The concentration of hydrogen ion in water is

Options

A. 8
B. `1 xx 10^(-7)`
C. 7
D. 43472

Explanation

To find the concentration of hydrogen ions (H⁺) in pure water, we can follow these steps:

### Step 1: Understand the Ionization of Water
In pure water, water molecules (H₂O) dissociate into hydrogen ions (H⁺) and hydroxide ions (OH⁻). This can be represented by the equation:
\[ H_2O \rightleftharpoons H^+ + OH^- \]

### Step 2: Define the Ionic Product of Water (K_w)
The ionic product of water (K_w) at a given temperature is defined as:
\[ K_w = [H^+][OH^-] \]
At 25 degrees Celsius, the value of K_w is known to be \( 1.0 \times 10^{-14} \).

### Step 3: Set Up the Equation for Pure Water
In pure water, the concentrations of hydrogen ions and hydroxide ions are equal, meaning:
\[ [H^+] = [OH^-] \]
Let’s denote the concentration of hydrogen ions as \( x \). Therefore:
\[ K_w = x \cdot x = x^2 \]
This simplifies to:
\[ K_w = x^2 \]

### Step 4: Substitute the Value of K_w
We know that:
\[ K_w = 1.0 \times 10^{-14} \]
Thus, we can write:
\[ x^2 = 1.0 \times 10^{-14} \]

### Step 5: Solve for x
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{1.0 \times 10^{-14}} \]
Calculating this gives:
\[ x = 1.0 \times 10^{-7} \]

### Step 6: Conclusion
The concentration of hydrogen ions in pure water is:
\[ [H^+] = 1.0 \times 10^{-7} \, \text{M} \]