Chapter 14, Problem 1STP

Interpretation Introduction

Interpretation:

Volume of bromine (Br₂) in 7.000 L of solution 1 has to be calculated.

Concept introduction:

Composition of a solution can be defined by expressing its concentration. Concentration can be expressed either qualitatively or quantitatively. There are several ways by which we can describe the concentration of the solution quantitatively. Some commonly used quantitative descriptions are percent by mass, percent by volume, molarity, molality and mole fraction.

Mass percentage or percent by mass (w/W): The mass percentage of a component of a solution is defined as:

$\mathrm{Mass}\%ofacomponent=\frac{Mass of the component in the solution}{Total mass of the solution}\times 100$

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.

In expression,

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

Answer to Problem 1STP

Answer is C. 18.03 mL of bromine (Br₂) is present in 7.000 L of solution 1.

Given information:

Total volume of the solution = 7 litre = 7000 mL

Percent by volume = 0.2575

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.

In expression,

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

$\begin{array}{l}Volumepercentage=\frac{Volumeof bromine}{Total volume of the solution}\times 100\\ Volumeof bromine=\frac{Volumepercentage\times Total volume of the solution}{100}\\ Volumeof bromine=\frac{0.2575\times 7000mL}{100}=18.03mL\end{array}$

Answer is C.

Reasons for incorrect options:

As it can be seen that volume of bromine calculated from the equation:

$\begin{array}{l}Volumepercentage=\frac{Volumeof bromine}{Total volume of the solution}\times 100\\ Volumeof bromine=\frac{Volumepercentage\times Total volume of the solution}{100}\\ Volumeof bromine=\frac{0.2575\times 7000mL}{100}=18.03mL\end{array}$

So, volume of bromine found to be 18.03 mL.

That means other options that is,

a. 55.63 mL

b. 8.808 mL

d. 27.18 mL are not found by this equation, that makes them incorrect.

Explanation of Solution

Given information:

Total volume of the solution = 7 litre = 7000 mL

Percent by volume = 0.2575

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.

In expression,

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

$\begin{array}{l}Volumepercentage=\frac{Volumeof bromine}{Total volume of the solution}\times 100\\ Volumeof bromine=\frac{Volumepercentage\times Total volume of the solution}{100}\\ Volumeof bromine=\frac{0.2575\times 7000mL}{100}=18.03mL\end{array}$

Answer is C.

Conclusion

Reasons for incorrect options:

As it can be seen that volume of bromine calculated from the equation:

$\begin{array}{l}Volumepercentage=\frac{Volumeof bromine}{Total volume of the solution}\times 100\\ Volumeof bromine=\frac{Volumepercentage\times Total volume of the solution}{100}\\ Volumeof bromine=\frac{0.2575\times 7000mL}{100}=18.03mL\end{array}$

So, volume of bromine found to be 18.03 mL.

That means other options that is,

a. 55.63 mL

b. 8.808 mL

d. 27.18 mL are not found by this equation, that makes them incorrect.