Answer :
Certainly! To solve this problem, we need to use the concept of dilution in chemistry. When a solution is diluted, the amount of solute remains the same, but the volume of the solvent increases. We can use the dilution equation:
[tex]\[ M_1 \times V_1 = M_2 \times V_2 \][/tex]
Here:
- [tex]\( M_1 \)[/tex] is the initial molarity (2.13 M)
- [tex]\( V_1 \)[/tex] is the initial volume (1.24 L)
- [tex]\( M_2 \)[/tex] is the final molarity (1.60 M)
- [tex]\( V_2 \)[/tex] is the final volume which we need to find
We can rearrange the equation to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{M_1 \times V_1}{M_2} \][/tex]
Substituting the given values into the equation:
[tex]\[ V_2 = \frac{2.13 \, \text{M} \times 1.24 \, \text{L}}{1.60 \, \text{M}} \][/tex]
[tex]\[ V_2 = \frac{2.6412 \, \text{M} \cdot \text{L}}{1.60 \, \text{M}} \][/tex]
[tex]\[ V_2 = 1.651375 \, \text{L} \][/tex]
Rounded to three significant figures, the volume of the new solution is 1.651 liters.
So, the volume of the new solution is [tex]\( \boxed{1.651} \)[/tex] liters.
[tex]\[ M_1 \times V_1 = M_2 \times V_2 \][/tex]
Here:
- [tex]\( M_1 \)[/tex] is the initial molarity (2.13 M)
- [tex]\( V_1 \)[/tex] is the initial volume (1.24 L)
- [tex]\( M_2 \)[/tex] is the final molarity (1.60 M)
- [tex]\( V_2 \)[/tex] is the final volume which we need to find
We can rearrange the equation to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{M_1 \times V_1}{M_2} \][/tex]
Substituting the given values into the equation:
[tex]\[ V_2 = \frac{2.13 \, \text{M} \times 1.24 \, \text{L}}{1.60 \, \text{M}} \][/tex]
[tex]\[ V_2 = \frac{2.6412 \, \text{M} \cdot \text{L}}{1.60 \, \text{M}} \][/tex]
[tex]\[ V_2 = 1.651375 \, \text{L} \][/tex]
Rounded to three significant figures, the volume of the new solution is 1.651 liters.
So, the volume of the new solution is [tex]\( \boxed{1.651} \)[/tex] liters.
