Step-by-step explanation:
According to the problem, carbon dioxide reacts with water to produce glucose and oxygen. The unbalanced reaction will be:
__ CO₂ + __ H₂O ---> __ C₆H₁₂O₆ + __ O₂
First we can balance the C atoms. We have 6 on the right and 1 on the left. We can change the coefficient for CO₂ to balance the C atoms.
6 CO₂ + __ H₂O ---> __ C₆H₁₂O₆ + __ O₂
Then we have 12 atoms of H on the right side of the equation and 2 on the left side. We can write a 6 in front of H₂O to balance the H atoms.
6 CO₂ + 6 H₂O ---> __ C₆H₁₂O₆ + __ O₂
Finally we have 18 atoms of O on the left and 8 on the right. We can change the coefficient for O₂ to balance the O atoms.
6 CO₂ + 6 H₂O ---> __ C₆H₁₂O₆ + 6 O₂
The balanced equation is:
6 CO₂ + 6 H₂O ---> C₆H₁₂O₆ + 6 O₂
Once we have the balanced equation we have to convert the mass of glucose into moles. To do that we will need the molar mass of glucose.
molar mass of C = 12.01 g/mol
molar mass of H = 1.01 g/mol
molar mass of O = 16.00 g/mol
molar mass of C₆H₁₂O₆ = 6 * 12.01 g/mol + 12 * 1.01 g/mol + 6 * 16.00 g/mol
molar mass of C₆H₁₂O₆ = 180.18 g/mol
moles of C₆H₁₂O₆ = 88.89 g * 1 mol/(180.18 g)
moles of C₆H₁₂O₆ = 0.4933 moles
6 CO₂ + 6 H₂O ---> C₆H₁₂O₆ + 6 O₂
According to the coefficients of the equation, 6 moles of H₂O are required to produce 1 mol of C₆H₁₂O₆. We can use this ratio to find the number of moles of H₂O that are necessary to produce 0.4933 moles of C₆H₁₂O₆.
6 moles of H₂O : 1 mol of C₆H₁₂O₆ molar ratio
moles of H₂O = 0.4933 moles of C₆H₁₂O₆* 6 moles of H₂O/(1 mol of C₆H₁₂O₆)
moles of H₂O = 2.960 moles
And finally we can convert the moles of H₂O back to grams using its molar mass.
molar mass of H₂O = 18.02 g/mol
mass of H₂O = 2.960 moles 18.02 g/(1 mol)
mass of H₂O = 53.34 g
Answer: 53.34 g of water are required to produce 88.89 g of glucose in plants.