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The average human requires 88.89 grams of glucose (C6H12O6) per day. How many grams of water are required to produce this amount of glucose in plants? The photosynthetic reaction is carbon dioxide reacts with water to produce glucose and oxygen.

User Tina
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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.

User Beetee
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