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$75.0\mathrm{mL}$

Short 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$0.51M$

Step-by-step solution

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$75.0\mathrm{mL}$

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

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 $\frac{\text{mass}\left(\mathrm{g}\right)}{\text{volume}\left(\mathrm{mL}\right)}$

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

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

(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:

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

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

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

$=0.9M$

The final concentration is$0.9M$

(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 :

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

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

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

$=6.0\%$

The final concentration is$6.0\%$

(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 :

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

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

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

$=0.51M$

The final concentration is $0.51M$