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Consider the potassium permanganate reaction:

[tex]\[
2 \text{KMnO}_4 + 16 \text{HCl} \rightarrow 2 \text{KCl} + 2 \text{MnCl}_2 + 8 \text{H}_2\text{O} + 5 \text{Cl}_2
\][/tex]

How many moles of water are produced when 3.45 moles of [tex]\(\text{KMnO}_4\)[/tex] react? Type in your answer using 3 significant figures (the same as the given moles).

[tex]\[ \boxed{\text{}} \text{ moles } \text{H}_2\text{O} \][/tex]



Answer :

GinnyAnswer
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]

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