The pH scale measures how acidic or basic a water-based solution is, ranging from 0 to 14. Values below 7 indicate acidity, above 7 indicate basicity, and 7 is neutral. pH is determined by the concentration of hydrogen ions (H⁺). Understanding pH is important in many fields, as it influences chemical reactions and biological processes. This article guides you through calculating pH for weak acids using the acid dissociation constant (Ka).
Understanding pH and the Acid Dissociation Constant
pH quantifies the acidity or basicity of an aqueous solution, directly relating to the concentration of hydrogen ions (H⁺) or hydronium ions (H₃O⁺). The formula for pH is pH = -log[H⁺], where brackets denote molar concentration. The pH scale is logarithmic; a change of one pH unit signifies a tenfold change in hydrogen ion concentration. For instance, a solution with a pH of 3 has ten times more hydrogen ions than a solution with a pH of 4.
The acid dissociation constant, Ka, is an equilibrium constant measuring the extent to which an acid dissociates in solution. For weak acids, Ka quantifies their strength by showing how readily they donate a proton (H⁺) to water. The dissociation of a generic weak acid (HA) is: HA ⇌ H⁺ + A⁻. The Ka expression is Ka = [H⁺][A⁻]/[HA], where [HA] is the undissociated acid, and [H⁺] and [A⁻] are the hydrogen ion and conjugate base concentrations at equilibrium. A larger Ka value indicates a stronger weak acid.
Strong Versus Weak Acids
Acids are categorized as strong or weak based on their dissociation in water. Strong acids dissociate almost entirely, releasing nearly all their hydrogen ions. For example, hydrochloric acid (HCl) breaks down completely into H⁺ and Cl⁻ ions. This complete dissociation means the hydrogen ion concentration in a strong acid solution can be directly determined from the initial acid concentration, simplifying pH calculations.
Weak acids, in contrast, only partially dissociate in water, establishing an equilibrium between undissociated acid molecules and their ions. Only a fraction of weak acid molecules release hydrogen ions, leaving most in their original form. The acid dissociation constant (Ka) quantifies this partial dissociation. A weak acid solution contains a mixture of intact acid molecules and their corresponding ions.
Calculating pH for Weak Acids
Calculating the pH of a weak acid solution involves several steps due to its partial dissociation. First, write the balanced chemical equation for the weak acid’s dissociation in water: HA(aq) ⇌ H⁺(aq) + A⁻(aq). This equation shows the reversible nature of the dissociation and the equilibrium between the undissociated acid and its ions.
Next, set up an ICE table (Initial, Change, Equilibrium). This table tracks the concentrations of the acid, hydrogen ions, and conjugate base. List the initial weak acid concentration and assume zero initial concentrations for products. Define ‘x’ as the change in concentration due to dissociation. At equilibrium, concentrations are expressed in terms of the initial concentration and ‘x’.
Then, write the Ka expression: Ka = ([H⁺][A⁻])/[HA]. Substitute the equilibrium concentrations from your ICE table into this expression. This results in an algebraic equation to solve for ‘x’.
If the Ka value is very small and the initial weak acid concentration is relatively large, an approximation can be made. This assumes ‘x’ is negligible compared to the initial concentration, simplifying the calculation. If this approximation is not valid, the quadratic formula must be used. Once ‘x’ is determined, it represents the equilibrium concentration of hydrogen ions ([H⁺]). Finally, calculate the pH using pH = -log[H⁺].
Applying the Calculation with Examples
Consider a 0.10 M solution of acetic acid (CH₃COOH), a common weak acid, with a Ka value of 1.8 × 10⁻⁵. The dissociation is: CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq).
Setting up an ICE table:
Initial: [CH₃COOH] = 0.10 M, [H⁺] = 0 M, [CH₃COO⁻] = 0 M
Change: [CH₃COOH] = -x, [H⁺] = +x, [CH₃COO⁻] = +x
Equilibrium: [CH₃COOH] = (0.10 – x) M, [H⁺] = x M, [CH₃COO⁻] = x M.
Substitute these equilibrium concentrations into the Ka expression:
Ka = ([H⁺][CH₃COO⁻])/[CH₃COOH]
1.8 × 10⁻⁵ = (x x)/(0.10 – x).
Given the small Ka value, approximate ‘x’ as much smaller than 0.10, simplifying (0.10 – x) to 0.10. The equation becomes:
1.8 × 10⁻⁵ = x² / 0.10
x² = (1.8 × 10⁻⁵) 0.10
x² = 1.8 × 10⁻⁶
x = √(1.8 × 10⁻⁶)
x ≈ 0.00134 M.
This ‘x’ value represents the equilibrium concentration of H⁺ ions. Calculate the pH:
pH = -log[H⁺]
pH = -log(0.00134)
pH ≈ 2.87.
This pH demonstrates the slightly acidic nature of the weak acetic acid solution.