Consider the following statement and select correct option:
(I) `K_(sp)` of `Fe(OH)_(3)` in aqueous solution is `3.8xx10^(-38)` at 298 K. The concentration of `Fe^(+)` will increase when `[H^(+)]` ion concentration decreases.
(II) In a mixture of `NH_(4)Cl` and `NH_(4)OH` in water, a further amountof `NH_(4)Cl` is added. The pH of the mixture will decreases.
(III) An aqueous solution of each of the following salt `(NH_(4)I,HCOOK)` will be basic, acidic respectively.

Options

A. only I is correct
B. only II is correct
C. only III is correct
D. II and III are correct

Answer

To solve the question, we need to analyze each statement one by one and determine whether they are correct or incorrect.

### Step-by-Step Solution:

**Statement I:**
- The solubility product constant (\(K_{sp}\)) of \(Fe(OH)_3\) is \(3.8 \times 10^{-38}\) at 298 K.
- The dissociation of \(Fe(OH)_3\) can be represented as:
\[ Fe(OH)_3 (s) \rightleftharpoons Fe^{3+} (aq) + 3OH^{-} (aq) \]
- If the concentration of \(H^+\) ions decreases, the concentration of \(OH^-\) ions will increase (since \(K_w = [H^+][OH^-]\) is constant at a given temperature).
- According to Le Chatelier's principle, if \(OH^-\) increases, the equilibrium will shift to the left to counteract the change, resulting in the formation of more \(Fe(OH)_3\) and a decrease in \(Fe^{3+}\) concentration.
- Therefore, this statement is **incorrect**.

**Statement II:**
- In a mixture of \(NH_4Cl\) (which is a salt of a weak base \(NH_4OH\) and a strong acid) and \(NH_4OH\) (a weak base), adding more \(NH_4Cl\) will increase the concentration of the acidic component.
- As a result, the pH of the solution will decrease because the solution becomes more acidic due to the increase in \(NH_4^+\) ions.
- Thus, this statement is **correct**.

**Statement III:**
- \(NH_4I\) is formed from a weak base \(NH_4OH\) and a strong acid \(HI\), which results in an acidic solution.
- \(HCOOK\) is formed from a weak acid \(HCOOH\) and a strong base \(KOH\), which results in a basic solution.
- The statement claims that \(NH_4I\) will be basic and \(HCOOK\) will be acidic, which is the opposite of what is true.
- Therefore, this statement is **incorrect**.

### Conclusion:
- Only Statement II is correct.

The correct answer is option **B**: Only statement II is correct.