Chapter 8, Problem 8.89P

Interpretation Introduction

(a)

Interpretation:

The weight/volume percent concentration of vitamin C solution that has been diluted from $100\text{ mL}$ to $200\text{ mL}$ 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:

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

The dilution formula is given as follows:

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

Answer to Problem 8.89P

The weight/volume percent concentration of vitamin C solution that has been diluted from $100\text{ mL}$ to $200\text{ mL}$ is $15\text{ \%}$.

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.

Initial volume is given as $\text{100 mL}$.

Initial weight/volume percent concentration is given as $\text{30 \%}$.

Final volume after dilution is given as $\text{200 mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in the formula above.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{30 \%}\right)\left(\text{100 mL}\right)={\text{C}}_2\left(\text{200 mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin C.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{30 \%}\right)\left(\text{100 mL}\right)}{\left(\text{200 mL}\right)}\\ =15\text{ \%}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The weight/volume percent concentration of vitamin C solution that has been diluted from $100\text{ mL}$ to $500\text{ mL}$ 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:

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

The dilution formula is given as follows:

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

Answer to Problem 8.89P

The weight/volume percent concentration of vitamin C solution that has been diluted from $100\text{ mL}$ to $500\text{ mL}$ is $6\text{ \%}$.

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.

Initial volume is given as $\text{100 mL}$.

Initial weight/volume percent concentration is given as $\text{30 \%}$.

Final volume after dilution is given as $500\text{ mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in above formula.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{30 \%}\right)\left(\text{100 mL}\right)={\text{C}}_2\left(500\text{ mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin C.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{30 \%}\right)\left(\text{100 mL}\right)}{\left(\text{500 mL}\right)}\\ =6\text{ \%}\end{array}$

Interpretation Introduction

(c)

Interpretation:

The weight/volume percent concentration of vitamin C solution that has been diluted from $250\text{ mL}$ to $1.5\text{ L}$ 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:

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

The conversion factor to convert the liters to milliliters is as follows:

  $1\text{ L}=\text{1000 mL}$

Answer to Problem 8.89P

The weight/volume percent concentration of vitamin C solution that has been diluted from $250\text{ mL}$ to $1.5\text{ L}$ is $5\text{ \%}$.

Explanation of Solution

The conversion factor to convert the liters to milliliters is as follows:

  $1\text{ L}=\text{1000 mL}$

Hence, convert the volume in liters to milliliters as follows:

  $\begin{array}{c}\text{Volume}\left(\text{mL}\right)=\left(1.5\text{ L}\right)\left(\frac{\text{1000 mL}}{1\text{ L}}\right)\\ =1500\text{ mL}\end{array}$

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 $250\text{ mL}$.

Initial weight/volume percent concentration is given as $\text{30 \%}$.

Final volume after dilution is given as $1500\text{ mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in above formula.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{30 \%}\right)\left(\text{250 mL}\right)={\text{C}}_2\left(1500\text{ mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin C.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{30 \%}\right)\left(\text{250 mL}\right)}{\left(1500\text{ mL}\right)}\\ =5\text{ \%}\end{array}$

Interpretation Introduction

(d)

Interpretation:

The weight/volume percent concentration of vitamin C solution that has been diluted from $\text{0}\text{.35 L}$ to $\text{750 mL}$ 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 8.89P

The weight/volume percent concentration of vitamin C solution that has been diluted from $\text{0}\text{.35 L}$ to $\text{750 mL}$ is $14\text{ \%}$.

Explanation of Solution

The conversion factor to convert the liters to milliliters is as follows:

  $1\text{ L}=\text{1000 mL}$

Hence convert the volume in liters to milliliters as follows:

  $\begin{array}{c}\text{Volume}\left(\text{mL}\right)=\left(\text{0}\text{.35 L}\right)\left(\frac{\text{1000 mL}}{1\text{ L}}\right)\\ =350\text{ mL}\end{array}$

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 $350\text{ mL}$.

Initial weight/volume percent concentration is given as $\text{30 \%}$.

Final volume after dilution is given as $\text{750 mL}$.

Final weight/volume percent concentration is to be calculated.

Substitute the values in above formula.

  $\begin{array}{c}{\text{C}}_1{\text{V}}_1={\text{C}}_2{\text{V}}_2\\ \left(\text{30 \%}\right)\left(350\text{ mL}\right)={\text{C}}_2\left(\text{750 mL}\right)\end{array}$

Rearrange the above expression to calculate the finalweight/volume percent concentrationof vitamin C.

  $\begin{array}{c}{\text{C}}_2=\frac{\left(\text{30 \%}\right)\left(\text{350 mL}\right)}{\left(\text{750 mL}\right)}\\ =14\text{ \%}\end{array}$