To determine how many moles of water ([tex]\(H_2O\)[/tex]) are produced when 3.45 moles of potassium permanganate ([tex]\(KMnO_4\)[/tex]) react, follow these steps:
1. Write the balanced chemical equation:
[tex]\[
2 KMnO_4 + 16 HCl \rightarrow 2 KCl + 2 MnCl_2 + 8 H_2O + 5 Cl_2
\][/tex]
2. Identify the stoichiometric coefficients:
From the balanced equation, the stoichiometric coefficient for [tex]\(KMnO_4\)[/tex] is 2 and for [tex]\(H_2O\)[/tex] is 8.
3. Set up the stoichiometric ratio:
According to the balanced equation, 2 moles of [tex]\(KMnO_4\)[/tex] produce 8 moles of [tex]\(H_2O\)[/tex].
4. Convert the given moles of [tex]\(KMnO_4\)[/tex] to moles of [tex]\(H_2O\)[/tex]:
Use the stoichiometric ratio from the balanced equation to find the moles of [tex]\(H_2O\)[/tex]:
[tex]\[
\text{Moles of } H_2O = \left(\frac{8 \text{ moles of } H_2O}{2 \text{ moles of } KMnO_4}\right) \times 3.45 \text{ moles of } KMnO_4
\][/tex]
5. Calculate the moles of [tex]\(H_2O\)[/tex]:
[tex]\[
\text{Moles of } H_2O = \left(\frac{8}{2}\right) \times 3.45 = 4 \times 3.45 = 13.8
\][/tex]
Therefore, 13.8 moles of water ([tex]\(H_2O\)[/tex]) are produced when 3.45 moles of [tex]\(KMnO_4\)[/tex] react. The result, given with 3 significant figures, is:
[tex]\[
13.8 \, \text{moles } H_2O
\][/tex]
