Q. 9.107 - An Introduction to General, Organic, and Biological Chemistry

Question

Table calculate the final concentration of the solution when water is added to prepare each of the following: (9.5)

a. $25.0 \mathrm{mL}$of a  $0.200\mathrm{MNaBr}$ solution is dilused to $50.0 \mathrm{mL}$

b. $15.0 \mathrm{mL}$ of a $12.0\%$ (m/v) ${\mathrm{K}}_2{\mathrm{SO}}_4$ solution is tiluted to $40.0 \mathrm{mL}$

c. $75.0 \mathrm{mL}$ of a $6.00\mathrm{MNaOH}$solution is diluted to$255 \mathrm{mL}$

Step-by-Step Solution

Answer

Part a). 

The concentration of diluted solution is 0.100 M.

Part b). 

The concentration of diluted solution is $4.5\%$

Part c).

The concentration of diluted solution is 1.76 M.

Step 1: Given information (Part a)

To obtain the final concentration of the solution when water is added to the following:

a. $25.0 \mathrm{mL}$ of  $0.200\mathrm{MNaBr}$ solution is diluted to a $50.0 \mathrm{mL}$

b.$15.0 \mathrm{mL}$ of $12.0\%( \mathrm{m}/\mathrm{v}){\mathrm{K}}_2{\mathrm{SO}}_4$ solution is diluted to a $40.0 \mathrm{mL}$

c. $75.0 \mathrm{mL}$ of $6.00\mathrm{MNaOH}$ solution is diluted to a $255 \mathrm{mL}$

Step 2: Definition of Molarity:

Molarity

The number of solutions per liter of solution is known as the morality of the solution. It is symbolized by $M$. The variety of solution is the ratio of the variety of solution per liter of solution. The formula below :

Molarity$\left(M\right)=\frac{\text{ moles of solutes }}{\text{ liter of solution }}$

Step 3: Definition of Density:

Density:

The density of a substance is equal to the ratio of mass to volume. In general, it can be said that the density of the substance is equal to the mass per unit volume.

density $\left(\mathrm{g}/{\mathrm{cm}}^3\right)=\frac{\text{ mass }\left(\mathrm{g}\right)}{\text{ volume }\left({\mathrm{cm}}^3\right)}$ or $\frac{\text{ mass }\left(\mathrm{g}\right)}{\text{ volume }\left(\mathrm{mL}\right)}$

Step 4: Definition of Mass percentage:

Mass percentage:

The mass percentage is an indication of the concentration of the solution, which may be a percentage of the mass of the solution. The company's goal is to increase profits.

Mass percentage of solute $=\frac{\text{ grams of solute }}{\text{ grams of solution }}\times 100\%$

Step 5: Process of Dilution:

When a solvent is added to a solution, the volume of the solution increases and the concentration decreases. This is a process of dilution.

The concentration of a diluted solution and a concentrated solution are the same. The volume of a diluted solution is smaller than the volume of a concentrated solution.

$C_1{V}_1 = C_2{V}_2$

concentrated solution             dilute solution

Step 6: Given information (Part a) Final concentration of the following :

The concentration and the volume of dilute and concentrated solution are given as:

$C_1{V}_{1 }= C_2{V}_2$

concentrated solution        Dilute solution 

Here $C_1$is  $0.200\mathrm{M},V_1=25.0 \mathrm{mL}$ and  $V_2$is $50.0 \mathrm{mL}$ 

Now calculate the concentration of diluted solution as:

 $C_{1}V= C_2{V}_2$

$C_2=\frac{V_1}{V_2}\times C_1$

$C_2=\frac{25.0 m\text{L }}{50.0 mL}\times 0.200\mathrm{M}$

$=0.100 M$

The final concentration solution is $0.100 M.$

Step 7: Given information: (Part b) Final concentration of the following :

The concentration and the volume of dilute and concentrated solution are given as:

$C_1{V}_{1 }= C_2{V}_2$

concentrated solution    dilute solution 

Here $C_1$is $12.0\%,V_1=15.0 \mathrm{mL}$ and $V_2$ is $40.0 \mathrm{mL}$.

Now calculate the concentration of diluted solution as:

$C_1{V}_{1 }=C_2{V}_2$

$C_2=\frac{V_1}{V_2}\times C_1$

$C_2=\frac{15.0\text{ mL }}{40.0 \text{m}L}\times 12\%$

$=4.5\%$

The final concentration solution is $4.5\%$

Step 8: Given information: (Part c) Final concentration of the following :

The concentration and the volume of dilute and concentrated solution are given as:

$C_1{V}_{1 }= C_2{V}_2$

concentration solution     dilute solution 

Here $C_1$is $6.00\mathrm{M},V_1=75.0 \mathrm{mL}$ and $V_2$is $255 \mathrm{mL}.$

Now calculate the concentration of diluted solution as:

$C_1{V}_{1=}{C}_2{V}_2$

$C_2=\frac{V_1}{V_2}\times C_1$

$C_2=\frac{75.0\text{ mL }}{255.0 mL}\times 6.00\mathrm{M}$

$=1.76 M$

The final concentration solution is $1.76 M.$