Sure, let's solve this step by step.
We are given the initial molarity [tex]\( M_1 \)[/tex] and volume [tex]\( V_1 \)[/tex] of a KF solution, and the final volume [tex]\( V_2 \)[/tex] after dilution. We need to determine the final molarity [tex]\( M_2 \)[/tex].
### Given Data:
- Initial molarity ([tex]\( M_1 \)[/tex]): 2.03 M
- Initial volume ([tex]\( V_1 \)[/tex]): 93 mL
- Final volume ([tex]\( V_2 \)[/tex]): 93 mL + 3920 mL = 4013 mL
### Formula:
To find the final molarity after dilution, we use the dilution formula:
[tex]\[ M_1 \times V_1 = M_2 \times V_2 \][/tex]
### Step-by-Step Solution:
1. Substitute the given values into the formula:
[tex]\[ 2.03 \times 93 = M_2 \times 4013 \][/tex]
2. Simplify and solve for [tex]\( M_2 \)[/tex]:
[tex]\[ M_2 = \frac{2.03 \times 93}{4013} \][/tex]
3. Calculate the numerator:
[tex]\[ 2.03 \times 93 = 188.79 \][/tex]
4. Divide by the final volume:
[tex]\[ M_2 = \frac{188.79}{4013} \approx 0.04704460503364066 \][/tex]
### Result:
The molarity of the diluted solution is approximately:
[tex]\[ 0.0470 \text{ M} \][/tex]
Therefore, the molarity of the diluted solution is [tex]\( 0.0470 \text{ M} \)[/tex].
