Here's the breakdown:
* Kw: This constant represents the equilibrium constant for the auto-ionization of water, where water molecules react with each other to form hydronium and hydroxide ions:
```
2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)
```
* Value of Kw: At 25°C, Kw has a value of 1.0 x 10⁻¹⁴. This means:
```
Kw = [H₃O⁺] [OH⁻] = 1.0 x 10⁻¹⁴
```
* Inverse Proportionality: The equation shows that the product of the concentrations of hydronium and hydroxide ions is constant. This means if one concentration increases, the other must decrease to maintain the constant value of Kw.
Key Points:
* Neutral Solutions: In a neutral solution, the concentrations of H₃O⁺ and OH⁻ are equal, both being 1.0 x 10⁻⁷ M.
* Acidic Solutions: In acidic solutions, [H₃O⁺] > [OH⁻].
* Basic Solutions: In basic solutions, [OH⁻] > [H₃O⁺].
Example:
If the concentration of hydronium ions in a solution is 1.0 x 10⁻⁵ M, then the concentration of hydroxide ions can be calculated as:
```
[OH⁻] = Kw / [H₃O⁺] = (1.0 x 10⁻¹⁴) / (1.0 x 10⁻⁵) = 1.0 x 10⁻⁹ M
```
This relationship is fundamental for understanding the acidity and basicity of aqueous solutions.
