Sure, let's solve this step-by-step based on the stoichiometric relationships in the balanced chemical equation: [tex]\( \text{Bi}_2\text{O}_3(s) + 3\text{C}(s) \rightarrow 2\text{Bi}(s) + 3\text{CO}(g) \)[/tex].
1. Identify the ratio of moles from the balanced equation:
- According to the balanced chemical equation, 3 moles of carbon (C) produce 2 moles of bismuth (Bi).
2. Determine the amount of bismuth that can be formed:
- You have 3.658 moles of carbon.
- Based on the stoichiometric ratio from the equation, the relationship between carbon and bismuth is as follows:
[tex]\[
3 \text{ moles of C} \rightarrow 2 \text{ moles of Bi}
\][/tex]
3. Set up the proportion to find the moles of bismuth produced:
[tex]\[
\frac{3 \text{ moles of C}}{2 \text{ moles of Bi}} = \frac{3.658 \text{ moles of C}}{x \text{ moles of Bi}}
\][/tex]
4. Solve for [tex]\( x \)[/tex], the moles of bismuth:
[tex]\[
x = \frac{2}{3} \times 3.658
\][/tex]
5. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 2.4386666666666663 \text{ moles of Bi}
\][/tex]
Therefore, from 3.658 moles of carbon, you can produce approximately 2.439 moles of bismuth.
