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Potassium permanganate [tex]$\left( KMnO_4 \right)$[/tex] reacts with hydrochloric acid [tex]$\left( HCl \right)$[/tex] to form potassium chloride [tex]$\left( KCl \right)$[/tex], manganese chloride [tex]$\left( MnCl_2 \right)$[/tex], water [tex]$\left( H_2O \right)$[/tex], and chlorine gas [tex]$\left( Cl_2 \right)$[/tex]. The balanced chemical equation is:

[tex]\[ 2 KMnO_4 + 16 HCl \rightarrow 2 KCl + 2 MnCl_2 + 8 H_2O + 5 Cl_2 \][/tex]

Select the correct ratios of each of the following substances.

[tex]\[
\begin{array}{l}
KMnO_4 : KCl = \square \\
HCl : H_2O = \square
\end{array}
\][/tex]

[tex]\[
KMnO_4 : Cl_2 = \square
\][/tex]

[tex]\[
HCl : MnCl_2 = \square
\][/tex]



Answer :

GinnyAnswer
To determine the ratios of the substances involved in the balanced chemical equation:

[tex]\[ 2 \, KMnO_4 + 16 \, HCl \rightarrow 2 \, KCl + 2 \, MnCl_2 + 8 \, H_2O + 5 \, Cl_2 \][/tex]

we break it down step-by-step.

1. Ratio of [tex]\( KMnO_4 \)[/tex] to [tex]\( KCl \)[/tex]:
From the balanced equation, 2 moles of [tex]\( KMnO_4 \)[/tex] produce 2 moles of [tex]\( KCl \)[/tex].
[tex]\[ \frac{KMnO_4}{KCl} = \frac{2}{2} = 1.0 \][/tex]

2. Ratio of [tex]\( HCl \)[/tex] to [tex]\( H_2O \)[/tex]:
From the balanced equation, 16 moles of [tex]\( HCl \)[/tex] produce 8 moles of [tex]\( H_2O \)[/tex].
[tex]\[ \frac{HCl}{H_2O} = \frac{16}{8} = 2.0 \][/tex]

3. Ratio of [tex]\( KMnO_4 \)[/tex] to [tex]\( Cl_2 \)[/tex]:
From the balanced equation, 2 moles of [tex]\( KMnO_4 \)[/tex] produce 5 moles of [tex]\( Cl_2 \)[/tex].
[tex]\[ \frac{KMnO_4}{Cl_2} = \frac{2}{5} = 0.4 \][/tex]

4. Ratio of [tex]\( HCl \)[/tex] to [tex]\( MnCl_2 \)[/tex]:
From the balanced equation, 16 moles of [tex]\( HCl \)[/tex] produce 2 moles of [tex]\( MnCl_2 \)[/tex].
[tex]\[ \frac{HCl}{MnCl_2} = \frac{16}{2} = 8.0 \][/tex]

Hence, the correct ratios of each of the substances are:

[tex]\[ \begin{array}{l} KMnO_4 : KCl = 1.0 \\ HCl : H_2O = 2.0 \\ KMnO_4 : Cl_2 = 0.4 \\ HCl : MnCl_2 = 8.0 \\ \end{array} \][/tex]

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