Q. 111 - An Introduction to General, Organic, and Biological Chemistry

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

Step-by-Step Solution

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 $300 \mathrm{mL}$.

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:

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

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:

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