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Chapter 15: Problem 23

Explain the relationship between the self-ionization of water and \(K_{w}\) .

Short Answer

Expert verified
The self-ionization of water describes how water molecules can split into hydronium and hydroxide ions. The water ion product, \(K_{w}\), is the equilibrium constant for this reaction that measures the concentrations of these ions in the solution at equilibrium. They are related in such a way that any changes in the concentration of one ion due to shifts in the ionization equilibrium will affect the other ion's concentration to maintain \(K_{w}\) constant.

Step by step solution

01

Understand the Self-Ionization of Water

Water can behave as both an acid (proton donor) and a base (proton receiver) - this dual nature enables water to self-ionize. In the self-ionization process, one water molecule (H2O) donates a proton (H+) to another water molecule, resulting in the formation of a hydronium ion (H3O+) and a hydroxide ion (OH-). This can be represented by the equation: 2H2O(l) ↔ H3O+(aq) + OH⁻(aq).
02

Understand the Water Ion Product (Kw)

The water ion product, denoted as \(K_{w}\), is the equilibrium constant for this self-ionization reaction. It describes the product of the molar concentration of hydrogen ions (H3O+) and hydroxide ions (OH-) in water at a specific temperature. Mathematically, it's represented as: \(K_{w} = [H3O+][OH-]\). At 25°C, Kw is equal to \(1.0 x 10^{-14}\).
03

Relate Self-Ionization and Kw

In a neutral solution at 25°C, due to the equal concentrations of H3O+ and OH-, each is equal to \(\sqrt{K_{w}} = 1.0 x 10^{-7}\) M. If the concentrations of these ions change, the solution may become acidic (if [H3O+] > [OH-]) or basic (if [OH-] > [H3O+]). However, at a given temperature, the product of their concentrations, \(K_{w}\), remains constant. This clearly shows the relationship between the self-ionization of water and \(K_{w}\), as any changes in one of these ions' concentration due to a shift in ionization equilibrium will influence the other to maintain a constant \(K_{w}\).

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Most popular questions from this chapter

What is the \(\mathrm{pH}\) of a solution whose hydronium ion concentration is \(2.2 \times 10^{-12} \mathrm{M} ?\)

Use the following terms to create a concept map: hydronium ions \(\left(H_{3} O^{+}\right),\) hydroxide ions \(\left(O H^{-}\right)\) , neutralization reaction, pH, and titration.

Three solutions have pHs of \(3,7,\) and \(11 .\) Which solution is basic? Which is acidic? Which is neutral?

Write an equation for the reaction between hydrocyanic acid, HCN, and water. Label the acid, base, conjugate acid, and conjugate base.

If 25 \(\mathrm{mL}\) of 1.00 \(\mathrm{M} \mathrm{HCl}\) is mixed with 75 \(\mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{NaOH},\) what are the final amounts and concentrations of all ions present?
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