To find the new concentration of the potassium fluoride (KF) solution after dilution, follow these steps:
1. Determine the initial volume in liters:
Given the initial volume is 115 mL, converting this to liters:
[tex]\( 115 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.115 \text{ L} \)[/tex]
2. Find the total final volume:
The solution is diluted with 1.28 liters of water. Add this to the initial volume in liters:
[tex]\( 0.115 \text{ L} + 1.28 \text{ L} = 1.395 \text{ L} \)[/tex]
3. Use the dilution formula:
The dilution formula is [tex]\( c_1v_1 = c_2v_2 \)[/tex], where:
- [tex]\( c_1 \)[/tex] is the initial concentration (2.35 M)
- [tex]\( v_1 \)[/tex] is the initial volume (0.115 L)
- [tex]\( c_2 \)[/tex] is the final concentration
- [tex]\( v_2 \)[/tex] is the final volume (1.395 L)
Rearrange the formula to solve for the final concentration [tex]\( c_2 \)[/tex]:
[tex]\[
c_2 = \frac{c_1 \times v_1}{v_2}
\][/tex]
Substituting the known values:
[tex]\[
c_2 = \frac{2.35 \text{ M} \times 0.115 \text{ L}}{1.395 \text{ L}}
\][/tex]
4. Calculate the new concentration:
[tex]\[
c_2 \approx 0.1937 \text{ M}
\][/tex]
So, the new concentration of the KF solution after dilution is approximately [tex]\( 0.194 \text{ M} \)[/tex].
