pH & Alkalinity – How are they related?

A primer on the relationship between the bicarbonate system & pH

The relationship between pH & alkalinity is intimately connected with the chemistry of the aqueous bicarbonate equilibrium system.  An understanding of this will help us to communicate with & understands our customer’s needs.

CO₂ +   H₂O     <=>     CO_2(aq)    <=>     H₂CO₃        <=>         H⁺             +              HCO₃^–

                                                                                      Carbonic acid        Hydrogen ion              Bicarbonate ion

Where <=>  represents a partial (equilibrium) reaction or dissociation

For H₂CO₃ dissociation constant, k_a  = [H⁺].[HCO₃^–]/[H₂CO₃]   is a measure of how much it dissociates as a function of [H⁺] concentration or pH

[H⁺]   = concentration of H⁺

[HCO₃^–]  = concentration of bicarbonate ion (alkalinity)

[H₂CO₃] = concentration of carbonic acid (incl. dissolved CO₂)

Taking log of both sides   =>  log₁₀ka = log₁₀[H⁺] + log₁₀{[HCO₃^–]/[H₂CO₃]}

Reorganising               -log₁₀[H⁺]    = -log₁₀k_a   + log₁₀{[HCO₃^–]/[H₂CO₃]

And by definition            pH            = constant + log₁₀{alkalinity/(carbonic acid+ dissolved CO₂)}

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