Certainly! Let's break down the process to calculate the required values step-by-step.
### Step 1: Find Moles of Glucose
First, we need to determine how many moles of glucose ([tex]\(C_6H_{12}O_6\)[/tex]) are present in the given 63.0 grams. To do this, we use the molecular weight of glucose, which is 180 g/mol.
[tex]\[
\text{Moles of glucose} = \frac{\text{mass of glucose}}{\text{molecular weight of glucose}} = \frac{63.0 \, \text{g}}{180 \, \text{g/mol}} = 0.35 \, \text{mol}
\][/tex]
### Step 2: Calculate Moles of Oxygen Required
The reaction shows that 1 mole of glucose reacts with 6 moles of oxygen ([tex]\(O_2\)[/tex]). Therefore, for 0.35 moles of glucose, the moles of oxygen required would be:
[tex]\[
\text{Moles of oxygen} = 6 \times \text{moles of glucose} = 6 \times 0.35 = 2.1 \, \text{mol}
\][/tex]
### Step 3: Calculate Mass of Oxygen Required
Using the moles of oxygen calculated in the previous step and the molecular weight of oxygen, which is 32 g/mol, we can find the mass of oxygen required:
[tex]\[
\text{Mass of oxygen} = \text{moles of oxygen} \times \text{molecular weight of oxygen} = 2.1 \, \text{mol} \times 32 \, \text{g/mol} = 67.2 \, \text{g}
\][/tex]
### Step 4: Calculate Moles of [tex]\(CO_2\)[/tex] Produced
According to the balanced chemical equation, 1 mole of glucose produces 6 moles of carbon dioxide ([tex]\(CO_2\)[/tex]). Therefore, for 0.35 moles of glucose, the moles of [tex]\(CO_2\)[/tex] produced would be:
[tex]\[
\text{Moles of } CO_2 = 6 \times \text{moles of glucose} = 6 \times 0.35 = 2.1 \, \text{mol}
\][/tex]
### Step 5: Calculate Mass of [tex]\(CO_2\)[/tex] Produced
Finally, we use the moles of [tex]\(CO_2\)[/tex] calculated in the previous step and the molecular weight of carbon dioxide, which is 44 g/mol, to find the mass of [tex]\(CO_2\)[/tex] produced:
[tex]\[
\text{Mass of } CO_2 = \text{moles of } CO_2 \times \text{molecular weight of } CO_2 = 2.1 \, \text{mol} \times 44 \, \text{g/mol} = 92.4 \, \text{g}
\][/tex]
Thus, the results are:
- Mass of [tex]\(O_2\)[/tex] required: [tex]\(\boxed{67.2 \, \text{g}}\)[/tex]
- Mass of [tex]\(CO_2\)[/tex] produced: [tex]\(\boxed{92.4 \, \text{g}}\)[/tex]
