Which of the following statement for pure water is wrong ?

Options

A. Number of `H^+` ions in 1mL `H_2O` is` 6.02 × 10^(13)` at `25^@C`
B. Number of `OH^–` ions is double the total molecules of `H_2O` at `25^@C`
C. Number of `H_2O` molecules are `55.5 x× 6.02 x× 10^23` in 1 lit `H_2O `at `25^@C `
D. For pure water at all temperatures
`rArr [H^+]=[OH^-]=sqrt(K_w)`

Answer

To determine which statement about pure water is incorrect, we will analyze each statement provided in the question step by step.

### Step 1: Understand the properties of pure water
Pure water at 25 degrees Celsius has a specific concentration of hydrogen ions (H⁺) and hydroxide ions (OH⁻). The concentration of both is equal and is given by:
\[ [H^+] = [OH^-] = 10^{-7} \text{ moles per liter} \]

### Step 2: Analyze the first statement
**Statement 1:** The number of H⁺ ions in 1 ml of water is \(6.02 \times 10^{13}\) at 25 degrees Celsius.

- Calculate the number of moles of H⁺ in 1 ml of water:
\[ \text{Number of moles} = [H^+] \times \text{Volume in liters} = 10^{-7} \times \frac{1}{1000} = 10^{-10} \text{ moles} \]

- Now, calculate the number of H⁺ ions:
\[ \text{Number of H⁺ ions} = 10^{-10} \text{ moles} \times 6.02 \times 10^{23} \text{ ions/mole} = 6.02 \times 10^{13} \text{ ions} \]

This statement is **correct**.

### Step 3: Analyze the second statement
**Statement 2:** The number of OH⁻ ions is double the total molecules of water at 25 degrees Celsius.

- In pure water, the concentration of OH⁻ ions is equal to the concentration of H⁺ ions, which is \(10^{-7}\) moles per liter. Therefore, the number of OH⁻ ions cannot be double that of H⁺ ions or the total number of water molecules.

This statement is **incorrect**.

### Step 4: Analyze the third statement
**Statement 3:** The number of water molecules is \(55.5 \times 6.02 \times 10^{23}\) in 1 liter of water at 25 degrees Celsius.

- The density of water is approximately 1 g/ml, so 1 liter of water weighs about 1000 grams. The molar mass of water is approximately 18 g/mol.
- Calculate the number of moles in 1 liter:
\[ \text{Number of moles} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.5 \text{ moles} \]

- Now, calculate the number of molecules:
\[ \text{Number of molecules} = 55.5 \text{ moles} \times 6.02 \times 10^{23} \text{ molecules/mole} \]

This statement is **correct**.

### Step 5: Analyze the fourth statement
**Statement 4:** For pure water at all temperatures, the concentration of H⁺ is equal to the concentration of OH⁻ and is equal to the square root of \(K_w\) (the ionic product of water).

- This is a true statement as the dissociation constant \(K_w\) relates to the concentrations of H⁺ and OH⁻ ions in pure water.

This statement is **correct**.

### Conclusion
After analyzing all statements, the incorrect statement is:

**Final Answer:** The second statement is wrong: "The number of OH⁻ ions is double the total molecules of water at 25 degrees Celsius."

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