Self-Ionisation of Water Revision Notes for Leaving Cert Chemistry

Self-Ionisation of Water

What is self-ionisation of water?

Even the purest water can conduct a tiny electrical current, which might seem surprising at first. This happens because water molecules can spontaneously break apart to form ions in a process called self-ionisation.

In this process, water molecules dissociate to produce hydrogen ions (H⁺) and hydroxide ions (OH⁻):

$\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-$

This can also be written showing the formation of hydronium ions:

$2\text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-$

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It's important to understand that this equilibrium lies heavily towards the left side, meaning that only a very small fraction of water molecules actually dissociate at any given time. The concentration of these ions in pure water is extremely small, but their presence is crucial for understanding pH and acid-base chemistry.

The ionic product of water (Kw)

The self-ionisation of water can be described mathematically using an equilibrium constant called the ionic product of water, represented by the symbol Kw.

The expression for Kw is:

$K_w = [\text{H}^+][\text{OH}^-]$

At 25°C, the value of Kw is:

$K_w = 1.0 \times 10^{-14}$

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This means that in any aqueous solution at 25°C, the product of hydrogen ion concentration and hydroxide ion concentration will always equal $1.0 \times 10^{-14}$ . This is a fundamental constant that helps us understand the relationship between acidity and basicity.

Temperature dependence of Kw

The value of Kw is not constant at all temperatures - it increases as temperature rises. This happens because the self-ionisation of water is an endothermic process, meaning it requires energy input.

The forwards reaction has an enthalpy change of $\Delta H = +55.8 \text{ kJ mol}^{-1}$ , which explains why higher temperatures favour the formation of more ions. When you increase the temperature, the equilibrium shifts to the right to absorb the added heat, producing more H⁺ and OH⁻ ions.

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Temperature Variation of Kw:

As shown in the data, Kw varies significantly with temperature:

At 0°C: $K_w = 0.11 \times 10^{-14}$
At 25°C: $K_w = 1.01 \times 10^{-14}$
At 100°C: $K_w = 51.3 \times 10^{-14}$

This temperature dependence is crucial for accurate pH calculations, especially in industrial processes or biological systems operating at different temperatures.

Calculating ion concentrations in pure water

In pure water at 25°C, we can use the Kw expression to calculate the concentrations of H⁺ and OH⁻ ions.

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Worked Example: Calculating Ion Concentrations in Pure Water

Since pure water is neutral, the concentration of H⁺ ions equals the concentration of OH⁻ ions:

$[\text{H}^+] = [\text{OH}^-]$

Using the Kw expression: $K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$

Since $[\text{H}^+] = [\text{OH}^-]$ , we can write: $[\text{H}^+]^2 = 1.0 \times 10^{-14}$

Therefore: $[\text{H}^+] = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \text{ M}$

And similarly: $[\text{OH}^-] = 1.0 \times 10^{-7} \text{ M}$

This gives us the baseline concentrations for a neutral solution at 25°C.

Understanding acidic and basic solutions

The Kw expression helps us understand what makes solutions acidic or basic. The key principle is that the product of hydrogen and hydroxide ion concentrations always remains constant at a given temperature.

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For neutral solutions at 25°C:

$[\text{H}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}$ M

For acidic solutions:

$[\text{H}^+] > 1.0 \times 10^{-7}$ M
$[\text{OH}^-] < 1.0 \times 10^{-7}$ M
The product $[\text{H}^+][\text{OH}^-]$ still equals $1.0 \times 10^{-14}$

For basic solutions:

$[\text{H}^+] < 1.0 \times 10^{-7}$ M
$[\text{OH}^-] > 1.0 \times 10^{-7}$ M
The product $[\text{H}^+][\text{OH}^-]$ still equals $1.0 \times 10^{-14}$

This inverse relationship means that when one concentration increases, the other must decrease to maintain the constant Kw value.

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Exam Tips for Self-Ionisation of Water:

Always remember that $K_w = 1.0 \times 10^{-14}$ at 25°C
In neutral solutions, $[\text{H}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}$ M
The self-ionisation process is endothermic, so Kw increases with temperature
Use the Kw expression to calculate missing ion concentrations in any aqueous solution
Remember that $[\text{H}^+] \times [\text{OH}^-]$ always equals Kw, regardless of whether the solution is acidic or basic

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Key Points to Remember:

Self-ionisation is the process where water molecules dissociate to form H⁺ and OH⁻ ions in equilibrium
The ionic product of water (Kw) equals $[\text{H}^+][\text{OH}^-]$ and has a value of $1.0 \times 10^{-14}$ at 25°C
Temperature affects Kw - higher temperatures increase Kw because the process is endothermic
In neutral solutions, $[\text{H}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}$ M at 25°C
The Kw expression allows you to calculate ion concentrations in any aqueous solution, maintaining the constant product relationship

Self-Ionisation of Water (Leaving Cert Chemistry): Revision Notes