Chapter 14, Problem 70A

Interpretation Introduction

Interpretation:

The percentage by volume of a solution created by adding 75 mL of acetic acid to 725 mL of water has to be calculated.

Concept Introduction:

The composition of a solution can be defined by expressing its concentration. The concentrations of solutions can be expressed in different ways, which are involved in the quantity of solute and the quantity of solution or solvent. Various methods are used to describe the concentration of the solution quantitatively. Some commonly used quantitative concentration terms are percent by mass, percent by volume, molarity, molality and mole fraction.

Volume/volume percentage (v/V percent): Percent by volume is expressed as the ratio of the volume of the solute to the total volume of the solution multiplied by 100. This is used when both chemicals in a solution are liquid.

In expression,

  $\mathrm{Volume}\hspace{0.17em}percentage\hspace{0.17em}\left(v/V\right)\hspace{0.17em}\%\hspace{0.17em}of\hspace{0.17em}a\hspace{0.17em}component=\frac{Volumeof the solute}{Total volume of the solution}\times 100$

Answer to Problem 70A

The percentage by volume of a solution created by adding 75 mL of acetic acid to 725 mL of water is 9.4 %.

Explanation of Solution

  $\mathrm{Volume}\hspace{0.17em}percentage\hspace{0.17em}\left(v/V\right)\hspace{0.17em}\%\hspace{0.17em}of\hspace{0.17em}a\hspace{0.17em}component=\frac{Volumeof the solute}{Total volume of the solution}\times 100$

Data given: Volume of the solute (CH₃ COOH) = 75 mL

Volume of the solvent (water) = 725 mL

Total volume of the solution = Volume of CH₃ COOH + Volume of water

            = (75 + 725) mL = 800 mL

  $\begin{array}{l}Volume\hspace{0.17em}percentage\hspace{0.17em}=\frac{Volumeof thesolute}{Total volume of the solution}\times 100\end{array}$

  $\begin{array}{c}Volume\hspace{0.17em}percentage\hspace{0.17em}=\frac{Volumeof C{H}_{3}COOH}{Total volume of the solution}\times 100\end{array}$

  $\begin{array}{c}Volume\hspace{0.17em}percentage\hspace{0.17em}=\frac{75mL}{800mL}\times 100=9.4\%\end{array}$