To determine the final volume of the diluted solution, we can use the dilution formula, which relates the initial and final concentrations and volumes of a solution:
[tex]\[ C_1 V_1 = C_2 V_2 \][/tex]
Here:
- [tex]\( C_1 \)[/tex] is the initial concentration of the solution.
- [tex]\( V_1 \)[/tex] is the initial volume of the solution.
- [tex]\( C_2 \)[/tex] is the final concentration of the solution.
- [tex]\( V_2 \)[/tex] is the final volume of the solution.
Given:
- The initial concentration [tex]\( C_1 = 5.0 \, \text{M} \)[/tex]
- The initial volume [tex]\( V_1 = 25.0 \, \text{mL} \)[/tex]
- The final concentration [tex]\( C_2 = 2.0 \, \text{M} \)[/tex]
We need to find the final volume [tex]\( V_2 \)[/tex].
Rearranging the dilution formula to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{C_1 \cdot V_1}{C_2} \][/tex]
Substituting the given values into the equation:
[tex]\[ V_2 = \frac{5.0 \, \text{M} \cdot 25.0 \, \text{mL}}{2.0 \, \text{M}} \][/tex]
[tex]\[ V_2 = \frac{125.0 \, \text{mL} \cdot \text{M}}{2.0 \, \text{M}} \][/tex]
[tex]\[ V_2 = 62.5 \, \text{mL} \][/tex]
So, the final volume of the diluted solution is 62.5 mL.
