Q. 9.41 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the grams or milliliters of solute needed to prepare the following:

a.$\text{ 50 }\mathrm{g}\text{ of a }5.0\% ( \mathrm{m}/\mathrm{m}) \mathrm{KCl}$ solution.

b. $1250 \mathrm{mL}\text{ of a }4.0\% ( \mathrm{m}/\mathrm{v} ){\mathrm{NH}}_4\mathrm{Cl}$ solution.

c. $\text{ 250 }\mathrm{mL}\text{ of a }10.0\% (\mathrm{v}/\mathrm{v})$ acetic acid solution.

Step-by-Step Solution

Answer

(part a) Weight of the $\text{ 50 }\mathrm{g}\text{ of a }5.0\% ( \mathrm{m}/\mathrm{m}) \mathrm{KCl}$ solution is $60 g.$

(part b) Weight of the $1250 \mathrm{mL}\text{ of a }4.0\% ( \mathrm{m}/\mathrm{v} ) {\mathrm{NH}}_4\mathrm{Cl}$ solution is $6 g.$

(part c) Volume of the $\mathrm{250 }\mathrm{mL}\text{ of a }10.0\% (\mathrm{v}/\mathrm{v})$ acetic acid solution is $33.75 mL$

Step 1: Given Information (part a).

The following information are used to find the mass or milliliters of solute:

$\text{ 50 }\mathrm{g}\text{ of a }5.0\% ( \mathrm{m}/\mathrm{m}) \mathrm{KCl}$ solution.

Step 2: To find the Weight's value (part a).

By using the following equation, find the mass percentage,

$\text{ Mass percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ Solute mass }}{\text{ Solution mass }}\times 100\mathrm{\%}$

Substitute the values by rearranging the equation ,

$$\begin{gathered} \text{ Solute mass }=\frac{\text{ Mass percent }(\mathrm{m}/\mathrm{m})\times \text{ Solution mass }}{100\mathrm{\%}} \\ =\frac{40.0\mathrm{\%}\times 150 \mathrm{g}}{100\mathrm{\%}} \\ =60 g \end{gathered}$$

Step 3: Given Information (part b).

The following information are used to find the mass or milliliters of solute:

$1250 \mathrm{mL}\text{ of a }4.0\% ( \mathrm{m}/\mathrm{v} ){\mathrm{NH}}_4\mathrm{Cl}$ solution.

Step 4: Explained the weight value (part b).

Find the mass using the equation,

$\text{ Mass percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ Solute mass }}{\text{ Solution mass }}\times 100\mathrm{\%}$

Substitute the values by rearranging the equation ,

$$\begin{gathered} \text{ Solute mass }=\frac{\text{ Mass percent }(\mathrm{m}/\mathrm{m})\times \text{ Solution mass }}{100\mathrm{\%}} \\ =\frac{2.0\mathrm{\%}\times 450 \mathrm{mL}}{100\mathrm{\%}} \\ =6 g \end{gathered}$$

Step 5: Given Information (part c).

The following information are used to find the mass or milliliters of solute:

$\text{ 250 }\mathrm{mL}\text{ of a }10.0\% (\mathrm{v}/\mathrm{v})$ acetic acid solution.

Step 6: Explained the Weight (part c).

The mass equation is as follows:

$\text{ Volume percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ Volume mass }}{\text{ Volume mass }}\times 100\mathrm{\%}$

Rearrange the equation to substitute the value,

$$\begin{gathered} \text{ Solute volume }=\frac{\text{ Volume percent }(\mathrm{m}/\mathrm{m})\times \text{ Solution volume }}{100\mathrm{\%}} \\ =\frac{15.0\mathrm{\%}\times 225 \mathrm{mL}}{100\mathrm{\%}} \\ =33.75 \mathrm{mL} \end{gathered}$$