Q. 9.34 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the mass percent $(m/m)$ for the solute in each of the following:

a. $75 g of NaOH$ in $325 g of NaOH$ solution.

b. $2.0 g of KOH$ and $20.0g of H_{2}O$

c. $48.5 g of N{a}_{2}C{O}_3$ in $250.0 g of N{a}_{2}C{O}_3$ solution.

Step-by-Step Solution

Answer

(part a) The mass percent of the given solute is $23\% (m/m) NaOH$solution.

(part b) The mass percent of the given solute is $9.1\% (m/m) KOH$ solution.

(part c) The mass percent of the given solute is $19.4\% (m/m) N{a}_{2}C{O}_3$ solution.

Step1: Introduction (part a).

By entering the mass of the solute and the mass of the solution into the mass percent affirmation, we could indeed quantify the mass percent of the given solution. The mass of the solution is equal to the sum of the solute and solvent masses.

$\text{ Mass of solution }\left(\mathrm{g}\right)=\text{ mass of solute }\left(\mathrm{g}\right)+\text{ mass of solvent }\left(\mathrm{g}\right)$

The mass fraction $(m/m)$ provides the solubility in terms of a solute mass in grammes for exactly $100 g$ of solution.

$\text{ Mass percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ mass of solute }\left(\mathrm{g}\right)}{\text{ mass of solution }\left(\mathrm{g}\right)}\times 100\mathrm{\%}$

Step2: Given Information (part a).

The solution containing $75 g of NaOH$ in a $325 g of NaOH$ solution.

Mass of $NaOH$ solution is $325 g.$

Step3: Explanation (part a).

The mass percent of the solute is,

$$\begin{gathered} \text{ Mass percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ mass of solute }\left(\mathrm{g}\right)}{\text{ mass of solution }\left(\mathrm{g}\right)}\times 100\mathrm{\%} \\ =\frac{75 \mathrm{g} \mathrm{NaOH}}{325 \mathrm{g}\text{ solution }}\times 100\mathrm{\%} \\ =23\% (\mathrm{m}/\mathrm{m}) \mathrm{NaOH} \end{gathered}$$

Step4: Given Information (part b).

The solution containing $2.0 g of KOH$ and $20.0g of H_{2}O.$

The mass of the $KOH$ solution is,

$$\begin{gathered} \text{ Mass of solution }\left(\mathrm{g}\right)=\text{ mass of solute }\left(\mathrm{g}\right)+\text{ mass of solvent }\left(\mathrm{g}\right) \\ =2.0 g+20.0 g \\ =22.0 g \end{gathered}$$

Step5: Explanation (part b).

The mass percent of the solute is,

$$\begin{gathered} \text{ Mass percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ mass of solute }\left(\mathrm{g}\right)}{\text{ mass of solution }\left(\mathrm{g}\right)}\times 100\mathrm{\%} \\ =\frac{2.0 \mathrm{g} K\mathrm{OH}}{22.0 \mathrm{g}\text{ solution }}\times 100\mathrm{\%} \\ =9.1\% (\mathrm{m}/\mathrm{m}) K\mathrm{OH} \end{gathered}$$

Step6: Given Information (part c).

The solution containing $48.5 g of N{a}_{2}C{O}_3$ in $250.0 g of N{a}_{2}C{O}_3$

Mass of $N{a}_{2}C{O}_3$ solution is $250.0 g.$

Step7: Explanation (part c).

The mass percent of the solute is,

$$\begin{gathered} \text{ Mass percent }(\mathrm{m}/\mathrm{m})=\frac{\text{ mass of solute }\left(\mathrm{g}\right)}{\text{ mass of solution }\left(\mathrm{g}\right)}\times 100\mathrm{\%} \\ =\frac{48.5 \mathrm{g} N{a}_{2}C{O}_3}{250.0 \mathrm{g}\text{ solution }}\times 100\mathrm{\%} \\ =19.4\% (\mathrm{m}/\mathrm{m}) N{a}_{2}C{O}_3 \end{gathered}$$