Weak Acid pH Calculator (Ka — ICE Table) – Tutorial

What Is Weak Acid pH Calculation?

Weak acids (HA) do not fully dissociate in water; only a fraction converts to H⁺ and A⁻ ions. Therefore, you cannot say "direct concentration = [H⁺]" as you would with strong acids. The pH must be found using an equilibrium approach.

The Fundamental Equilibrium Reaction

The dissociation of a weak acid in water is written as:

HA ⇌ H⁺ + A⁻

The acid dissociation constant (Ka) for this equilibrium is defined as:

Ka = ([H⁺][A⁻]) / [HA]

ICE Table Logic (I-C-E)

The ICE table is the most systematic method for equilibrium problems:

• I (Initial): Initial concentrations
• C (Change): Changes as the reaction proceeds
• E (Equilibrium): Concentrations at equilibrium

Step-by-Step ICE

Suppose only the acid is present at the start (HA = C molar), with no ions:

• I: [HA] = C, [H⁺] ≈ 0, [A⁻] = 0
• C: -x, +x, +x
• E: [HA] = C - x, [H⁺] = x, [A⁻] = x

Setting Up the Equilibrium Equation

Substituting the E row into the equilibrium expression:

Ka = (x · x) / (C - x) = x² / (C - x)

Rearranging:

Ka(C - x) = x²

Ka·C - Ka·x = x²

x² + Ka·x - Ka·C = 0

The problem thus reduces to solving a quadratic equation. This is exactly what this calculator does.

Quadratic Equation Solution

General form: ax² + bx + c = 0

• a = 1
• b = Ka
• c = -Ka·C

Discriminant: Δ = b² - 4ac
Roots: x = (-b ± √Δ) / (2a)

Since [H⁺] cannot be negative, the positive root is selected. This calculator uses the positive root.

pH Calculation

Once the equilibrium [H⁺] concentration is found:

pH = -log₁₀([H⁺])

What Is the 5% Approximation?

In some problems, "x is very small" is assumed, so C - x ≈ C. This simplifies the calculation:

Ka ≈ x² / C → x ≈ √(Ka·C)

However, this is only valid if x is sufficiently small relative to C. The standard criterion is:

(x / C) × 100 < 5%

This calculator:

• First performs the exact solution (quadratic).
• Then calculates the dissociation percentage (x/C)×100.
• If less than 5%: states "Approximation valid."

What Do the Result Values Mean?

• [H⁺] (equilibrium): Equilibrium hydrogen ion concentration (M)
• pH: Logarithmic measure of acidity
• Dissociation percentage: Shows what fraction of the acid has dissociated
• Approximation valid?: 5% rule check

Common Errors and Precautions

• Ka notation: You can use scientific notation like 1.8e-5.
• Entering pKa instead of Ka: pKa = -log(Ka). This calculator requires Ka.
• Very high concentrations: Ionic interactions increase; ideal assumptions may deviate.
• Very dilute concentrations: Water autoionization (10⁻⁷) may become significant.
• Temperature: Ka depends on temperature; this calculator assumes 25°C.

Example (To Solidify the Logic)

For Ka = 1.8×10⁻⁵ and C = 0.10 M, the calculator finds x = [H⁺] via quadratic solution, then calculates the pH. Finally, if the dissociation percentage is less than 5%, it notes that the approximate method is also appropriate.

Note: This tool is for educational purposes. Concentrated solutions, activity coefficients, and ionic strength effects are not accounted for.