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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 2.13 M solution of magnesium nitrate. If the chemist dilutes the solution to 1.60 M, 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 :

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.