Which of the following statement (s) is/are correct about the ionic prodict of water ?

Options

A. `K_(i)` (ionization constant of water) `ltK_(w)` (ionic product of water )
B. `pK_(i)gtpK_(w)`
C. `At300 K`, `K_w` of water becomes `10^(-12)`
D. Ionic product of water at `25^(@)C"is"10^(-14)`

Answer

To determine which statements are correct about the ionic product of water (Kw), let's analyze each statement step by step.

### Step 1: Understanding the Ionization Constant of Water (Ki)
The ionization constant of water (Ki) is defined as the equilibrium constant for the dissociation of water into hydrogen ions (H⁺) and hydroxide ions (OH⁻). The expression for Ki is given by:

\[ K_i = \frac{[H^+][OH^-]}{[H_2O]} \]

Since the concentration of pure water ([H₂O]) remains relatively constant, we can say that Ki is less than Kw, the ionic product of water.

### Step 2: Understanding the Ionic Product of Water (Kw)
The ionic product of water (Kw) is defined as the product of the concentrations of hydrogen ions and hydroxide ions at a given temperature:

\[ K_w = [H^+][OH^-] \]

At 25°C (298 K), Kw is equal to \( 1.0 \times 10^{-14} \).

### Step 3: Analyzing the First Statement
The first statement claims that Ki is less than Kw. Since we established that Ki is derived from Kw and is less than it, this statement is **correct**.

### Step 4: Analyzing the Second Statement
The second statement claims that pKi is greater than pKw.

Using the relationship between pK values:
- pKi = -log(Ki)
- pKw = -log(Kw)

Since Ki < Kw, it follows that pKi > pKw. Thus, this statement is also **correct**.

### Step 5: Analyzing the Third Statement
The third statement claims that at 300 K, Kw becomes \( 10^{-12} \).

At higher temperatures, the ionization of water increases, leading to a higher Kw. Since at 25°C, Kw is \( 10^{-14} \), and it is known that Kw increases with temperature, this statement is **correct**.

### Step 6: Analyzing the Fourth Statement
The fourth statement claims that the ionic product of water at 25°C is \( 10^{-14} \). This is a well-established fact, so this statement is also **correct**.

### Conclusion
All statements (A, B, C, and D) regarding the ionic product of water are correct.

### Summary of Correct Statements:
1. Ki < Kw (Correct)
2. pKi > pKw (Correct)
3. Kw at 300 K is \( 10^{-12} \) (Correct)
4. Kw at 25°C is \( 10^{-14} \) (Correct)