Question

A solution is prepared by dissolving $22.0gofNaOH$in $118.0g$of water. The $NaOH$solution has a density of $1.15g/mL.$

a. What is the mass percent $(m/m)$of the $NaOH$solution?

b. What is the total volume, in milliliters, of the solution?

c. What is the mass/volume percent $(m/v)$of the solution?

d. What is the molarity $\left(M\right)$of the solution?

Short answer

(Part a) The Mass percent$(m/m)$of the$NaOH$solution is$15.7\%.$

(Part b) The Total Volume in milliliters of the solution is$122mL.$

(Part c) The mass/volume percent$(m/v)$of the solution is$18\%.$

(Part d) The Molarity of the solution is$4.5MNaOH.$

Step-by-step solution

Introduction.(Part a)

A mass percentage is a density of solute affirmation that can be approximated from the volume of the solution. The following formula expresses it:

$\mathrm{Mass}\mathrm{percentage}\mathrm{of}\mathrm{solute}=\frac{\text{grams of solute}}{\text{grams of solution}}\times 100\mathrm{\%}$

Given Information (part a).

Mass of Solute$\left(NaOH\right)=22.0g$

Mass of Solvent$\left(H_{2}O\right)=118.0g$

Mass of Solutionrole="math" localid="1652768856855" $(NaOH+H_{2}O)=22.0g+118.0g=140g$

Explanation (part a). 

Determine the Mass percentage:

$$\begin{gathered} \mathrm{Mass}\mathrm{percentage}\mathrm{of}\mathrm{solute}=\frac{\text{grams of solute}}{\text{grams of solution}}\times 100\mathrm{\%} \\ \mathrm{Mass}\mathrm{percent}=\left(\frac{22.0\mathrm{g}}{140.0\mathrm{g}}\right)\times 100\mathrm{\%} \\ =15.7\% \end{gathered}$$

Given Information (part b).

Mass of Solute$\left(NaOH\right)=22.0g$

Mass of Solvent$\left(H_{2}O\right)=118.0g$

Mass of Solutionrole="math" localid="1652768846726" $(NaOH+H_{2}O)=22.0g+118.0g=140g$

Explanation (part b). 

Calculate the Total Volume in milliliters:

$$\begin{gathered} \text{density}=\frac{\text{mass}\left(\mathrm{g}\right)}{\text{volume}\left(\mathrm{mL}\right)} \\ \mathrm{volume}\left(\mathrm{mL}\right)=\frac{\text{mass}\left(\mathrm{g}\right)}{\mathrm{density}} \\ \text{volume}\left(\mathrm{mL}\right)=\frac{140.0\mathrm{g}}{1.15\mathrm{g}{\mathrm{mL}}^{-1}} \\ =122mL \end{gathered}$$

Given Information (part c).

Mass of Solute $\left(NaOH\right)=22.0g$

Volume of the solution is$122mL.$

Explanation (part c). 

Find the mass/volume percent:

$$\begin{gathered} \text{Mass percentin}\mathrm{m}/\mathrm{V}=\left(\frac{\text{mass of solute}}{\text{Volume of solution}}\right)\times 100\mathrm{\%} \\ \text{Mass percent}=\left(\frac{22.0\mathrm{g}}{122\mathrm{mL}}\right)\times 100\mathrm{\%} \\ \mathrm{Mass}percent=18\% \end{gathered}$$

Given Information (part d).

Volume of Solution is $122mL.$

convert it into Liters,

$$\begin{gathered} 1L=1000mL \\ =122m\mathrm{L}\times \frac{1.00\mathrm{L}}{1000m\mathrm{L}} \\ =0.122\mathrm{mL} \end{gathered}$$

Number of moles,

localid="1652769682452" $$\begin{gathered} \mathrm{Molar}\mathrm{mass}\mathrm{of}\mathrm{NaOH}=39.997\mathrm{g}/\mathrm{mol} \\ =22.0\mathrm{g}\mathrm{NaOH}\times \frac{1\mathrm{molNaOH}}{39.997\mathrm{g}\mathrm{NaOH}} \\ =0.55\mathrm{mol}\mathrm{NaOH} \end{gathered}$$

Explanation (part d). 

Find the Concentration of$NaOH:$

$$\begin{gathered} \mathrm{Concentration}\mathrm{of}NaOH=\frac{\text{number of}\mathrm{mol}NaOH}{\text{volume in}\mathrm{L}} \\ =\frac{0.55\mathrm{mol}NaOH}{0.122\mathrm{L}} \\ =4.5MNaOH \end{gathered}$$