Chapter 15, Problem 34A

Interpretation Introduction

Interpretation: The volume of the water is to be needed to form the solution needs to be calculated.

Concept Introduction:

The equation of dilution is given as,

  $M_1{V}_1=M_2{V}_2$

Where, $M_1$ is the molarity in initial conditions while $M_2$ is the molarity of the solution in final conditions. Similarly, $V_1$ is the volume of the solution in initial conditions while $V_2$ is the volume in final conditions.

Answer to Problem 34A

The required volume of the water is 167 mL.

Explanation of Solution

Given information:

The initial volume of the solution is, $V_1=500.\text{0mL}$

The initial molarity and final molarity of the solution is $M_1=0.2\text{00M}$ and $M_2=0.150M$ respectively.

Calculation:

The equation of dilution is given as,

  $M_1{V}_1=M_2{V}_2$

By substituting the given values in the above formula and then the result is,

  $\begin{array}{l}{M}_1{V}_1=M_2{V}_2\\ V_2=\frac{M_1{V}_1}{M_2}=\frac{\text{0}\text{.200M×500}\text{.0mL}}{\text{0}\text{.150M}}\\ \text{=}\text{667mL}\end{array}$

Now, the final volume of the solution after addition of water is 667mL. So the amount of added water is,

  $667-500=16\text{7mL}$

Conclusion

The volume of the water is $\text{167mL}$ .