Certainly! Let's go through the question step by step using the balanced chemical equation provided:
The balanced chemical equation is:
[tex]\[ 3C (s) + 2O_2 (g) \rightarrow CO_2 (g) + 2CO (g) \][/tex]
### Step 1: Calculate the moles of [tex]\( CO_2 \)[/tex] produced based on moles of [tex]\( C \)[/tex]
From the balanced equation, 3 moles of carbon ([tex]\( C \)[/tex]) produce 1 mole of [tex]\( CO_2 \)[/tex].
The given moles of [tex]\( C \)[/tex] is 0.130 moles.
To find the moles of [tex]\( CO_2 \)[/tex] produced from 0.130 moles of [tex]\( C \)[/tex]:
[tex]\[ \text{moles of } CO_2 \text{ from } C = \frac{\text{moles of } C}{3} \][/tex]
[tex]\[ \text{moles of } CO_2 \text{ from } C = \frac{0.130}{3} \approx 0.0433 \][/tex]
### Step 2: Calculate the moles of [tex]\( CO_2 \)[/tex] produced based on moles of [tex]\( O_2 \)[/tex]
From the balanced equation, 2 moles of oxygen ([tex]\( O_2 \)[/tex]) produce 1 mole of [tex]\( CO_2 \)[/tex].
The given moles of [tex]\( O_2 \)[/tex] is 0.117 moles.
To find the moles of [tex]\( CO_2 \)[/tex] produced from 0.117 moles of [tex]\( O_2 \)[/tex]:
[tex]\[ \text{moles of } CO_2 \text{ from } O_2 = \frac{\text{moles of } O_2}{2} \][/tex]
[tex]\[ \text{moles of } CO_2 \text{ from } O_2 = \frac{0.117}{2} = 0.0585 \][/tex]
### Step 3: Determine the limiting reagent
The reagent that produces the smaller amount of [tex]\( CO_2 \)[/tex] is the limiting reagent.
We have:
[tex]\[ \text{moles of } CO_2 \text{ from } C = 0.0433 \][/tex]
[tex]\[ \text{moles of } CO_2 \text{ from } O_2 = 0.0585 \][/tex]
Since 0.0433 is less than 0.0585, the smaller amount of [tex]\( CO_2 \)[/tex] produced is based on the moles of [tex]\( C \)[/tex]. Therefore, the limiting reagent is [tex]\( C \)[/tex].
### Step 4: Theoretical yield of [tex]\( CO_2 \)[/tex]
Based on the limiting reagent [tex]\( C \)[/tex], the moles of [tex]\( CO_2 \)[/tex] produced is:
[tex]\[ \text{Theoretical moles of } CO_2 \text{ produced} = 0.0433 \][/tex]
### Summary
- Moles of [tex]\( CO_2 \)[/tex] produced based on [tex]\( C \)[/tex]: 0.0433
- Moles of [tex]\( CO_2 \)[/tex] produced based on [tex]\( O_2 \)[/tex]: 0.0585
- Limiting reagent: [tex]\( C \)[/tex]
- Theoretical yield of [tex]\( CO_2 \)[/tex]: 0.0433 moles
The theoretical production of [tex]\( CO_2 \)[/tex] is determined by the limiting reagent [tex]\( C \)[/tex], which produces 0.0433 moles of [tex]\( CO_2 \)[/tex].
