To find the volume of the new solution after dilution, we can use the formula for dilution:
[tex]\[ C_1 \times V_1 = C_2 \times V_2 \][/tex]
where:
- [tex]\( C_1 \)[/tex] is the initial concentration,
- [tex]\( V_1 \)[/tex] is the initial volume,
- [tex]\( C_2 \)[/tex] is the final concentration,
- [tex]\( V_2 \)[/tex] is the final volume.
Given:
- [tex]\( C_1 = 2.13 \)[/tex] M
- [tex]\( V_1 = 1.24 \)[/tex] liters
- [tex]\( C_2 = 1.60 \)[/tex] M
We need to calculate [tex]\( V_2 \)[/tex].
Rearrange the formula to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{C_1 \times V_1}{C_2} \][/tex]
Substitute the given values into the formula:
[tex]\[ V_2 = \frac{2.13 \times 1.24}{1.60} \][/tex]
Perform the multiplication and division:
[tex]\[ V_2 = \frac{2.6412}{1.60} = 1.65075 \][/tex]
Round the result to three significant figures:
[tex]\[ V_2 = 1.65 \][/tex]
Thus, the volume of the new solution is [tex]\( 1.65 \)[/tex] liters.
The volume of the new solution is [tex]\(\boxed{1.65}\)[/tex] liters.
