Let's consider the task of labeling the solutions as concentrated ([tex]$C$[/tex]) or dilute ([tex]$D$[/tex]) based on their molarities compared to other given values. Molarity is defined as the number of moles of solute per liter of solution, and higher molarity indicates a more concentrated solution.
We start by analyzing each substance's concentrations:
1. HCl:
- 12 M: This is a relatively high concentration, so we label it as concentrated. It is already given as [tex]$A[C]$[/tex].
- 0.5 M: This is significantly lower than 12 M, so it is dilute. Thus, [tex]$B$[/tex] is labeled as [tex]$D$[/tex].
2. NaOH:
- 0.01 M: This is a very low concentration, so we label it as dilute. Thus, [tex]$C$[/tex] is labeled as [tex]$D$[/tex].
- 6.0 M: This is a substantially higher concentration than 0.01 M, so we label it as concentrated. Therefore, [tex]$D$[/tex] is labeled as [tex]$C$[/tex].
3. H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex]:
- 0.05 M: Although it’s a moderate concentration, it is still much lower than 10 M. Hence, it is considered dilute. Thus, [tex]$E$[/tex] is labeled as [tex]$D$[/tex].
- 10 M: This is a high concentration, making it concentrated. Therefore, [tex]$F$[/tex] is labeled as [tex]$C$[/tex].
Using the analysis above, we have our labels as follows:
- [tex]$B$[/tex]: Dilute ([tex]$D$[/tex])
- [tex]$C$[/tex]: Dilute ([tex]$D$[/tex])
- [tex]$D$[/tex]: Concentrated ([tex]$C$[/tex])
- [tex]$E$[/tex]: Dilute ([tex]$D$[/tex])
- [tex]$F$[/tex]: Concentrated ([tex]$C$[/tex])
So the final assignment is:
[tex]\[
\begin{tabular}{|l|l|l|}
\hline \begin{tabular}{l}
acid $I$ \\
base
\end{tabular} & molarity & \begin{tabular}{l}
concentrated $I$ \\
dilute
\end{tabular} \\
\hline \multirow{2}{*}{ HCl } & 12 M & A[C] \\
\hline & 0.5 M & $B$[D] \\
\hline \multirow{2}{*}{ NaOH } & 0.01 M & C[D] \\
\cline { 2 - 3 } & 6.0 M & D[C] \\
\hline \multirow{2}{*}{$H _2 SO _4$} & 0.05 M & E[D] \\
\cline { 2 - 3 } & 10 M & F[C] \\
\hline
\end{tabular}
\][/tex]
