Answer :
To determine the volume of 0.244 M KCl solution required to react with 50.0 mL of 0.210 M Pb(NO₃)₂ solution, follow these steps:
1. Write the Balanced Chemical Equation:
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]
From this, you can see that 2 moles of KCl react with 1 mole of Pb(NO₃)₂.
2. Calculate Moles of Pb(NO₃)₂:
First, find the moles of Pb(NO₃)₂ in the solution using its molarity and volume:
[tex]\[
\text{Moles of Pb(NO}_3)_2 = \text{Concentration} \times \text{Volume}
\][/tex]
[tex]\[
= 0.210 \, \text{M} \times \frac{50.0 \, \text{mL}}{1000}
\][/tex]
[tex]\[
= 0.210 \, \text{M} \times 0.050 \, \text{L}
\][/tex]
[tex]\[
= 0.0105 \, \text{moles}
\][/tex]
3. Determine Moles of KCl Needed:
According to the stoichiometry of the equation, 1 mole of Pb(NO₃)₂ requires 2 moles of KCl.
[tex]\[
\text{Moles of KCl needed} = 2 \times 0.0105 \, \text{moles} = 0.021 \, \text{moles}
\][/tex]
4. Calculate the Volume of KCl Solution:
Now, use the moles of KCl and its molarity to find the required volume of KCl solution. The formula is:
[tex]\[
\text{Volume of KCl} = \frac{\text{Moles of KCl}}{\text{Molarity of KCl}}
\][/tex]
[tex]\[
= \frac{0.021 \, \text{moles}}{0.244 \, \text{M}}
\][/tex]
[tex]\[
= 0.08606557377049181 \, \text{L}
\][/tex]
5. Convert Volume to Milliliters:
Convert the volume from liters to milliliters:
[tex]\[
\text{Volume in milliliters} = 0.08606557377049181 \times 1000
\][/tex]
[tex]\[
\approx 86.1 \, \text{mL}
\][/tex]
So, approximately 86.1 mL of 0.244 M KCl solution is required to completely react with 50.0 mL of 0.210 M Pb(NO₃)₂ solution.
1. Write the Balanced Chemical Equation:
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]
From this, you can see that 2 moles of KCl react with 1 mole of Pb(NO₃)₂.
2. Calculate Moles of Pb(NO₃)₂:
First, find the moles of Pb(NO₃)₂ in the solution using its molarity and volume:
[tex]\[
\text{Moles of Pb(NO}_3)_2 = \text{Concentration} \times \text{Volume}
\][/tex]
[tex]\[
= 0.210 \, \text{M} \times \frac{50.0 \, \text{mL}}{1000}
\][/tex]
[tex]\[
= 0.210 \, \text{M} \times 0.050 \, \text{L}
\][/tex]
[tex]\[
= 0.0105 \, \text{moles}
\][/tex]
3. Determine Moles of KCl Needed:
According to the stoichiometry of the equation, 1 mole of Pb(NO₃)₂ requires 2 moles of KCl.
[tex]\[
\text{Moles of KCl needed} = 2 \times 0.0105 \, \text{moles} = 0.021 \, \text{moles}
\][/tex]
4. Calculate the Volume of KCl Solution:
Now, use the moles of KCl and its molarity to find the required volume of KCl solution. The formula is:
[tex]\[
\text{Volume of KCl} = \frac{\text{Moles of KCl}}{\text{Molarity of KCl}}
\][/tex]
[tex]\[
= \frac{0.021 \, \text{moles}}{0.244 \, \text{M}}
\][/tex]
[tex]\[
= 0.08606557377049181 \, \text{L}
\][/tex]
5. Convert Volume to Milliliters:
Convert the volume from liters to milliliters:
[tex]\[
\text{Volume in milliliters} = 0.08606557377049181 \times 1000
\][/tex]
[tex]\[
\approx 86.1 \, \text{mL}
\][/tex]
So, approximately 86.1 mL of 0.244 M KCl solution is required to completely react with 50.0 mL of 0.210 M Pb(NO₃)₂ solution.
