Question

Write the general equation for the ionization of a weak acid, \(\mathrm{H} A,\) in water. Give the equilibrium law corresponding to \(K_{a}\).

Short answer

\(HA (aq) + H_2O (l) \rightleftharpoons A^- (aq) + H_3O^+ (aq)\), \(K_a = \frac{[A^-][H_3O^+]}{[HA]}\)

Step-by-step solution

Ionization Reaction of a Weak Acid

Write the chemical equation for the ionization of a weak acid \(HA\) in water. The weak acid donates a proton \(H^+\) to the water, which results in the formation of hydronium ion \(H_3O^+\) (in aqueous solution, we often refer to \(H^+\) as \(H_3O^+\)) and the conjugate base \(A^−\). The ionization reaction for the weak acid \(HA\) can be represented as: \[ HA (aq) + H_2O (l) \rightleftharpoons A^- (aq) + H_3O^+ (aq) \]

Writing the Equilibrium Constant Expression

To write the equilibrium law (expression) corresponding to \(K_a\), use the equilibrium concentrations of the products and reactants. For the ionization of \(HA\), the expression for the acid dissociation constant \(K_a\) is given by: \[ K_a = \frac{[A^-][H_3O^+]}{[HA]} \] where the brackets \[ [ ] \] denote the equilibrium concentrations of each species in moles per liter \(mol/L\). The activity of solvent (water) is considered to be constant and is not included in the equilibrium expression.

Key concepts

Acid Dissociation Constant

Understanding acid-base reactions is key to grasping many principles of chemistry. One particularly important concept is the acid dissociation constant, often denoted as Ka. This value measures the strength of an acid in solution. In simple terms, the higher the Ka value, the stronger the acid, meaning it donates protons more readily.

When you dissolve a weak acid such as HA in water, it doesn't completely dissociate into its ions. Instead, a dynamic equilibrium is established between the non-ionized acid and the ions that are formed. The acid dissociation constant is a ratio that compares the concentration of the products (the ions) to the concentration of the reactants (the non-ionized acid).

Why is Ka Important?

Understanding Ka is vital for predicting how substances will behave in different chemical reactions, especially in buffer solutions which are essential in biological systems. It allows chemists to determine the degree of ionization of an acid, which is crucial for understanding pH changes and the buffering capacity of the solution.

• For weak acids, the smaller the Ka, the weaker the acid.
• Strong acids have a Ka that is so large it is often not even expressed in typical pH calculations.
• Calculating the pH of a solution often involves knowing the Ka value of the acids present.

In summary, the acid dissociation constant is pivotal in quantifying the strength of a weak acid and predicting its behavior in aqueous solutions.

Chemical Equilibrium

Diving deeper into the world of chemical reactions, we encounter the concept of chemical equilibrium. This state is achieved when a reversible reaction occurs simultaneously forward and backward at the same rate, leading to no net change in the concentration of reactants and products over time. However, it is important to note that this does not mean the concentrations are equal; it just means they are stable.

Chemical equilibrium is dynamic rather than static. The reactions are still occurring, but because they proceed at equal rates in both directions, the system appears stable. The point at which this equilibrium is reached depends on various factors, including temperature, concentration, and the presence of catalysts.

Dynamic Balance

This balance is essential for many processes in nature and technology, such as the formation of some minerals, the behavior of the ozone layer, and the synthesis of industrial chemicals.

In the context of acid ionization, equilibrium becomes significant as it marks the point where the amount of weak acid that has ionized is balanced by the amount that has recombined to form the non-ionized acid. Understanding this equilibrium allows for the calculation of pH, the design of buffer solutions, and various applications across chemical industries and biological systems.

Equilibrium Constant Expression

At the heart of understanding chemical equilibrium for reactions like the ionization of weak acids is the equilibrium constant expression. For the specific case of acid dissociation, the equilibrium constant is represented as Ka. The expression embodies the ratio of the concentration of the products to the reactants at equilibrium, with each raised to the power of their stoichiometric coefficients.

The general form of the equilibrium constant expression for a reversible reaction aA + bB ⇌ cC + dD is given by: \[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] where:

• \( K \) is the equilibrium constant.
• \( [C] \) and \( [D] \) are the equilibrium concentrations of the products.
• \( [A] \) and \( [B] \) are the equilibrium concentrations of the reactants.

For the ionization of a weak acid \( HA \), the equilibrium constant expression excludes water because it is the solvent and its concentration remains relatively constant during the reaction. This leads to the specific expression for Ka as illustrated in our exercise: \[ K_a = \frac{[A^-][H_3O^+]}{[HA]} \]
It's crucial to remember that the equilibrium constant is only affected by changes in temperature. Changes in concentrations, pressures, or the addition of inert gases do not affect the value of the equilibrium constant, although they can shift the position of the equilibrium. The equilibrium constant expression is a foundational tool for chemists to understand and predict the behavior of chemical systems.