Question

What is the final volume, in milliliters, when $25.0\mathrm{mL}$of each of the following solutions is diluted to provide the given concentration? $(9.5)$

a. $10\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution to give a $2.50\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution.

b. $5.00\mathrm{M}\mathrm{HCl}$solution to give a$1.00\mathrm{M}\mathrm{HCl}$ solution

c. $6.00\mathrm{M}\mathrm{HCl}$solution to give a $0.500\mathrm{M}\mathrm{HCl}$solution

Short answer

a. The final volume of $10\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution to give a $2.50\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution is$100\mathrm{mL}$.

b. The final volume of$5.00\mathrm{M}\mathrm{HCl}$ solution to give a $1.00\mathrm{M}\mathrm{HCl}$ solution is$125\mathrm{mL}$.

c. The final volume of $6.00\mathrm{M}\mathrm{HCl}$solution to give a $0.500\mathrm{M}\mathrm{HCl}$ solution is$300\mathrm{mL}$.

Step-by-step solution

Part (a) step 1: Given Information

We need to find the final volume when $10\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution to give a $2.50\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution.

Part (a) step 2: Simplify

Now,

Using the formula below, calculate the final volume of $25.0\mathrm{mL}\mathrm{of}10.0\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}$solution diluted to $2.50\%\mathrm{HCl}$solution:

$$\begin{gathered} {\mathrm{C}}_1{\mathrm{V}}_1={\mathrm{C}}_2{\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{{\mathrm{C}}_1{\mathrm{V}}_1}{{\mathrm{C}}_2} \\ {\mathrm{V}}_2=\frac{\left(10.0\%(\mathrm{m}/\mathrm{v}\right)\mathrm{HCl}\mathrm{solution}\left)\right(25.0\mathrm{mL})}{2.50\%(\mathrm{m}/\mathrm{v})\mathrm{HCl}\mathrm{solution}} \\ {\mathrm{V}}_2=100\mathrm{mL} \end{gathered}$$

Part (b) step 1: Given Information

We need to find the final volume when $5.00\mathrm{M}\mathrm{HCl}$ solution to give a$1.00\mathrm{M}\mathrm{HCl}$solution.

Part (b) step 2: Simplify

Now,

Using the formula below, calculate the final volume of $25.0\mathrm{mL}\mathrm{of}5.00\mathrm{M}\mathrm{HCl}$solution diluted to $1.00\mathrm{M}\mathrm{HCl}$solution:

role="math" localid="1653294053632" $$\begin{gathered} {\mathrm{C}}_1{\mathrm{V}}_1={\mathrm{C}}_2{\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{{\mathrm{C}}_1{\mathrm{V}}_1}{{\mathrm{C}}_2} \\ {\mathrm{V}}_2=\frac{(5.0\mathrm{M}\mathrm{HCl}\mathrm{solution})(25.0\mathrm{mL})}{1.00\mathrm{M}\mathrm{HCl}\mathrm{solution}} \\ {\mathrm{V}}_2=125\mathrm{mL} \end{gathered}$$

Part (c) step 1: Given Information

We need to find the final volume when $6.00\mathrm{M}\mathrm{HCl}$solution to give a $0.500\mathrm{M}\mathrm{HCl}$solution.

Part (c) step 2: Simplify

Now,

Using the formula below, calculate the final volume of $25.0\mathrm{mL}\mathrm{of}6.00\mathrm{M}\mathrm{HCl}$solution diluted to $0.500\mathrm{M}\mathrm{HCl}$the solution:

$$\begin{gathered} {\mathrm{C}}_1{\mathrm{V}}_1={\mathrm{C}}_2{\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{{\mathrm{C}}_1{\mathrm{V}}_1}{{\mathrm{C}}_2} \\ {\mathrm{V}}_2=\frac{(6.0\mathrm{M}\mathrm{HCl}\mathrm{solution})(25.0\mathrm{mL})}{0.500\mathrm{M}\mathrm{HCl}\mathrm{solution}} \\ {\mathrm{V}}_2=300\mathrm{mL} \end{gathered}$$