Chapter 16.2, Problem 15SP

Interpretation Introduction

Interpretation: To prepare the solution $250$ mL of $0.20$ M $\text{NaCl}$ from $1.0$ M $\text{NaCl}$ .

Concept introduction: Dilution is the process in which there is an addition of solvent in the solution due to which the concentration of solute decreases in the solution. In the dilution process, the number of moles of solute remains constant in the solution.

Answer to Problem 15SP

The volume of solution needed to make $250.0$ mL of $0.20$ M $\text{NaCl}$ from $1.0$ M $\text{NaCl}$ is $50$ milliliters.

Explanation of Solution

Dilution means to make the concentrated solution, less concentrated. In the dilution process, the volume of solvent in the solution increases but the number of moles of solute remains the same.

The formula for dilution can be derived as below:

  $C=\frac{n}{V}$

Where:

C is the concentration of the solution.

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:

  $n=C\times V$

Hence, the formula used for dilution is:

  $C1V1=C2V2$

Where:

  $C1$ is the concentration of the initial solution.

  $C2$ is the concentration of the final solution.

  $V1$ is the volume of the initial solution.

  $V2$ is the volume of the final solution.

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

• Molarity of the initial solution is $1.0$M.
• Molarity of the diluted solution is $0.20$ M.
• Volume of the diluted solution is $250.0$ milliliters.

Put all the values to find the volume of the final solution.

  $C1V1=C2V2$

  $1.0M\times V1=0.20M\times 0.25L$

  $V1=0.05$ L

Hence, the volume needed to take is $50$ mL.

Conclusion

The volume of solution needed to make $250.0$ mL of $0.2$ M $\text{NaCl}$ from $1.0$ M $\text{NaCl}$ is $50$ milliliters.