Q. 9.118 - An Introduction to General, Organic, and Biological Chemistry

Question

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

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?

Step-by-Step Solution

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 $122 mL.$

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

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

Step1: 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:

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

Step2: Given Information (part a).

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

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

Mass of Solution  $(NaOH+H_{2}O)=22.0 g+118.0 g=140 g$

Step3: Explanation (part a).

Determine the Mass percentage:

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

Step4: Given Information (part b).

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

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

Mass of Solution  $(NaOH+H_{2}O)=22.0 g+118.0 g=140 g$

Step5: Explanation (part b).

Calculate the Total Volume in milliliters:

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

Step6: Given Information (part c).

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

Volume of the solution is $122 mL.$

Step7: Explanation (part c).

Find the mass/volume percent:

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

Step8: Given Information (part d).

Volume of Solution is $122 mL.$

convert it into Liters,

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

Number of moles,

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

Step9: Explanation (part d).

Find the Concentration of $NaOH:$

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