Q. 9.112 - An Introduction to General, Organic, and Biological Chemistry

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. $20.0 \% (\mathrm{m}/\mathrm{v}) \mathrm{NaOH}$ 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

Step-by-Step Solution

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 $40.0 \mathrm{mL}$.

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 $40ml$