To determine how many grams of water we would get from 833 grams of glucose using the chemical reaction
[tex]\[
C_6H_{12}O_6 + 6 O_2 \rightarrow 6 CO_2 + 6 H_2O + \text{energy}
\][/tex]
we need to follow these steps:
1. Determine the molar mass of glucose (C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex]):
- Carbon (C) has an atomic mass of approximately 12.01 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1.01 g/mol.
- Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
Therefore, the molar mass of glucose:
[tex]\[
(6 \times 12.01) + (12 \times 1.01) + (6 \times 16.00) = 72.06 + 12.12 + 96.00 = 180.16 \text{ g/mol}
\][/tex]
2. Convert the given mass of glucose to moles:
Given mass of glucose = 833 grams
Moles of glucose can be calculated using the molar mass:
[tex]\[
\text{Moles of glucose} = \frac{\text{mass of glucose}}{\text{molar mass of glucose}}
\][/tex]
[tex]\[
\text{Moles of glucose} = \frac{833 \text{ g}}{180.16 \text{ g/mol}} = 4.62366785079929 \text{ moles}
\][/tex]
3. Determine the moles of water produced:
According to the balanced chemical equation, 1 mole of glucose produces 6 moles of water.
[tex]\[
\text{Moles of water} = 4.62366785079929 \text{ moles of glucose} \times 6 = 27.74200710479574 \text{ moles of water}
\][/tex]
4. Convert the moles of water to grams:
The molar mass of water (H[tex]\(_2\)[/tex]O) is:
[tex]\[
(2 \times 1.01) + 16.00 = 2.02 + 16.00 = 18.02 \text{ g/mol}
\][/tex]
Therefore, the mass of water can be calculated using:
[tex]\[
\text{Mass of water} = \text{moles of water} \times \text{molar mass of water}
\][/tex]
[tex]\[
\text{Mass of water} = 27.74200710479574 \text{ moles} \times 18.02 \text{ g/mol} = 499.91096802841923 \text{ grams}
\][/tex]
So, the amount of water you would get from 833 grams of glucose is approximately:
[tex]\[
\boxed{499.91} \text{ grams}
\][/tex]
