3.2. Weak Acids and Bases

For a weak acid HA in water:

HA ⇌ H plus + A minus

● Ka = ([H plus] × [A minus]) ÷ [HA] at equilibrium.

We denote the initial concentration of HA as C₀, and assume initially [H plus] and [A minus] are zero (unless acid or base is already present). At equilibrium, let [H plus] = x, [A minus] = x, and [HA] = C₀ – x. Then:

Ka = x × x ÷ (C₀ – x) = x² ÷ (C₀ – x)

In this section, we explore the concept of the acid dissociation constant, denoted as Ka. This constant is essential for understanding how weak acids behave in aqueous solutions.

• The dissociation reaction shows that a weak acid (HA) can lose a proton (H+) to form its conjugate base (A−).
• The equilibrium constant Ka quantifies this process, giving a ratio of the products to reactants at equilibrium.
• The formula Ka = ([H plus] × [A minus]) ÷ [HA] explains how to calculate the dissociation constant from the concentrations of the ions produced and the undissociated acid in equilibrium.
• We measure Ka under conditions where the initial concentration (C₀) of the weak acid is known, allowing us to determine the extent of the acid's ionization in solution.

Consider a sponge soaking up water. The sponge represents the weak acid (HA), and the water it absorbs represents the protons (H+) that it releases into the solution. Not all of the water can be absorbed at once, just as a weak acid doesn't completely dissociate in solution. The ability of the sponge to absorb water slowly mirrors how weak acids partially release protons, reflected in the value of Ka.

● Percent ionization = ([A minus] at equilibrium ÷ C₀) × 100% = (x ÷ C₀) × 100%. As C₀ increases, percent ionization decreases.

The percent ionization is a crucial concept that helps us understand the effectiveness of a weak acid in solution.

• It shows how much of the acid has converted into ions at equilibrium compared to its initial concentration (C₀).
• By using the formula Percent Ionization = (x ÷ C₀) × 100%, where x represents the concentration of the dissociated component at equilibrium, we can assess the strength of the acid.
• As the initial concentration (C₀) increases, the percent ionization tends to decrease, indicating that stronger acids (higher C₀) do not ionize fully in proportion to their amount.

Imagine pouring sugar into a glass of water. If you add a small amount of sugar to a glass, it dissolves easily, representing a high percent ionization for a weak acid. However, if you keep adding sugar, at some point, it won't dissolve; instead, it settles at the bottom. This illustrates how higher concentrations of weak acids yield lower percent ionization; just as not all sugar can dissolve, not all acid can ionize.

For a weak base B in water:

B + H₂O ⇌ BH plus + OH minus

● Kb = ([BH plus] × [OH minus]) ÷ [B] at equilibrium.

If initial [B] = C₀, and initially [BH plus] and [OH minus] are zero (ignoring water), then at equilibrium [B] = C₀ – x, [BH plus] = x, [OH minus] = x. So:

Kb = x² ÷ (C₀ – x)

Now, we shift our focus onto weak bases and how they interact in water.

• The reaction shows how a weak base (B) can accept a proton from water, forming its conjugate acid (BH+) and hydroxide ions (OH−).
• The base dissociation constant (Kb) quantifies this equilibrium, just like Ka does for acids.
• In the equation Kb = ([BH plus] × [OH minus]) ÷ [B], we see how the concentrations at equilibrium relate to the initial concentration of the weak base.
• Similar to the weak acid, Kb helps us understand the ionization capacity of weak bases in solution.

Think about baking soda (a weak base) mixed into a small glass of vinegar (an acid). When added, it reacts, producing bubbles of carbon dioxide while the baking soda forms a new compound (its conjugate acid) that increases pH. Like dissolving a weak base, not all of the baking soda interacts with the acid; thus, the Kb of baking soda reflects how effectively it can make the solution basic.

For the conjugate pair HA / A minus:

Ka × Kb = Kw (at a given temperature, usually 25 °C so Kw = 1.0 × 10⁻¹⁴)

Therefore:

Kb = Kw ÷ Ka

● If Ka is large (stronger acid), Kb is small (weaker conjugate base), and vice versa.

This section discusses the relationship between the acid and base dissociation constants for a conjugate acid-base pair.

• The equation Ka × Kb = Kw illustrates how the strength of an acid (reflected by Ka) is inversely related to the strength of its conjugate base (reflected by Kb).
• This means that if an acid is strong (large Ka), its conjugate base will be weak (small Kb) and vice versa.
• This relationship helps chemists understand how an acid and its conjugate base interact in chemical reactions, impacting solution pH and behavior.

Imagine a tug-of-war between two opposing teams—the stronger team is the acid (with a high Ka), easily overpowering the weaker team (the conjugate base with low Kb). As one team pulls stronger (more acidic), the opposing team (the base) has a harder time pulling back, demonstrating how their strengths inversely influence each other.

Example 1: Formic Acid (HCOOH, Ka = 1.8 × 10⁻⁴) at 0.020 M ● C₀ = 0.020 M. Ka = 1.8 × 10⁻⁴. ● x ≈ sqrt(Ka × C₀) = sqrt[(1.8 × 10⁻⁴) × 0.020] = sqrt(3.6 × 10⁻⁶) ≈ 1.9 × 10⁻³ M. ● [H plus] = 1.9 × 10⁻³ M → pH = – log₁₀ (1.9 × 10⁻³) ≈ 2.72. ● Percent ionization = (1.9 × 10⁻³ ÷ 0.020) × 100% = 9.5%.

Here, we perform calculations using the previously discussed concepts with an example of formic acid.

• We begin with the initial concentration (C₀) and the known value of its acid dissociation constant (Ka).
• We apply the square root approximation for weak acids, utilizing x ≈ sqrt(Ka × C₀) to find the concentration of hydrogen ions produced at equilibrium.
• We then use this value to calculate the pH, following the logarithmic conversion for hydrogen ion concentration. Lastly, we compute percent ionization, showing how much of the acid has dissociated relative to the initial concentration.

Imagine measuring how much lemonade (acid) you can taste in a large pitcher of water (total solution). The more concentrated your lemonade mix, the more you'll taste it, but if you dilute it too much (increase C₀), you'll barely taste it, analogous to lower percent ionization. These calculations give you precise insight into how effective the acid is, just like realizing how strong your lemonade mix is.

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