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]
