To determine the molarity of the diluted potassium fluoride [tex]\( (KF) \)[/tex] solution, we need to follow several steps. Let's go through the process in detail:
1. Convert the initial volume from mL to L:
The initial volume of the solution is 93.2 mL. We need to convert this volume to liters since molarity is defined in terms of liters.
[tex]\[
\text{Initial volume in liters} = \frac{93.2 \text{ mL}}{1000} = 0.0932 \text{ L}
\][/tex]
2. Calculate the amount of substance (moles) in the initial solution:
Molarity (M) is defined as the number of moles of solute per liter of solution. The initial molarity is 2.03 M, and the initial volume is 0.0932 L.
[tex]\[
\text{Initial moles of KF} = \text{Initial volume in liters} \times \text{Initial molarity} = 0.0932 \text{ L} \times 2.03 \text{ M} = 0.189196 \text{ moles}
\][/tex]
3. Determine the volume of water added:
The volume of water added to the solution is 3.92 L.
4. Calculate the total volume after dilution:
To find the total volume of the solution after dilution, we add the initial volume to the volume of water added.
[tex]\[
\text{Total volume after dilution} = \text{Initial volume in liters} + \text{Volume of water added} = 0.0932 \text{ L} + 3.92 \text{ L} = 4.0132 \text{ L}
\][/tex]
5. Calculate the molarity of the diluted solution:
The final molarity is determined by dividing the number of moles of solute by the total volume of the solution after dilution.
[tex]\[
\text{Final molarity} = \frac{\text{Initial moles of KF}}{\text{Total volume after dilution}} = \frac{0.189196 \text{ moles}}{4.0132 \text{ L}} = 0.04714342669191667 \text{ M}
\][/tex]
Therefore, the molarity of the diluted solution is approximately [tex]\( 0.0471 \text{ M KF} \)[/tex].
