Question

What is the final volume, in milliliters, when $5.00\mathrm{mL}$of each of the following solutions is diluted to provide the given concentration? $\left(9.5\right)$

a. localid="1653294892486" $20.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution to give a$4.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution

b. $0.600\mathrm{M}\mathrm{NaOH}$the solution to give a $0.100\mathrm{M}\mathrm{NaOH}$solution

c. $16.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution to give a $2.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution

Short answer

a. The final volume of $20.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution to give a $4.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution is $25.0\mathrm{mL}$.

b. The final volume of $0.600\mathrm{M}\mathrm{NaOH}$solution to give a $0.100\mathrm{M}\mathrm{NaOH}$solution is $30.0\mathrm{mL}$.

c. The final volume of $16.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution to give a $2.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution is $40.0\mathrm{mL}$.

Step-by-step solution

Part (a) Step 1: Given Information

$20.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution to give a $4.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution.

Part (a) Step 2: Explanation

Now,

Using the concentration formula-

$$\begin{gathered} {\mathrm{C}}_1{\mathrm{V}}_1={\mathrm{C}}_2{\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{{\mathrm{C}}_1{\mathrm{V}}_1}{{\mathrm{C}}_2} \\ {\mathrm{V}}_2=\frac{(20.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}\mathrm{solution})(5.00\mathrm{mL})}{4.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}\mathrm{sloution}} \\ {\mathrm{V}}_2=25.0\mathrm{mL} \end{gathered}$$

Hence the final volume is$25ml$

Part (b) Step 1: Given Information

$0.600\mathrm{M}\mathrm{NaOH}$solution to give a $0.100\mathrm{M}\mathrm{NaOH}$solution.

Part (b) Step 2: Explanation

Now,

Using the concentration formula-

$$\begin{gathered} {\mathrm{C}}_1{\mathrm{V}}_1={\mathrm{C}}_2{\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{{\mathrm{C}}_1{\mathrm{V}}_1}{{\mathrm{C}}_2} \\ {\mathrm{V}}_2=\frac{(0.600\mathrm{M}\mathrm{HCl}\mathrm{solution})(5.00\mathrm{mL})}{0.100\mathrm{M}\mathrm{HCl}\mathrm{sloution}} \\ {\mathrm{V}}_2=30.0\mathrm{mL} \end{gathered}$$

Hence the final volume is$30ml$

Part (c) Step 1: Given Information

$16.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution to give a$2.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}$solution.

Part (c) Step 2: Explanation

Now,

Using the concentration formula-

$$\begin{gathered} {\mathrm{C}}_1{\mathrm{V}}_1={\mathrm{C}}_2{\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{{\mathrm{C}}_1{\mathrm{V}}_1}{{\mathrm{C}}_2} \\ {\mathrm{V}}_2=\frac{(16.0\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}\mathrm{solution})(5.00\mathrm{mL})}{2.00\%(\mathrm{m}/\mathrm{v})\mathrm{NaOH}\mathrm{sloution}} \\ {\mathrm{V}}_2=40.0\mathrm{mL} \end{gathered}$$

Hence the final volume is$40ml$