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

Short 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-by-step solution

Given information (Part a)

That are given sentences are :

According to the dilution expression:

Explanation

According to the dilution expression:

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

Here.

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

Given information

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

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 $75\mathrm{mL}$.

Given information (b)

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

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 $90\mathrm{mL}$.

Given information (c)

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

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 $117\mathrm{mL}$.