Using the following equation, calculate how many grams of water you would get from [tex]833 \, g[/tex] of glucose:

[tex]C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + \text{energy}[/tex]

Your Answer:
[tex]\square[/tex]
[tex]\square[/tex]



Answer :

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]