Question

Determine the initial volume, in milliliter, requires preparing each of the following:

a. $255\mathrm{mL}\mathrm{of}\mathrm{a}0.200\mathrm{M}{\mathrm{HNO}}_3$solution using a$4.00\mathrm{M}{\mathrm{HNO}}_3$ solution

b. $715\mathrm{mL}\mathrm{of}\mathrm{a}0.100\mathrm{M}{\mathrm{MgCl}}_2$solution using a $6.00\mathrm{M}{\mathrm{MgCl}}_2$solution

c. $0.100\mathrm{L}\mathrm{of}\mathrm{a}0.150\mathrm{M}\mathrm{KCl}$solution using an $8.00\mathrm{M}\mathrm{KCl}$solution

Short answer

a. The initial volume of $255\mathrm{mL}\mathrm{of}\mathrm{a}0.200\mathrm{M}{\mathrm{HNO}}_3$solution using an $4.00\mathrm{M}{\mathrm{HNO}}_3$is $12.75\mathrm{mL}$.

b. The initial volume of $715\mathrm{mL}\mathrm{of}\mathrm{a}0.100\mathrm{M}{\mathrm{MgCl}}_2$solution using an $6.00\mathrm{M}{\mathrm{MgCl}}_2$is $11.9\mathrm{mL}$.

c. The initial volume of $0.100\mathrm{L}\mathrm{of}\mathrm{a}0.150\mathrm{M}\mathrm{KCl}$solution using an $8.00\mathrm{M}\mathrm{KCl}$ is$1.875\mathrm{mL}$.

Step-by-step solution

Part (a) Step 1: Given Information

We need to find the initial volume.

Part (a) Step 2: Explanation

The addition of solvent increases the volume, and the amount of solute does not change. The concentrated solution or the diluted solution. Moles or grams of solute$=$moles or grams of solute

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

Consider:

$$\begin{gathered} {\mathrm{C}}_1=4\mathrm{M} \\ {\mathrm{C}}_2=0.2\mathrm{M} \\ {\mathrm{V}}_2=255\mathrm{mL} \end{gathered}$$

Now, finding the value of $V_1$:

$$\begin{gathered} {\mathrm{V}}_1=\frac{{\mathrm{C}}_2{\mathrm{V}}_2}{{\mathrm{C}}_1} \\ =\frac{(0.2\mathrm{M})(255\mathrm{mL})}{4\mathrm{M}} \\ =12.75\mathrm{mL} \end{gathered}$$

Part (b) Step 1: Given Information

We need to find the initial volume.

Part (b) Step 2: Explanation

The addition of solvent increases the volume, and the amount of solute does not change. The concentrated solution or the diluted solution. Moles or grams of solute$=$moles or grams of solute

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

Consider:

$$\begin{gathered} {\mathrm{C}}_1=6\mathrm{M} \\ {\mathrm{C}}_2=0.1\mathrm{M} \\ {\mathrm{V}}_2=715\mathrm{mL} \end{gathered}$$

Now, finding the value of $V_1$:

localid="1653464875591" $$\begin{gathered} {\mathrm{V}}_1=\frac{{\mathrm{C}}_2{\mathrm{V}}_2}{{\mathrm{C}}_1} \\ =\frac{(0.1\mathrm{M})(715\mathrm{mL})}{6\mathrm{M}} \\ =11.09\mathrm{mL} \end{gathered}$$

Part (c) Step 1: Given Information

We need to find the initial volume.

Part (c) Step 2: Explanation

Here,

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

Consider:

role="math" localid="1653464984133" $$\begin{gathered} {\mathrm{C}}_1=0.150\mathrm{M} \\ {\mathrm{C}}_2=8\mathrm{M} \\ {\mathrm{V}}_2=0.100\mathrm{L}=100\mathrm{mL} \end{gathered}$$

Now, finding the value of $V_1$:

role="math" localid="1653464974800" $$\begin{gathered} {\mathrm{V}}_1=\frac{{\mathrm{C}}_2{\mathrm{V}}_2}{{\mathrm{C}}_1} \\ =\frac{(0.150\mathrm{M})(100\mathrm{mL})}{8\mathrm{M}} \\ =1.875\mathrm{mL} \end{gathered}$$