Chapter 8, Problem 8.90P

Interpretation Introduction

(a)

Interpretation:

The weight/volume percent concentration of vitamin ${\text{B}}_3$ is to be calculated.

Concept introduction:

Several concentration units may be used to express the concentration. It is often useful to express the concentration in terms of percentage. This can be expressed as the amount of solute in grams dissolved in $100\text{ mL}$ of solution that is termed as weight by volume percentage. This is useful to express the concentration of solid solutes. The other way is to express the number of milliliters of solute per $100\text{ mL}$ of the solution. This is called the volume /volume percentage which is useful to express the concentrations of liquid solutes.

The formula to calculate the weight/volume percent concentrationis as follows:

  $\text{Weight/volume percent}\left(\frac{\text{m}}{\text{v}}\right)\%=\frac{\text{Mass of solute}\left(\text{g}\right)}{\text{Volume of solution}\left(\text{mL}\right)}\times 100\%$

The dilution formula is given as follows:

  ${\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2$

Answer to Problem 8.90P

The weight/volume percent concentration of vitamin ${\text{B}}_3$ is $10\%$.

Explanation of Solution

The formula to calculate the weight/volume percent is as follows:

  $\text{Weight/volume percent }\left(\frac{\text{m}}{\text{v}}\right)\%=\frac{\text{Mass of solute}\left(\text{g}\right)}{\text{Volume of solution}\left(\text{mL}\right)}\times 100\%$

The mass of solute is given as $1\text{ g}$.

Volume of solution is $10\text{ mL}$

Substitute the values in the formula above.

  $\begin{array}{c}\text{Weight/volume percent }\left(\frac{\text{m}}{\text{v}}\right)\%=\frac{\text{Mass of solute}\left(\text{g}\right)}{\text{Volume of solution}\left(\text{mL}\right)}\times 100\%\\ =\frac{1\text{ g}}{10\text{ mL}}\times 100\%\\ =10\%\end{array}$

Interpretation Introduction

(b)

Interpretation:

The concentrations of vitamin ${\text{B}}_3$ solution that has been diluted from $1\text{ mL}$ to $\text{10 mL}$ , $\text{2}\text{.5 mL}$ , $\text{50 mL}$ and $\text{120 mL}$ is to be calculated.

Concept introduction:

Several concentration units may be used to express the concentration. It is often useful to express the concentration in terms of percentage. This can be expressed as the amount of solute in grams dissolved in $100\text{ mL}$ of solution that is termed as weight by volume percentage. This is useful to express the concentration of solid solutes. The other way is to express the number of milliliters of solute per $100\text{ mL}$ of the solution. This is called the volume /volume percentage which is useful to express the concentrations of liquid solutes.

The formula to calculate the weight/volume percent is as follows:

  $\text{Weight/volume percent concentration}\left(\frac{\text{m}}{\text{v}}\right)\%=\frac{\text{Mass of solute}\left(\text{g}\right)}{\text{Volume of solution}\left(\text{mL}\right)}\times 100\%$

The dilution formula is given as follows:

  ${\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2$

Answer to Problem 8.90P

The concentrations of vitamin ${\text{B}}_3$ solution that has been diluted from $1\text{ mL}$ to $\text{10 mL}$ , $\text{2}\text{.5 mL}$ , $\text{50 mL}$ and $\text{120 mL}$ is $1\text{ \%}$ , $4\text{ \%}$ , $0.2\text{ \%}$ and $0.083\text{ \%}$ respectively.

Explanation of Solution

The dilution formula is given as follows:

  ${\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2$

Where,

• ${\text{C}}_1$denotes the initial concentration before dilution.
• ${\text{V}}_1$denotes the initial volume of solution.
• ${\text{C}}_2$denotes the final concentration after dilution.
• ${\text{V}}_2$ denotes the final volume of solution.

For [1], when volume after dilution is as $\text{10 mL}$.

Initial volume is given as $1\text{ mL}$.

Initial weight/volume percent concentration is given as $\text{10 \%}$.

Final volume after dilution is given as $\text{10 mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in above formula.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{10 \%}\right)\left(\text{1 mL}\right)={\text{C}}_2\left(\text{10 mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin ${\text{B}}_3$.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{10 \%}\right)\left(\text{1 mL}\right)}{\left(\text{10 mL}\right)}\\ =1\text{ \%}\end{array}$

For [2], when volume after dilution is as $\text{2}\text{.5 mL}$.

The dilution formula is given as follows:

  ${\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2$

Where,

• ${\text{C}}_1$denotes the initial concentration before dilution.
• ${\text{V}}_1$denotes the initial volume of solution.
• ${\text{C}}_2$denotes the final concentration after dilution.
• ${\text{V}}_2$ denotes the final volume of solution.

Initial volume is given as $1\text{ mL}$.

Initial weight/volume percent concentration is given as $\text{10 \%}$.

Final volume after dilution is given as $\text{2}\text{.5 mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in the formula above.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{10 \%}\right)\left(\text{1 mL}\right)={\text{C}}_2\left(\text{2}\text{.5 mL}\right)\end{array}$

Rearrange the above expression to calculate the final weight/volume percent concentration of vitamin ${\text{B}}_3$.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{10 \%}\right)\left(\text{1 mL}\right)}{\left(\text{2}\text{.5}\text{mL}\right)}\\ =4\text{ \%}\end{array}$

For [3], when volume after dilution is as $\text{50 mL}$.

The dilution formula is given as follows:

  ${\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2$

Where,

• ${\text{C}}_1$denotes the initial concentration before dilution.
• ${\text{V}}_1$denotes the initial volume of solution.
• ${\text{C}}_2$denotes the final concentration after dilution.
• ${\text{V}}_2$ denotes the final volume of solution.

Initial volume is given as $1\text{ mL}$.

Initial weight/volume percent concentrationof vitamin ${\text{B}}_3$ is given as $\text{10 \%}$.

Final volume after dilution is given as $\text{50 mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in the formula above.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{10 \%}\right)\left(\text{1 mL}\right)={\text{C}}_2\left(\text{50 mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin ${\text{B}}_3$.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{10 \%}\right)\left(\text{1 mL}\right)}{\left(\text{50 mL}\right)}\\ =0.2\text{ \%}\end{array}$

For [4], when volume after dilution is as $\text{120 mL}$.

The dilution formula is given as follows:

  ${\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2$

Where,

• ${\text{C}}_1$denotes the initial concentration before dilution.
• ${\text{V}}_1$denotes the initial volume of solution.
• ${\text{C}}_2$denotes the final concentration after dilution.
• ${\text{V}}_2$ denotes the final volume of solution.

Initial volume is given as $1\text{ mL}$.

Initial weight/volume percent concentration is given as $\text{10 \%}$.

Final volume after dilution is given as $\text{120 mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in the formula above.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{10 \%}\right)\left(\text{1 mL}\right)={\text{C}}_2\left(\text{120 mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin ${\text{B}}_3$.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{10 \%}\right)\left(\text{1 mL}\right)}{\left(\text{120 mL}\right)}\\ =0.083\text{ \%}\end{array}$