Chapter 16.2, Problem 14SP

Interpretation Introduction

Interpretation: To find the volume of solution needed to make $4.00$ M $\text{KI}$ from $250.0$ mL of $0.760$ $\text{KI}$ .

Concept introduction: Dilution is defined as the addition of solvent due to which the concentration of solute decreases in the solution. During dilution, the number of moles of solute must remain constant in the solution.

Answer to Problem 14SP

The volume of solution needed to make $4.00$ M $\text{KI}$ from $250.0$ mL of $0.760$ $\text{KI}$ is $47.5$ mL.

Explanation of Solution

To make the concentrated solution, less concentrated is known as dilution. In dilution, the volume of solvent increases but the number of moles of solute remains the same. The formula used for dilution is as follows:

  $C1V1=C2V2$

Where:

  $C1$ is the concentration of the concentrated solution.

  $C2$ is the concentration of the diluted solution.

  $V1$ is the volume of concentrated solution.

  $V2$ is the volume of the diluted solution.

The formula for dilution is derived as:

  $C=\frac{n}{V}$

Where:

C is the concentration.

n is the number of moles of solute.

V is the volume of the solution.

Hence, for the same number of moles of solute, the equation can be written as:

  $n=C\times V$

Now, the data given in the question to find the volume of diluted solution is as follows:

• Molarity of the concentrated solution is $4.00$M.
• Molarity of the diluted solution is $0.760$ M.
• Volume of the diluted solution is $250.0$ mL.

Substitute all the values to find the volume of the concentrated solution.

  $C1V1=C2V2$

  $4.00M\times V1=0.760M\times 0.25L$

  $V1=0.0475$ L

Hence, the volume needed to take is $47.5$ mL.

Conclusion

The volume of solution needed to make $4.00$ M $\text{KI}$ from $250.0$ mL of $0.760$

  $\text{KI}$ is $47.5$ mL.