Sure, let's solve the problem step by step to find out which reactant is the limiting reactant.
1. Identify the balanced equation:
The balanced chemical equation for the reaction is:
[tex]\[
2 \text{CuCl}_2 + 4 \text{KI} \rightarrow 2 \text{CuI} + 4 \text{KCl} + \text{I}_2
\][/tex]
2. List the initial moles of each reactant:
- [tex]\( \text{CuCl}_2 \)[/tex]: 4 moles
- [tex]\( \text{KI} \)[/tex]: 4 moles
3. Determine the stoichiometric coefficients from the balanced equation:
- The stoichiometric coefficient for [tex]\( \text{CuCl}_2 \)[/tex] is 2.
- The stoichiometric coefficient for [tex]\( \text{KI} \)[/tex] is 4.
4. Calculate the mole-to-coefficient ratio for each reactant:
- For [tex]\( \text{CuCl}_2 \)[/tex]:
[tex]\[
\text{Ratio}_{\text{CuCl}_2} = \frac{\text{Initial moles of CuCl}_2}{\text{Stoichiometric coefficient of CuCl}_2} = \frac{4}{2} = 2.0
\][/tex]
- For [tex]\( \text{KI} \)[/tex]:
[tex]\[
\text{Ratio}_{\text{KI}} = \frac{\text{Initial moles of KI}}{\text{Stoichiometric coefficient of KI}} = \frac{4}{4} = 1.0
\][/tex]
5. Identify the limiting reactant:
The limiting reactant is the one that has the smallest mole-to-coefficient ratio. Comparing the ratios calculated:
- [tex]\(\text{Ratio}_{\text{CuCl}_2} = 2.0\)[/tex]
- [tex]\(\text{Ratio}_{\text{KI}} = 1.0\)[/tex]
Since [tex]\( \text{Ratio}_{\text{KI}} \)[/tex] is smaller than [tex]\( \text{Ratio}_{\text{CuCl}_2} \)[/tex], [tex]\( \text{KI} \)[/tex] is the limiting reactant.
Hence, the limiting reactant is [tex]\( \text{KI} \)[/tex].
