Question

A chemist mixes solid AgCl, CuCl₂, and MgCl₂ in enough water to give a final volume of 50.0 mL.

(a) With ions shown as spheres and solvent molecules omitted for clarity, which of the following best represents the resulting mixture?

(b) If each sphere represents 5.0x10^-3mol of ions, what is the total concentration of dissolved(separated) ions?

(c) What is the total mass of solid?

Short answer

a. Figure A represents the resulting mixture.

b. The concentration of the ions which are dissolved is 1.2 M.

c. The total mass of the solid is 2.9 g.

Step-by-step solution

(a) Determination of resulting mixture

In figure A, solid AgCl is formed and the remaining ions are Cu²⁺, Cl^-, and Mg²⁺.

In figure B, solid MgCl₂ is formed and the remaining ions are Cu²⁺ and Cl^-.

In figure C, solid CuCl₂ is formed and the remaining ions are Ag⁺, Cl^-, and Mg²⁺.

In figure D, solid CuCl₂ is formed and the remaining ions are Cl^-, and Mg²⁺.

According to the solubility rules, AgCl is insoluble and MgCl₂ and CuCl₂ are soluble. SO, in the mixture, AgCl should be insoluble and MgCl₂ and CuCl₂ should be present in the form of ions.

Thus, figure A represents the resulting mixture.

(b) Determination of total concentration of ions

In figure A, there are 12 spheres. It means that each sphere consist of 5.0x10^-3mol of ions.

Total number of moles of ions are,

$\frac{\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{mol}}{\mathbf{1}\mathbf{sphere}}\mathbf{\times }\mathbf{12}\mathbf{spheres}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{060}\mathbf{}\mathbf{moles}$

Now, the concentration of the ions is,

$$\begin{gathered} \mathbf{Concentration}\mathbf{=}\frac{\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{moles}}{\mathbf{Volume}\mathbf{}\mathbf{inL}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{060}\mathbf{mol}}{\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{L}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{M} \end{gathered}$$

Thus, the concentration of the ions which are dissolved is 1.2 M.

(c) Determination of mass of solid

In figure A, there are 4 spheres of Ag. The mass of solid AgCl is,

$\mathbf{4}\mathbf{}\mathbf{Ag}\mathbf{}\mathbf{spheres}\mathbf{\times }\frac{\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{mol}\mathbf{}\mathbf{Ag}}{\mathbf{1}\mathbf{sphere}}\mathbf{\times }\frac{\mathbf{1}\mathbf{mol}\mathbf{}\mathbf{AgCI}}{\mathbf{1}\mathbf{mol}\mathbf{}\mathbf{Ag}}\mathbf{\times }\frac{\mathbf{143}\mathbf{.}\mathbf{4}\mathbf{g}\mathbf{}\mathbf{AgCI}}{\mathbf{1}\mathbf{mol}\mathbf{}\mathbf{AgCI}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{9}\mathbf{g}\mathbf{}\mathbf{AgCI}$

Thus, the total mass of the solid is 2.9 g.