Which of the following statements about pH and `H^(+)` ion concentration is incorrect ?

Options

A. Addition of one drop of concentrated HCl in `NH_(4)OH` solution decreases pH of the solution
B. A solution of the mixture of one equivalent of each of `CH_(3)COOH` and NaOH has a pH of 7.
C. pH of pure neutral water is not zero
D. A cold and concentrated `H_(2)SO_(4)` has lower `H^(+)` ion concentration than a dilute solution of `H_(2)SO_(4)`.

Explanation

To determine which statement about pH and \( H^+ \) ion concentration is incorrect, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement:** Addition of one drop of concentrated HCl in NH4OH solution decreases the pH of the solution.

**Analysis:**
- NH4OH (ammonium hydroxide) is a weak base.
- Adding concentrated HCl (a strong acid) will increase the \( H^+ \) ion concentration, thereby decreasing the pH.
- This statement is **correct**.

### Step 2: Analyze the second statement
**Statement:** A solution of the mixture of one equivalent of each of CH3COOH and NaOH has a pH of 7.

**Analysis:**
- CH3COOH (acetic acid) is a weak acid, while NaOH (sodium hydroxide) is a strong base.
- When mixed in equal equivalents, the strong base (NaOH) will dominate, resulting in a basic solution rather than a neutral one.
- Therefore, the pH will be greater than 7, making this statement **incorrect**.

### Step 3: Analyze the third statement
**Statement:** pH of pure neutral water is not zero.

**Analysis:**
- The pH of pure neutral water at 25°C is 7, not 0.
- A pH of 0 indicates a highly acidic solution, which is not the case for neutral water.
- This statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** A cold and concentrated H2SO4 has lower \( H^+ \) ion concentration than a dilute solution of H2SO4.

**Analysis:**
- Concentrated H2SO4 does not fully dissociate in solution compared to a dilute solution, which dissociates more completely.
- Therefore, the \( H^+ \) ion concentration is indeed lower in concentrated H2SO4 than in a dilute solution.
- This statement is **correct**.

### Conclusion
The only incorrect statement among the options provided is the second one: "A solution of the mixture of one equivalent of each of CH3COOH and NaOH has a pH of 7."

### Final Answer
The incorrect statement is: **A solution of the mixture of one equivalent of each of CH3COOH and NaOH has a pH of 7.**

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