IB Chemistry Topic R3.1.5 the Ion Product of Water Revision Notes (SL/HL)

IB Chemistry Topic R3.1.5 the Ion Product of Water Revision Notes (SL/HL) | RevisionDojo

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The Ion Product of Water ($K_w$) and Its Implications

Water, even in its pure form, undergoes a process called self-ionization (or autoionization), where two water molecules interact to form a hydronium ion ($H_3O^+$) and a hydroxide ion ($OH^-$): $$
H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)
$$
For simplicity, we often represent the hydronium ion as $H^+$, so the equation becomes: $$
H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)
$$
The equilibrium constant for this reaction is called the ion product of water, symbolized as $K_w$: $$
K_w = [H^+][OH^-]
$$
Here, $[H^+]$ and $[OH^-]$ are the molar concentrations of hydrogen ions and hydroxide ions, respectively.

$K_w$ at 298 K (25°C)

At 298 K (room temperature), the value of $K_w$ is: $$
K_w = 1.0 \times 10^{-14} \, \text{mol}^2 \, \text{dm}^{-6}
$$
This means that in pure water at 25°C: $$
[H^+] = [OH^-] = \sqrt{K_w} = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \, \text{mol} \ \text{dm}^{-3}
$$

Note

The equal concentrations of $H^+$ and $OH^-$ ions make pure water neutral, with a pH of 7.0.

Tip

At temperatures other than 298 K, the value of $K_w$ changes because the self-ionization of water is endothermic.
For example, as temperature increases, $K_w$ increases, so both $[H^+]$ and $[OH^-]$ increase equally and the pH of pure water decreases even though it remains neutral.

Interpreting $K_w$: Acidic, Neutral, and Basic Solutions

The value of $K_w$ is constant for a given temperature, so any change in $[H^+]$ or $[OH^-]$ must be balanced to maintain the relationship:

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The Ion Product of Water ($K_w$) and Its Implications

Water, even in its pure form, undergoes a process called self-ionization (or autoionization), where two water molecules interact to form a hydronium ion ($H_3O^+$) and a hydroxide ion ($OH^-$): $$
H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)
$$
For simplicity, we often represent the hydronium ion as $H^+$, so the equation becomes: $$
H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)
$$
The equilibrium constant for this reaction is called the ion product of water, symbolized as $K_w$: $$
K_w = [H^+][OH^-]
$$
Here, $[H^+]$ and $[OH^-]$ are the molar concentrations of hydrogen ions and hydroxide ions, respectively.

$K_w$ at 298 K (25°C)

At 298 K (room temperature), the value of $K_w$ is: $$
K_w = 1.0 \times 10^{-14} \, \text{mol}^2 \, \text{dm}^{-6}
$$
This means that in pure water at 25°C: $$
[H^+] = [OH^-] = \sqrt{K_w} = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \, \text{mol} \ \text{dm}^{-3}
$$

Note

The equal concentrations of $H^+$ and $OH^-$ ions make pure water neutral, with a pH of 7.0.

Tip

At temperatures other than 298 K, the value of $K_w$ changes because the self-ionization of water is endothermic.
For example, as temperature increases, $K_w$ increases, so both $[H^+]$ and $[OH^-]$ increase equally and the pH of pure water decreases even though it remains neutral.

Interpreting $K_w$: Acidic, Neutral, and Basic Solutions

The value of $K_w$ is constant for a given temperature, so any change in $[H^+]$ or $[OH^-]$ must be balanced to maintain the relationship:

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Structure 1. Models of the particulate nature of matter5 subtopics

Structure 2. Models of bonding and structure4 subtopics

Structure 3. Classification of matter2 subtopics

Reactivity 1. What drives chemical reactions?4 subtopics

Reactivity 2. How much, how fast and how far?3 subtopics

Reactivity 3. What are the mechanisms of chemical change?4 subtopics

IB Chemistry R3.1.5 the Ion Product of Water Notes

Structure 1. Models of the particulate nature of matter5 subtopics

Structure 2. Models of bonding and structure4 subtopics

Structure 3. Classification of matter2 subtopics

Reactivity 1. What drives chemical reactions?4 subtopics

Reactivity 2. How much, how fast and how far?3 subtopics

Reactivity 3. What are the mechanisms of chemical change?4 subtopics

The Ion Product of Water ($K_w$) and Its Implications

$K_w$ at 298 K (25°C)

Interpreting $K_w$: Acidic, Neutral, and Basic Solutions

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The Ion Product of Water ($K_w$) and Its Implications

$K_w$ at 298 K (25°C)

Interpreting $K_w$: Acidic, Neutral, and Basic Solutions

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