Answered

In photosynthesis, plants use energy from the sun to produce glucose, [tex]C_6H_{12}O_6[/tex], and oxygen from the reaction of carbon dioxide and water.

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

What mass, in grams, of glucose is produced when 3.00 mol of water react with carbon dioxide?

A. 180 g
B. 720 g
C. 360 g
D. 90 g



Answer :

GinnyAnswer
Certainly! Let's solve the given problem step by step.

### Step 1: Write Down the Balanced Chemical Equation

The balanced chemical equation for photosynthesis is:
[tex]\[ 6 \; \text{CO}_2 + 6 \; \text{H}_2\text{O} \rightarrow \; \text{C}_6\text{H}_{12}\text{O}_6 + 6 \; \text{O}_2 \][/tex]

This equation tells us that 6 moles of water (H[tex]\(_2\)[/tex]O) are needed to produce 1 mole of glucose (C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex]).

### Step 2: Determine the Moles of Glucose Produced

According to the given information, we start with 3.00 moles of water.

Using the mole ratio from the balanced equation:
- 6 moles of H[tex]\(_2\)[/tex]O produce 1 mole of C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex].

Given:
[tex]\[ \text{moles of H}_2\text{O} = 3.00 \][/tex]

We can calculate the moles of glucose:
[tex]\[ \text{moles of glucose} = \frac{\text{moles of H}_2\text{O}}{6} \][/tex]
[tex]\[ \text{moles of glucose} = \frac{3.00}{6} \][/tex]
[tex]\[ \text{moles of glucose} = 0.5 \][/tex]

### Step 3: Calculate the Mass of Glucose Produced

To find the mass of glucose produced, we need to know the molar mass of glucose (C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex]). The molar mass of glucose is given as 180 g/mol.

Given:
[tex]\[ \text{molar mass of glucose} = 180 \; \text{g/mol} \][/tex]

Now, we can calculate the mass using the molar mass and the moles of glucose:
[tex]\[ \text{mass of glucose} = \text{moles of glucose} \times \text{molar mass of glucose} \][/tex]
[tex]\[ \text{mass of glucose} = 0.5 \times 180 \; \text{g/mol} \][/tex]
[tex]\[ \text{mass of glucose} = 90 \; \text{grams} \][/tex]

### Conclusion

Therefore, the mass of glucose produced when 3.00 moles of water react with carbon dioxide is:
[tex]\[ 90 \; \text{grams} \][/tex]

So, the correct answer is:
[tex]\[ \boxed{90 \; \text{grams}} \][/tex]

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