Chapter 21, Problem 94A

Interpretation Introduction

Interpretation: The method to prepare 500 mL of 1.0 M ${\text{HNO}}_{\text{3}}$ from the concentration nitric acid of 16 M needs to be determined.

Concept Introduction: The problem is based on the concept of dilution law. The mathematical expression for the same is as follows:

  $M_1{V}_1=M_2{V}_2$

Here, M is molarity of solution, V is volume and 1 and 2 represents the initial and final states.

Explanation of Solution

The molarity of concentrated nitric acid is given 16 M. Let the volume of nitric acid in the same be V mL. To prepare 1.0 M of nitric acid, the concentrated solution must be diluted. Now, the final volume is 500 mL thus, V is less than 500 mL. The volume of water added in the concentrated solution can be obtained by taking difference of final and initial volume.

Apply dilution law to first determine the initial volume of the concentrated acid.

  $M_1{V}_1=M_2{V}_2$

Substitute the values,

  $\left(16\text{ M}\right)V=\left(1.0\text{ M}\right)\left(500\text{ mL}\right)$

Thus,

  $\begin{array}{c}V=\frac{500}{16}\\ =31.25\text{ mL}\end{array}$

Thus, the amount of water added to the concentrated solution will be:

  $\begin{array}{c}{V}_{\text{added}}=V_2-V\\ =\left(500-31.25\right)\text{ mL}\\ =468.75\text{ mL}\end{array}$

Thus, the given solution can be prepared by adding 468.75 mL of water to the initial concentrated solution of acid.