3.2.1. Acid Dissociation Constant (Ka)

For a weak acid HA in water:

HA ⇌ H plus + A minus

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

The acid dissociation constant, denoted as Ka, is a value that indicates the strength of a weak acid. When a weak acid (HA) is dissolved in water, it partially dissociates into hydrogen ions (H plus) and its conjugate base (A minus). This reaction can be represented with the equilibrium expression, where Ka is the ratio of the concentration of the products ([H plus] and [A minus]) to the concentration of the undissociated weak acid ([HA]) at equilibrium. A higher Ka value means the acid is stronger and dissociates more in solution.

Think of a sponge that can hold water. A weak acid is like a sponge that can hold a limited amount of water (the undissociated acid). As you start to squeeze the sponge (add water), some of it will drip out (dissociate), but it won't release all its water at once. The Ka value tells us how effectively the sponge lets water out compared to how much it can still hold.

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)

To calculate the acid dissociation constant (Ka), we first need to establish initial conditions. We start with the initial concentration of the weak acid, C₀, while the hydrogen ions [H plus] and the conjugate base [A minus] are initially zero. As the acid dissociates, we assume that 'x' is the concentration that dissociates into [H plus] and [A minus], while the concentration of the undissociated weak acid changes to C₀ - x. By substituting these values into the Ka expression, we can find the value of Ka. We often use the approximation C₀ - x ≈ C₀ when Ka is much smaller than C₀, simplifying our calculations.

Imagine you have a glass of orange juice. Initially, the juice represents the weak acid (HA) before any is consumed. The juice starts to spill out when you take a sip (the dissociation). The amount of juice left in the glass would be C₀ - x, where x is the amount you've sipped. If you know how much you've sipped and how much was initially in the glass, you can figure out how strong the juice is in the glass, like calculating the Ka.

Approximations:

● If Ka is significantly smaller than C₀ (for example, Ka < 10⁻² and C₀ > 0.01), then x will be small compared to C₀, so C₀ – x ≈ C₀, and we use x ≈ sqrt(Ka × C₀).

After finding x, calculate pH = – log₁₀ (x).

In many cases, especially when dealing with weak acids, the dissociation constant (Ka) is much smaller than the initial concentration (C₀) of the acid. In such situations, we can simplify our calculations by assuming that the change in concentration (x) is negligible compared to C₀. Therefore, we can treat C₀ - x as approximately equal to C₀. This allows us to derive x using the square root approximation, x ≈ sqrt(Ka × C₀). Once we determine 'x', which represents the [H plus] produced, we can calculate the pH of the solution using the formula pH = – log₁₀ (x).

Consider a small container with just a few drops of essential oil mixed with a lot of water. The amount of essential oil (like our weak acid) is so small compared to the water (C₀) that we can treat it as if it's unchanged when adding more water. This makes calculating how strong the scent is easier because we can focus on the tiny contribution from the oil, helping us estimate its effect without getting bogged down in details.

Percent Ionization:

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

Percent ionization is a measure of how effectively a weak acid actually dissociates in solution, expressed as a percentage. It is calculated by taking the concentration of the conjugate base [A minus] at equilibrium (which is equal to x) and dividing it by the initial concentration of the acid (C₀), then multiplying by 100. This concept illustrates that as the initial concentration of the acid increases, the fraction that ionizes into [A minus] decreases, highlighting that weak acids do not dissociate significantly at higher concentrations.

Imagine you have a strong light source (high C₀) shining through a window. As you pull back the curtain (representing the weak acid dissociation), a small amount of light gets through (ionization). If you close the curtain further (increasing C₀), even less light gets in compared to the initial amount, which illustrates how the ionization decreases with increasing concentration of the curtain (acid) in front of the light source.

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