Q. 9.109 - An Introduction to General, Organic, and Biological Chemistry

Question

9 What is the initial volume, in milliliters, needed to prepare each of the following diluted solutions? (9.5)

a.$250 \mathrm{mL}$ of $3.0\%( \mathrm{m}/\mathrm{v})\mathrm{HCl}$ from $10.0\%( \mathrm{m}/\mathrm{v})\mathrm{HCl}$

b. $500.\mathrm{mL}$of $0.90\%(\mathrm{ma}/\mathrm{v})\mathrm{NaCl}$ from $5.0\%$(m/v) $\mathrm{NaCl}$

c. 350 . mL of $2.00\mathrm{MNaOH}$from 6.00 M NaOH

Step-by-Step Solution

Answer

Part a)

The required initial volume of $\mathrm{HCl}$ solution is $75 \mathrm{mL}$

Part b)

The required initial volume of $\mathrm{NaCl}$solution is $90 \mathrm{mL}$

Part c)

The required initial volume of $\mathrm{NaOH}$ solution is $117 \mathrm{mL}$.

Step 1: Given information (Part a)

That are given sentences are : 

According to the dilution expression:

Step 2: Explanation

According to the dilution expression:

${\mathrm{C}}_1\times {\mathrm{V}}_1={\mathrm{C}}_2\times {\mathrm{V}}_2$

Here.

$$\begin{gathered} C_1=\text{ concentration of the concentrated solution } \\ {V}_1=\text{ volume of the concentrated solution } \\ {C}_2=\text{ concentration of the diluted solution } \\ {V}_2=\text{ volume of the diluted solution } \end{gathered}$$

Step 3: Given information

The dilution expression to solve tor the unknown quantity $V_1$.

Step 4: Explanation (a)

According to the problem,

$$\begin{gathered} C_2=3.0\%( \mathrm{m}/\mathrm{v}) \\ {\mathrm{V}}_2=250 \mathrm{mL} \\ {\mathrm{C}}_1=10.0\%( \mathrm{m}/\mathrm{v}) \\ {\mathrm{V}}_1=? \end{gathered}$$

Rearrange the dilution expression to solve for the unknown quantity $V_1$.

$$\begin{gathered} V_1=\frac{{\mathrm{C}}_2\times {\mathrm{V}}_2}{{\mathrm{C}}_1} \\ { \mathrm{V}}_1=\frac{3.0\%( \mathrm{m}/\mathrm{v})\times 250 \mathrm{mL}}{10.0\%( \mathrm{m}/\mathrm{v})} \\ =75 \mathrm{mL} \end{gathered}$$

The required initial volume of $\mathrm{HCl}$ solution is $75 \mathrm{mL}$.

Step 5: Given information (b)

Rearrange the dilution expression to solve for the unknown quantity $V_1$

Step 6: Explanation (b)

According to the problem,

$$\begin{gathered} C_2=0.9\%( \mathrm{m}/\mathrm{v}) \\ {\mathrm{V}}_2=500 \mathrm{mL} \\ {\mathrm{C}}_1=5.0\%( \mathrm{m}/\mathrm{v}) \\ {\mathrm{V}}_1=? \end{gathered}$$

Rearrange the dilution expression to solve for the unknown quantity $V_1$.

$$\begin{gathered} V_1=\frac{C_2\times V_2}{C_1} \\ {V}_1=\frac{0.9\%( \mathrm{m}/\mathrm{v})\times 500 \mathrm{mL}}{5.0\%( \mathrm{m}/\mathrm{v})} \\ =90 \mathrm{mL} \end{gathered}$$

The required initial volume of $\mathrm{NaCl}$ solution is $90 \mathrm{mL}$.

Step 7: Given information (c)

Rearrange the dilution expression to solve for the unknown quantity $V_1$.

Step 8: Explanation (c)

According to the problem,

$$\begin{gathered} C_2=2.0\mathrm{M} \\ {V}_2=350 \mathrm{mL} \\ {C}_1=6.0\mathrm{M} \\ {V}_1=? \end{gathered}$$

Rearrange the dilution expression to solve for the unknown quantity $V_1$.

$$\begin{gathered} V_1=\frac{C_2\times V_2}{C_1} \\ {V}_1=\frac{2.0\mathrm{M}\times 350 \mathrm{mL}}{6.0\mathrm{M}} \\ =117 \mathrm{mL} \end{gathered}$$

The required initial volume of $\mathrm{NaOH}$solution is $117 \mathrm{mL}$.