Question

What is the molar concentration of hydronium ion and hydroxide ion in pure water at \(25{ }^{\circ} \mathrm{C}\) ?

Short answer

In pure water at 25°C, the molar concentration of hydronium ion (H₃O⁺) and hydroxide ion (OH⁻) is: \[ [H_3O^+] = [OH^-] = 1.0 × 10^{-7} \mathrm{\: M} \]

Step-by-step solution

Understand autoionization of water

In pure water, a small fraction of the water molecules break down to form hydronium and hydroxide ions through the process called autoionization: \[ 2H_2O \rightleftharpoons H_3O^+ + OH^- \] At equilibrium, the concentrations of these ions can be related using the ion product of water, Kw: \[K_w = [H_3O^+][OH^-] \]

Find the ion product of water, Kw, at 25°C

At 25°C, the ion product constant of water is known and equals: \[ K_w = 1.0 × 10^{-14} \mathrm{\: M^2} \]

Determine the concentrations of hydronium and hydroxide ions

In pure water, the molar concentration of hydronium ions is equal to the concentration of hydroxide ions: \[ [H_3O^+] = [OH^-] \] We can substitute this fact into the \(K_w\) equation: \[ K_w = [H_3O^+][H_3O^+] = ([H_3O^+])^2 \] Solve for the concentration of hydronium ions: \[ [H_3O^+] = \sqrt{K_w} = \sqrt{1.0 × 10^{-14}} = 1.0 × 10^{-7} \mathrm{\: M} \] Since the concentration of the hydroxide ions is equal to the concentration of hydronium ions in pure water, the concentration of hydroxide ions is: \[ [OH^-] = [H_3O^+] = 1.0 × 10^{-7} \mathrm{\: M} \]

Present the final answer

In pure water at 25°C, the molar concentration of hydronium ion (H₃O⁺) and hydroxide ion (OH⁻) is: \[ [H_3O^+] = [OH^-] = 1.0 × 10^{-7} \mathrm{\: M} \]

Key concepts

Molar Concentration

Molar concentration, also known as molarity, is a measure of the number of moles of a solute present in one liter of solution. It is expressed in moles per liter (mol/L) and is an important concept in chemistry because it allows us to calculate the amount of substances involved in chemical reactions.

When we talk about the molar concentration of hydronium ion, \( [H_3O^+] \), and hydroxide ion, \( [OH^-] \), in water, we're observing a rare case where a solvent autoionizes. This autoionization can be thought of as water spontaneously splitting into these ions.

Understanding molarity is crucial when we discuss water's autoionization because it allows us to clearly define the concentration of the ions produced in this process.

Hydronium Ion

The hydronium ion, \( H_3O^+ \), is a water molecule that has an extra hydrogen ion attached to it. This happens through the autoionization of water, where two water molecules interact, and one donates a hydrogen ion to the other. The presence of hydronium ions is a key factor in establishing acidity in solutions.

In pure water at room temperature, \( [H_3O^+] \) is typically very low, but it is profoundly important in chemical equilibrium and acid-base chemistry. The molar concentration of hydronium ions reflects water's neutrality or its shift towards being acidic or basic.

Hydroxide Ion

The hydroxide ion, \( OH^- \), is the counterpart to the hydronium ion in the autoionization of water. It is a negatively charged ion formed by one oxygen and one hydrogen atom. When a hydronium ion is created, a hydroxide ion is produced at the same time to maintain electrical neutrality.

The concentration of hydroxide ions in a solution is also used to determine the solution’s basicity. Pure water has a unique characteristic in which the \( [H_3O^+] \) equals the \( [OH^-] \) concentration, meaning that it is neither acidic nor basic but neutral.

Ion Product of Water

The ion product of water, often denoted as \( K_w \), is a constant value at a given temperature that represents the product of the molar concentrations of the hydronium and hydroxide ions in water. At 25°C, the ion product of water is \( 1.0 \times 10^{-14} \ M^2 \).

\( K_w \) implies that the concentrations of \( H_3O^+ \) and \( OH^- \) are inversely related. If the concentration of one increases, the other must decrease for the ion product to remain constant at \( 1.0 \times 10^{-14} \ M^2 \). The ion product is foundational for understanding acid-base equilibrium and calculating \( p \) values like \( pH \) and \( pOH \) in aqueous solutions.