Q. 9.108 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the final concentration of the solution when water is added to prepare each of the following: 

a. $25.0 \mathrm{mL}$ of $18.0\mathrm{MHCl}$ solution is diluted to a$500 \mathrm{mL}$

b.$50.0 \mathrm{mL}$ of $15.0\%( \mathrm{m}/\mathrm{v}){\mathrm{NH}}_4\mathrm{Cl}$ solution is diluted to a$125 \mathrm{mL}$

c. $4.50 \mathrm{mL}$of  $8.50\mathrm{MKOH}$ solution is diluted to a $75.0 \mathrm{mL}$

Step-by-Step Solution

Answer

(Part a). $25.0 \mathrm{mL}$ of a $18.0\mathrm{MHCl}$ solution is diluted to a $500 \mathrm{mL}$ is $0.9$

(Part b). $50.0 \mathrm{mL}$ of a $15.0\%( \mathrm{m}/\mathrm{v}){\mathrm{NH}}_4\mathrm{Cl}$ solution is diluted to a $125 \mathrm{mL}$ is $6.0\%$

(Part c). $4.50 \mathrm{mL}$ of a $8.50\mathrm{MKOH}$ solution is diluted to a $75.0 \mathrm{mL}$ is $0.51 M$

Step 1: Introduction (Part a)

a. $25.0 \mathrm{mL}$ of $18.0\mathrm{MHCl}$solution is diluted to a $500 \mathrm{mL}$

b. $50.0 \mathrm{mL}$ of  $15.0\%( \mathrm{m}/\mathrm{v}){\mathrm{NH}}_4\mathrm{Cl}$ solution is dilute to a  $125 \mathrm{mL}$

c.$4.50 \mathrm{mL}$ of $8.50\mathrm{MKOH}$ solution is diluted to a$75.0 \mathrm{mL}$

Step 2: Definition of molarity:

Molarity:

Solute moths per liter of solution are known as the Molarity of solution. It represents $M$.The molecularity of any solution is the ratio of moles to solution per liter. It was expressed by 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 its mass to its volume. Generally speaking, we can say that the density of a substance is 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 massage percentage is the percentage of the concentration of the solution and may be the percentage of the concentration of the solution. It is expressed by the following formula:

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

Step 5: Process of dilution:

When the solvent is put into a solution, the volume of the solution increases and the concentration decreases. Dilution is a process by which a concentrated solution is made more diluted. 

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

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

concentrated solution     dilute solution 

Step 6: (Part a) Final concentration of solution :

The concentration and size of the solution is as follows:

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

concentration solution    dilute solution 

Here $C_1$ is $18.0\mathrm{M},V_1=25.0 \mathrm{mL}$and  $V_2$ is $500.0 \mathrm{mL}$.

To calculate the concentration of dilute solution as:

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

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

$C_2=\frac{25.0\text{ mL }}{500.0 mL}\times 18.00\mathrm{M}$

$=0.9 M$

The final concentration is $0.9 M$

Step 7: (Part b) Final concentration of a solution:

The concentration and size of the solution is as follows:

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

concentration solution     dilute solution 

Here $C_1$ is $15.0\%,V_1=50.0 \mathrm{mL}$ and $V_2$ is $125.0 \mathrm{mL}$

To calculate the concentration of dilute solution as :

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

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

$C_2=\frac{50.0\text{ mL }}{125.0 mL}\times 15\%$

$=6.0\%$

The final concentration is $6.0\%$

Step 8: (Part c) Final concentration of the solution:

The concentration and size of a solution is as follows:

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

concentration solution     dilute solution

Here $C_1$is $8.50\mathrm{M},V_1=4.50 \mathrm{mL}$ and $V_2$ is $575.0 \mathrm{mL}$

To calculate the concentration of dilute solution as :

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

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

$C_2=\frac{\text{4.50 mL }}{75.0 mL}\times 8.50 M$

$=0.51 M$

The final concentration is $0.51 M$