Green plants use light from the Sun to drive photosynthesis. Photosynthesis is a chemical reaction in which water H2O and carbon dioxide CO2 chemically react to form the simple sugar glucose C6H12O6 and oxygen gas O2 . What mass of simple sugar glucose is produced by the reaction of 6.6g of carbon dioxide? Round your answer to 2 significant digits. g
The Correct Answer and Explanation is:
The balanced chemical equation for photosynthesis is:
6CO2+6H2O→lightC6H12O6+6O26CO_2 + 6H_2O \xrightarrow{\text{light}} C_6H_{12}O_6 + 6O_26CO2+6H2OlightC6H12O6+6O2
This equation tells us that 6 moles of carbon dioxide (CO₂) react to produce 1 mole of glucose (C₆H₁₂O₆). To determine the mass of glucose produced from 6.6g of CO₂, we’ll follow these steps:
Step 1: Molar Mass of CO₂
The molar mass of CO₂ is calculated as:MCO2=12.01 g/mol (C)+2×16.00 g/mol (O)=44.01 g/molM_{CO_2} = 12.01 \, \text{g/mol} \, (\text{C}) + 2 \times 16.00 \, \text{g/mol} \, (\text{O}) = 44.01 \, \text{g/mol}MCO2=12.01g/mol(C)+2×16.00g/mol(O)=44.01g/mol
Step 2: Calculate Moles of CO₂
Using the mass of CO₂ (6.6g), we can calculate the number of moles of CO₂:moles of CO2=mass of CO2molar mass of CO2=6.6 g44.01 g/mol=0.150 mol\text{moles of CO}_2 = \frac{\text{mass of CO}_2}{\text{molar mass of CO}_2} = \frac{6.6 \, \text{g}}{44.01 \, \text{g/mol}} = 0.150 \, \text{mol}moles of CO2=molar mass of CO2mass of CO2=44.01g/mol6.6g=0.150mol
Step 3: Molar Mass of Glucose (C₆H₁₂O₆)
The molar mass of glucose (C₆H₁₂O₆) is:MC6H12O6=6×12.01 g/mol+12×1.008 g/mol+6×16.00 g/mol=180.18 g/molM_{\text{C}_6\text{H}_{12}\text{O}_6} = 6 \times 12.01 \, \text{g/mol} + 12 \times 1.008 \, \text{g/mol} + 6 \times 16.00 \, \text{g/mol} = 180.18 \, \text{g/mol}MC6H12O6=6×12.01g/mol+12×1.008g/mol+6×16.00g/mol=180.18g/mol
Step 4: Use Mole Ratios
From the balanced equation, 6 moles of CO₂ produce 1 mole of glucose. Therefore, the moles of glucose produced from 0.150 moles of CO₂ will be:moles of glucose=1 mol glucose6 mol CO2×0.150 mol CO2=0.0250 mol glucose\text{moles of glucose} = \frac{1 \, \text{mol glucose}}{6 \, \text{mol CO}_2} \times 0.150 \, \text{mol CO}_2 = 0.0250 \, \text{mol glucose}moles of glucose=6mol CO21mol glucose×0.150mol CO2=0.0250mol glucose
Step 5: Calculate Mass of Glucose
Now, we can calculate the mass of glucose produced using its molar mass:mass of glucose=moles of glucose×MC6H12O6=0.0250 mol×180.18 g/mol=4.50 g\text{mass of glucose} = \text{moles of glucose} \times M_{\text{C}_6\text{H}_{12}\text{O}_6} = 0.0250 \, \text{mol} \times 180.18 \, \text{g/mol} = 4.50 \, \text{g}mass of glucose=moles of glucose×MC6H12O6=0.0250mol×180.18g/mol=4.50g
Final Answer
The mass of glucose produced from the reaction of 6.6g of carbon dioxide is 4.5g.
