Answer :
To solve this problem, we need to determine the volume of a 0.244 M KCl solution required to completely react with 50.0 mL of a 0.210 M Pb(NO₃)₂ solution according to the balanced chemical equation:
[tex]\[ 2 \text{KCl(aq)} + \text{Pb(NO}_3\text{)}_2\text{(aq)} \rightarrow \text{PbCl}_2\text{(s)} + 2 \text{KNO}_3\text{(aq)} \][/tex]
### Step-by-Step Solution:
1. Calculate the moles of Pb(NO₃)₂:
First, use the concentration and volume of the Pb(NO₃)₂ solution to find the number of moles.
[tex]\[
\text{Concentration of Pb(NO}_3\text{)}_2 = 0.210 \, \text{M}
\][/tex]
[tex]\[
\text{Volume of Pb(NO}_3\text{)}_2 = 50.0 \, \text{mL} = 0.0500 \, \text{L}
\][/tex]
[tex]\[
\text{Moles of Pb(NO}_3\text{)}_2 = \text{Concentration} \times \text{Volume}
\][/tex]
[tex]\[
\text{Moles of Pb(NO}_3\text{)}_2 = 0.210 \, \text{mol/L} \times 0.0500 \, \text{L} = 0.0105 \, \text{moles}
\][/tex]
2. Determine the moles of KCl required:
From the balanced chemical equation, 1 mole of Pb(NO₃)₂ reacts with 2 moles of KCl. Therefore, the moles of KCl required are:
[tex]\[
\text{Moles of KCl} = 2 \times \text{Moles of Pb(NO}_3\text{)}_2
\][/tex]
[tex]\[
\text{Moles of KCl} = 2 \times 0.0105 \, \text{moles} = 0.0210 \, \text{moles}
\][/tex]
3. Calculate the volume of KCl solution needed:
Now, use the moles of KCl and its concentration to find the volume of the KCl solution needed:
[tex]\[
\text{Concentration of KCl} = 0.244 \, \text{M}
\][/tex]
[tex]\[
\text{Volume of KCl solution} = \frac{\text{Moles of KCl}}{\text{Concentration}}
\][/tex]
[tex]\[
\text{Volume of KCl solution} = \frac{0.0210 \, \text{moles}}{0.244 \, \text{mol/L}} \approx 0.0861 \, \text{L}
\][/tex]
Convert this volume from liters to milliliters:
[tex]\[
0.0861 \, \text{L} \times 1000 \, \text{mL/L} = 86.1 \, \text{mL}
\][/tex]
Therefore, the volume of 0.244 M KCl solution required is 86.1 mL.
[tex]\[ 2 \text{KCl(aq)} + \text{Pb(NO}_3\text{)}_2\text{(aq)} \rightarrow \text{PbCl}_2\text{(s)} + 2 \text{KNO}_3\text{(aq)} \][/tex]
### Step-by-Step Solution:
1. Calculate the moles of Pb(NO₃)₂:
First, use the concentration and volume of the Pb(NO₃)₂ solution to find the number of moles.
[tex]\[
\text{Concentration of Pb(NO}_3\text{)}_2 = 0.210 \, \text{M}
\][/tex]
[tex]\[
\text{Volume of Pb(NO}_3\text{)}_2 = 50.0 \, \text{mL} = 0.0500 \, \text{L}
\][/tex]
[tex]\[
\text{Moles of Pb(NO}_3\text{)}_2 = \text{Concentration} \times \text{Volume}
\][/tex]
[tex]\[
\text{Moles of Pb(NO}_3\text{)}_2 = 0.210 \, \text{mol/L} \times 0.0500 \, \text{L} = 0.0105 \, \text{moles}
\][/tex]
2. Determine the moles of KCl required:
From the balanced chemical equation, 1 mole of Pb(NO₃)₂ reacts with 2 moles of KCl. Therefore, the moles of KCl required are:
[tex]\[
\text{Moles of KCl} = 2 \times \text{Moles of Pb(NO}_3\text{)}_2
\][/tex]
[tex]\[
\text{Moles of KCl} = 2 \times 0.0105 \, \text{moles} = 0.0210 \, \text{moles}
\][/tex]
3. Calculate the volume of KCl solution needed:
Now, use the moles of KCl and its concentration to find the volume of the KCl solution needed:
[tex]\[
\text{Concentration of KCl} = 0.244 \, \text{M}
\][/tex]
[tex]\[
\text{Volume of KCl solution} = \frac{\text{Moles of KCl}}{\text{Concentration}}
\][/tex]
[tex]\[
\text{Volume of KCl solution} = \frac{0.0210 \, \text{moles}}{0.244 \, \text{mol/L}} \approx 0.0861 \, \text{L}
\][/tex]
Convert this volume from liters to milliliters:
[tex]\[
0.0861 \, \text{L} \times 1000 \, \text{mL/L} = 86.1 \, \text{mL}
\][/tex]
Therefore, the volume of 0.244 M KCl solution required is 86.1 mL.
