Chemistry & Materials Science

Hydrogen Ion Concentration Calculator

Calculate the hydrogen ion [H+] concentration from the pH of a solution. Essential for analyzing the acidity of chemical and biological systems.

M
Equilibrium [H⁺]
1.3416e-3
Solution pH2.87
Degree of Dissociation1.34
ICE Table StatusValid Approximation (< 5% dissociated)

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Weak Acids and Equilibrium

In laboratory chemistry, determining the hydrogen ion concentration ([H⁺]) of a strong acid is trivial because strong acids dissociate 100%. A 0.1 M solution of HCl yields exactly 0.1 M of H⁺.

However, weak acids (like acetic acid or citric acid) only partially dissociate. To find the true [H⁺] in a weak acid solution, chemists use the Acid Dissociation Constant (Ka) alongside an ICE (Initial, Change, Equilibrium) table.

The Approximation Formula

Setting up a full quadratic equation from an ICE table can be mathematically tedious. Fortunately, if the weak acid dissociates less than 5%, chemists use a simplified approximation formula to instantly find the equilibrium concentration.

The Equation

[H+]=Ka×C\begin{aligned} [H⁺] = \sqrt{K_a \times C} \end{aligned}

Where:
[H⁺]=
Equilibrium Hydrogen Ion Concentration (Molar)
KaK_a=
Acid Dissociation Constant
C=
Initial Concentration of Weak Acid

Example Calculation

You prepare a 0.2 M solution of acetic acid ($K_a = 1.8 \times 10^{-5}$). To find the equilibrium [H⁺]:

  1. Multiply $K_a$ by Concentration: $(1.8 \times 10^{-5}) \times 0.2 = 3.6 \times 10^{-6}$
  2. Take the square root: $\sqrt{3.6 \times 10^{-6}}$
  3. Result: $1.89 \times 10^{-3}$ M

The resulting [H⁺] is $0.00189$ M, meaning only about 0.9% of the acid actually dissociated!

Frequently Asked Questions

The square root approximation fails if the acid is relatively strong (Ka > 10^-3) or if the initial concentration is extremely dilute. In these cases, the acid dissociates more than 5%, and you must solve the exact quadratic equation: x^2 + Ka(x) - Ka(C) = 0.

Yes, in practical aqueous chemistry, they are treated as identical. A bare proton (H⁺) is incredibly unstable and immediately attaches to a water molecule (H₂O) to form a hydronium ion (H₃O⁺). We use [H⁺] purely as a shorthand notation.

Once you have calculated the equilibrium [H⁺] using the approximation formula, you simply take the negative base-10 logarithm of that value: pH = -log([H⁺]).

It is the percentage of the initial acid molecules that successfully broke apart into ions. It is calculated by dividing the equilibrium [H⁺] by the initial acid concentration, then multiplying by 100.

According to Le Chatelier's Principle and Ostwald's dilution law, as you add more water to a weak acid, the overall [H⁺] decreases, but the PERCENTAGE of dissociation actually increases.

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