Q19.154 CP - Chemistry: Molecular Nature Of Matter And Change

Question

Scenes A to C represent aqueous solutions of the slightly soluble salt MZ (only the ions of this salt are shown):

$\mathbf{MZ}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{M}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{Z}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}$

 (a) Which scene represents the solution just after solid MZ is stirred thoroughly in distilled water?

(b) If each sphere represents $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{M}$ of ions, what is the ${\mathbf{K}}_{\mathbf{sp}}$ of MZ?

(c) Which scene represents the solution after ${\mathbf{Na}}_{\mathbf{2}}\mathbf{Z}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}$is added?

(d) If ${\mathbf{Z}}^{\mathbf{2}\mathbf{-}}$is $\mathbf{C}{{\mathbf{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}$, which scene represents the solution after the  has been lowered?

Step-by-Step Solution

Answer

1. The scene represents the solution just after solid MZ is stirred thoroughly in distilled water is picture B.
2.  The value of MZ is $1.0\times {10}^{-10}\mathrm{M}$.
3. The picture C is the correct situation.
4. The correct option is picture A.

Step 1: Definition of Concept.

Solubility: The maximum amount of solute that can be dissolved in the solvent at equilibrium is defined as solubility.

Constant of soluble product: For equilibrium between solids and their respective ions in a solution, the solubility product constant is defined. In general, the term "solubility product" refers to water-equilibrium insoluble or slightly soluble ionic substances.

Step 2: Find the scene represents the solution just after solid MZ is stirred thoroughly in distilled water.

(a)

First we can write the dissolution equation for MZ: 

$\begin{array}{l}\mathrm{MZ}\left(\mathrm{s}\right)\mathrm{C}{\mathrm{M}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{Z}}^{2-}\left(\mathrm{aq}\right)\\ \mathrm{Ksp}=\left[{\mathrm{M}}^{2+}\right]\left[{\mathrm{Z}}^{2-}\right]\end{array}$

Simply look for the picture in which the concentrations of ${\mathrm{M}}^{2+}$ and ${\mathrm{Z}}^{2-}$ are equal, which is picture B.

Therefore, the required answer is picture B.

Step 3: Find the K s p of MZ.

(b)

Considering the given information:

$\mathrm{c}\left(\mathrm{eachion}\right)=2.5\times {10}^{-6}\mathrm{M}$

We can see that each species has four ions, so ${\text{K}}_{\text{sp}}$ expression will look like this.

as an example:

$\begin{array}{c}\mathrm{Ksp}=\left[{\mathrm{M}}^{2+}\right]\left[{\mathrm{Z}}^{2-}\right]\\ =4\times 2.5\times {10}^{-6}\times 4\times 2.5\times {10}^{-6}\\ =1\times {10}^{-10}\end{array}$

Therefore, the required value is $1\times {10}^{-10}$.

Step 4: Find the scene represents the solution after Na 2 Z ( aq ) is added

(c)

If we add ${\mathrm{Na}}_2\mathrm{Z}$, the concentration of ${\mathrm{Z}}^{2+}$ increases and the concentration of ${\mathrm{M}}^{2+}$ decreases, so that would be picture $C$.

 

Step 5: Find the scene represents the solution after the pH has been lowered.

(d)

A lower pH indicates that there is less base in the solution. It is said that ${\mathrm{Z}}^{2-}$ represents carbonate ion, which is basic, so picture A would have lowered pH .