Green plants use light from the Sun to drive photosynthesis. Photosynthesis is a chemical reaction in which water (
) and carbon dioxide (
) chemically react to form the simple sugar glucose (
) and oxygen gas (
). What mass of carbon dioxide is consumed by the reaction of 2.85 g of water? Round your answer to 3 significant digits.
The Correct Answer and Explanation is:
Here is a step-by-step solution to the problem:
Step 1: Write and balance the chemical equation for photosynthesis.
The problem states that water (H₂O) and carbon dioxide (CO₂) react to form glucose (C₆H₁₂O₆) and oxygen (O₂).
The unbalanced equation is:
H₂O + CO₂ → C₆H₁₂O₆ + O₂
To balance the equation, we need to ensure there are equal numbers of each type of atom on both sides of the reaction.
The balanced chemical equation is:
6H₂O + 6CO₂ → C₆H₁₂O₆ + 6O₂
This equation tells us that 6 moles of water react with 6 moles of carbon dioxide to produce 1 mole of glucose and 6 moles of oxygen.
Step 2: Calculate the molar masses of water (H₂O) and carbon dioxide (CO₂).
- Molar mass of H₂O:
- Hydrogen (H): 2 × 1.01 g/mol = 2.02 g/mol
- Oxygen (O): 1 × 16.00 g/mol = 16.00 g/mol
- Total = 2.02 + 16.00 = 18.02 g/mol
- Molar mass of CO₂:
- Carbon (C): 1 × 12.01 g/mol = 12.01 g/mol
- Oxygen (O): 2 × 16.00 g/mol = 32.00 g/mol
- Total = 12.01 + 32.00 = 44.01 g/mol
Step 3: Convert the mass of water to moles.
We are given 2.85 g of water. We use its molar mass to find the number of moles.
- Moles of H₂O = Mass / Molar Mass
- Moles of H₂O = 2.85 g / 18.02 g/mol = 0.158157… mol
Step 4: Use the mole ratio to find the moles of carbon dioxide.
From the balanced equation (6H₂O + 6CO₂ → …), the ratio of moles of water to moles of carbon dioxide is 6:6, which simplifies to 1:1. This means for every mole of water that reacts, one mole of carbon dioxide also reacts.
- Moles of CO₂ = Moles of H₂O × (6 mol CO₂ / 6 mol H₂O)
- Moles of CO₂ = 0.158157… mol H₂O × 1 = 0.158157… mol CO₂
Step 5: Convert the moles of carbon dioxide to mass.
Now, we convert the moles of CO₂ back to mass using its molar mass.
- Mass of CO₂ = Moles × Molar Mass
- Mass of CO₂ = 0.158157… mol × 44.01 g/mol = 6.96049… g
Step 6: Round to the correct number of significant digits.
The initial measurement (2.85 g) has 3 significant digits. Therefore, our final answer must also be rounded to 3 significant digits.
- 6.96049… g rounded to 3 significant digits is 6.96 g.
Answer:
The mass of carbon dioxide consumed is 6.96 g
