To find the final concentration of 500 mL of a solution made from 125 mL of 3.0 M NaOH, follow these steps:
1. Determine the moles of solute in the initial solution:
- The initial volume of the solution is 125 mL.
- The initial concentration is 3.0 M (moles per liter).
- First, convert the initial volume from mL to L: [tex]\( 125 \, \text{mL} = 0.125 \, \text{L} \)[/tex].
- Calculate the number of moles of NaOH in the initial solution using the formula:
[tex]\[
\text{moles of solute} = \text{concentration} \times \text{volume}
\][/tex]
Substituting the values:
[tex]\[
\text{moles of solute} = 3.0 \, \text{M} \times 0.125 \, \text{L} = 0.375 \, \text{moles}
\][/tex]
2. Calculate the final concentration after dilution:
- The final volume of the solution is 500 mL.
- Convert the final volume from mL to L: [tex]\( 500 \, \text{mL} = 0.500 \, \text{L} \)[/tex].
- Use the number of moles of solute (which remains unchanged during dilution) and the final volume to find the final concentration:
[tex]\[
\text{final concentration} = \frac{\text{moles of solute}}{\text{final volume}}
\][/tex]
Substituting the values:
[tex]\[
\text{final concentration} = \frac{0.375 \, \text{moles}}{0.500 \, \text{L}} = 0.75 \, \text{M}
\][/tex]
Therefore, the final concentration of the solution is:
[tex]\[ 0.75 \, \text{M NaOH} \][/tex]
