Answer :
To solve the problem of finding the volume of 0.244 M KCl solution needed to react with 50.0 mL of 0.210 M Pb(NO3)2 solution, we can follow a series of steps based on stoichiometry:
1. Understand the Reaction:
The balanced chemical equation is:
[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]
This shows that 1 mole of Pb(NO3)2 reacts with 2 moles of KCl.
2. Calculate Moles of Pb(NO3)2:
Use the concentration and volume of the Pb(NO3)2 solution to find the number of moles:
[tex]\[
\text{Moles of Pb(NO}_3\text{)}_2 = \text{Molarity} \times \text{Volume (in liters)} = 0.210 \, \text{M} \times \frac{50.0 \, \text{mL}}{1000} = 0.0105 \, \text{moles}
\][/tex]
3. Determine Moles of KCl Needed:
From the balanced equation, 2 moles of KCl are required for every 1 mole of Pb(NO3)2. Therefore, calculate the moles of KCl needed:
[tex]\[
\text{Moles of KCl} = 2 \times \text{Moles of Pb(NO}_3\text{)}_2 = 2 \times 0.0105 \, \text{moles} = 0.021 \, \text{moles}
\][/tex]
4. Calculate Volume of KCl Solution Required:
Use the moles of KCl and the molarity of the KCl solution to find the required volume:
[tex]\[
\text{Volume of KCl (in liters)} = \frac{\text{Moles of KCl}}{\text{Molarity of KCl}} = \frac{0.021 \, \text{moles}}{0.244 \, \text{M}} \approx 0.08606 \, \text{L}
\][/tex]
5. Convert Volume to Milliliters:
Convert the volume from liters to milliliters:
[tex]\[
\text{Volume of KCl (in milliliters)} = 0.08606 \, \text{L} \times 1000 = 86.1 \, \text{mL}
\][/tex]
Thus, the volume of 0.244 M KCl solution required is approximately 86.1 mL. The correct answer is option D) 86.1 mL.
1. Understand the Reaction:
The balanced chemical equation is:
[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]
This shows that 1 mole of Pb(NO3)2 reacts with 2 moles of KCl.
2. Calculate Moles of Pb(NO3)2:
Use the concentration and volume of the Pb(NO3)2 solution to find the number of moles:
[tex]\[
\text{Moles of Pb(NO}_3\text{)}_2 = \text{Molarity} \times \text{Volume (in liters)} = 0.210 \, \text{M} \times \frac{50.0 \, \text{mL}}{1000} = 0.0105 \, \text{moles}
\][/tex]
3. Determine Moles of KCl Needed:
From the balanced equation, 2 moles of KCl are required for every 1 mole of Pb(NO3)2. Therefore, calculate the moles of KCl needed:
[tex]\[
\text{Moles of KCl} = 2 \times \text{Moles of Pb(NO}_3\text{)}_2 = 2 \times 0.0105 \, \text{moles} = 0.021 \, \text{moles}
\][/tex]
4. Calculate Volume of KCl Solution Required:
Use the moles of KCl and the molarity of the KCl solution to find the required volume:
[tex]\[
\text{Volume of KCl (in liters)} = \frac{\text{Moles of KCl}}{\text{Molarity of KCl}} = \frac{0.021 \, \text{moles}}{0.244 \, \text{M}} \approx 0.08606 \, \text{L}
\][/tex]
5. Convert Volume to Milliliters:
Convert the volume from liters to milliliters:
[tex]\[
\text{Volume of KCl (in milliliters)} = 0.08606 \, \text{L} \times 1000 = 86.1 \, \text{mL}
\][/tex]
Thus, the volume of 0.244 M KCl solution required is approximately 86.1 mL. The correct answer is option D) 86.1 mL.
