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Chapter 18: Problem 18

Relate the strength of a weak acid to the strength of its conjugate base.

Short Answer

Expert verified
A weak acid has a strong conjugate base due to the inverse relationship between their equilibrium constants.

Step by step solution

01

Understanding Acid and Base Strength

A weak acid is an acid that partially dissociates in solution. This means that only a fraction of its molecules donate protons (H extsuperscript{+}) to water. The conjugate base is what's left after the acid has donated a proton. The weaker the acid, the stronger its conjugate base will be, because the base retains a stronger tendency to accept protons back.
02

Dissociation and Equilibrium

At equilibrium, the dissociation of a weak acid can be represented as: \[ HA ightleftharpoons H^+ + A^- \] where \(HA\) is the weak acid and \(A^-\) is the conjugate base. The equilibrium constants for this reaction are given by: \[ K_a = \frac{[H^+][A^-]}{[HA]} \] A smaller \(K_a\) value indicates a weaker acid, meaning less dissociation.
03

Relationship between \(K_a\) and \(K_b\)

The conjugate base of a weak acid has an equilibrium constant for accepting protons, called \(K_b\). The product of the equilibrium constant of the acid \(K_a\) and its conjugate base \(K_b\), is related to the ion product of water, \(K_w\): \[ K_a \cdot K_b = K_w = 1.0 \times 10^{-14} \] Thus, as \(K_a\) decreases, \(K_b\) must increase for the same \(K_w\). This shows that a weak acid correlates to a stronger conjugate base.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Weak Acid
A weak acid is characterized by its partial dissociation in an aqueous solution. This means that when a weak acid, represented as \(HA\), is added to water, only a small portion of \(HA\) molecules release protons \(H^+\) into the solution. As a result, not all acid molecules contribute to the acidity of the solution, distinguishing weak acids from strong acids that completely dissociate.
An important aspect to understand about weak acids is that:
  • They create an equilibrium between the undissociated acid and the ions produced from its dissociation.
  • The presence of equilibrium indicates that dissociation is not complete.
  • Because not all \(HA\) donates protons, the solution has a lower concentration of \(H^+\), resulting in a higher pH compared to strong acids.
Conjugate Base
Once the weak acid \(HA\) donates a proton, the substance that remains is called the conjugate base, noted as \(A^-\). In simple terms, a conjugate base forms when the original acidic molecule loses its proton. This conjugate base is crucial to understanding acid-base chemistry:
  • The conjugate base is capable of accepting \(H^+\) ions, meaning it can potentially reform the acid \(HA\).
  • There is an inverse relationship between the strength of an acid and the strength of its conjugate base: as an acid becomes weaker, its conjugate base becomes stronger.
  • A stronger conjugate base has a better ability to capture free \(H^+\) ions in solution.
This relationship is fundamental when predicting the behavior of substances in acid-base reactions and in determining their equilibrium positions.
Equilibrium Constant
In the context of weak acids and their conjugate bases, the equilibrium constant, specifically the acid dissociation constant \(K_a\), plays a significant role in quantifying the strength of the acid.
To elaborate:
  • The equation \(K_a = \frac{[H^+][A^-]}{[HA]}\) represents the state of equilibrium for the dissociation of the weak acid.
  • A smaller \(K_a\) value suggests less dissociation, indicating a weaker acid.
  • The relationship between \(K_a\) and the base equilibrium constant \(K_b\) is defined by \( K_a \cdot K_b = K_w\), where \(K_w\) is the ion product of water, valued at \(1.0 \times 10^{-14}\).
Understanding these constants helps in determining how acids and bases behave in solution and how they can transform into each other during reactions. As the \(K_a\) decreases, \(K_b\) must increase to maintain the balance with \(K_w\), underscoring that a weaker acid has a stronger conjugate base.

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Most popular questions from this chapter

Challenge Calculate the \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in a sample of seawater with a pOH \(=5.60 .\)

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Explain the significance of \(K_{w}\) in aqueous solutions.

When might a pH meter be better than an indicator to determine the end point of an acid-base titration?

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