Consider a sturated solution of silver chloride that is in contact with solid silver chloride. The solubility equilibrium can be represented as
`AgCl(s)hArrAg^(+)(aq.)+Cl^(-)(aq.)," "K_(sp)=[Ag^(+)(aq.)][Cl^(-)(aq.)]`
Where `K_(sp)` is clled the solubility product constant or simply the solubility product. In general, the solubility product of a compound is the product of the molar concentrations of the constituent ions, each raised to the power of its stoichiometric coefficient in the equilibrium equation.
For concentrations of ions that do not necessarliy correpond to equilibrium conditions we use the reaction quotient (Q) which is clled the ion or ionic prodect (Q) to predict whether a precipitate will from. Note that (Q) has the same for as `K_(sp)` are
`QltK_(sp)` Unsaturated solution
`Q=K_(sp)` Saturated solution
`Qgt_(sp)` Supersaturated solution, precipitate will from
The soluvility molar solubility of ferric hydroxide in aqueous solution is `6xx10^(-38)` at 298 K. the solubility of `Fe^(3+)` ion will increase when the :

Options

A. pH is increased
B. pH is 7.0
C. pH is decreased
D. strurated solution is exposed to the atomosphere

Answer

To solve the problem regarding the solubility of ferric hydroxide and how the concentration of Fe³⁺ ions is affected by pH, we can follow these steps:

### Step 1: Understand the Dissolution Reaction
The dissolution of ferric hydroxide (Fe(OH)₃) can be represented as:
\[ \text{Fe(OH)}_3(s) \rightleftharpoons \text{Fe}^{3+}(aq) + 3\text{OH}^-(aq) \]

### Step 2: Write the Expression for Ksp
The solubility product constant (Ksp) for ferric hydroxide can be expressed as:
\[ K_{sp} = [\text{Fe}^{3+}][\text{OH}^-]^3 \]

### Step 3: Define Molar Solubility
Let the molar solubility of Fe(OH)₃ be \( s \). At equilibrium:
- The concentration of Fe³⁺ ions will be \( s \).
- The concentration of OH⁻ ions will be \( 3s \).

### Step 4: Substitute into the Ksp Expression
Substituting these values into the Ksp expression gives:
\[ K_{sp} = s(3s)^3 = 27s^4 \]

### Step 5: Set Ksp Value
We know from the problem that:
\[ K_{sp} = 6 \times 10^{-38} \]

### Step 6: Solve for s
Now we can set up the equation:
\[ 27s^4 = 6 \times 10^{-38} \]
\[ s^4 = \frac{6 \times 10^{-38}}{27} \]
\[ s^4 = 2.22 \times 10^{-39} \]
\[ s = (2.22 \times 10^{-39})^{1/4} \]

Calculating \( s \):
\[ s \approx 1.57 \times 10^{-10} \, \text{M} \]

### Step 7: Effect of pH on Solubility
The solubility of Fe(OH)₃ will increase when the concentration of OH⁻ ions decreases, which occurs when the pH of the solution increases. This is because a lower concentration of OH⁻ ions shifts the equilibrium to the right, increasing the solubility of Fe(OH)₃ and thus increasing the concentration of Fe³⁺ ions.

### Conclusion
Therefore, the solubility of Fe³⁺ ions will increase when the pH is increased, as it leads to a decrease in the concentration of hydroxide ions.

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