An Introduction to Thermal Physics · Problem 5.91

Free Energy and Chemical Thermodynamics — Daniel Schroeder

Physics — Statistical Mechanics · carbonic-acid-pH-rainwater

Problem

When carbon dioxide ``dissolves'' in water, essentially all of it reacts to form carbonic acid, H2CO3\mathrm{H}_2\mathrm{CO}_3: CO2(g)+H2O(l)⟷H2CO3(aq).\mathrm{CO}_2(\mathrm{g}) + \mathrm{H}_2\mathrm{O}(\mathrm{l}) \longleftrightarrow \mathrm{H}_2\mathrm{CO}_3(\mathrm{aq}). The carbonic acid can then dissociate into H+\mathrm{H}^+ and bicarbonate ions, H2CO3(aq)⟷H+(aq)+HCO3−(aq).\mathrm{H}_2\mathrm{CO}_3(\mathrm{aq}) \longleftrightarrow \mathrm{H}^+(\mathrm{aq}) + \mathrm{HCO}_3^-(\mathrm{aq}). (The table at the back of this book gives thermodynamic data for both of these reactions.) Consider a body of otherwise pure water (or perhaps a raindrop) that is in equilibrium with the atmosphere near sea level, where the partial pressure of carbon dioxide is 3.4×10−43.4 \times 10^{-4} bar (or 340 parts per million). Calculate the molality of carbonic acid and of bicarbonate ions in the water, and determine the pH of the solution. Note that even ``natural'' precipitation is somewhat acidic.

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