume of carbon dioxide available affects how much glucose plants can produce.

By grasping the involvement of \(\text{CO}_2\) in photosynthesis, one can better appreciate its role in larger ecological and environmental contexts.