The concentration of hydronium `(H_(3)O^(+))` ion in water is

Options

A. Zero
B. `1 xx 10^(-7)` gm ion /litre
C. `1 xx 10^(-14)` gm ion/litre
D. `1 xx 10^(-7)` gm ion/litre

Explanation

To find the concentration of hydronium ions (H₃O⁺) in pure water, we can follow these steps:

### Step 1: Understand the dissociation of water
Water (H₂O) undergoes self-ionization to produce hydronium ions (H₃O⁺) and hydroxide ions (OH⁻):
\[ H_2O \rightleftharpoons H_3O^+ + OH^- \]

### Step 2: Recognize the relationship between H₃O⁺ and OH⁻ concentrations
In pure water, the concentration of hydronium ions is equal to the concentration of hydroxide ions:
\[ [H_3O^+] = [OH^-] \]

### Step 3: Use the ion product of water (Kw)
At 25°C, the ion product of water (Kw) is given by:
\[ K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14} \]

### Step 4: Set up the equation using the concentrations
Since \( [H_3O^+] = [OH^-] \), we can denote the concentration of hydronium ions as \( x \):
\[ K_w = x \cdot x = x^2 \]
Thus,
\[ x^2 = 1.0 \times 10^{-14} \]

### Step 5: Solve for x
Taking the square root of both sides:
\[ x = \sqrt{1.0 \times 10^{-14}} \]
Calculating this gives:
\[ x = 1.0 \times 10^{-7} \, \text{mol/L} \]

### Step 6: State the concentration of hydronium ions
Therefore, the concentration of hydronium ions in pure water is:
\[ [H_3O^+] = 1.0 \times 10^{-7} \, \text{mol/L} \]

### Step 7: Conclusion
The concentration of hydronium ions in pure water is \( 1.0 \times 10^{-7} \, \text{mol/L} \).

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