To determine how many grams of glucose can be made from 27.66 grams of carbon dioxide (CO₂), we will follow these steps:
1. Calculate the moles of carbon dioxide:
- We start with the given mass of CO₂: 27.66 grams.
- The molar mass of CO₂ is 44.01 grams per mole.
[tex]\[
\text{Moles of CO₂} = \frac{\text{Mass of CO₂}}{\text{Molar mass of CO₂}} = \frac{27.66 \text{ g}}{44.01 \text{ g/mol}} \approx 0.6285 \text{ mol}
\][/tex]
2. Determine the moles of glucose that can be formed:
- According to the balanced chemical equation, 6 moles of CO₂ are required to produce 1 mole of glucose (C₆H₁₂O₆).
- Hence, the moles of glucose formed can be found by dividing the moles of CO₂ by 6.
[tex]\[
\text{Moles of glucose} = \frac{\text{Moles of CO₂}}{\text{Molar ratio of CO₂ to glucose}} = \frac{0.6285 \text{ mol}}{6} \approx 0.1047 \text{ mol}
\][/tex]
3. Calculate the mass of glucose formed:
- The molar mass of glucose (C₆H₁₂O₆) is 180.16 grams per mole.
- Using the moles of glucose calculated previously, we can find the mass of glucose.
[tex]\[
\text{Mass of glucose} = \text{Moles of glucose} \times \text{Molar mass of glucose} = 0.1047 \text{ mol} \times 180.16 \text{ g/mol} \approx 18.87 \text{ g}
\][/tex]
Therefore, from 27.66 grams of carbon dioxide, approximately 18.87 grams of glucose can be made.
