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Some fertilizer blends contain magnesium nitrate [tex] \left( Mg \left( NO_3\right)_2 \right) [/tex]. Suppose that a chemist has 1.24 liters of a [tex] 2.13 \, M [/tex] solution of magnesium nitrate. If the chemist dilutes the solution to [tex] 1.60 \, M [/tex], what is the volume of the new solution?

Express your answer to three significant figures.

The volume of the new solution is [tex]$\square$[/tex] liters.



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.