Carbonation in Lambic: Difference between revisions
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CO<sub>2</sub> + H<sub>2</sub>O -> H<sub>2</sub>CO<sub>3</sub> | CO<sub>2</sub> + H<sub>2</sub>O -> H<sub>2</sub>CO<sub>3</sub> | ||
at a ratio of about one H<sub>2</sub>CO<sub>3</sub> molecule per 590 dissolved CO<sub>2</sub> molecules [REF, CRC handbook?]. Carbonic acid has pKas of ~3.49 and ~10.32 [PINES 2016], which are defined as: | at a ratio of about one H<sub>2</sub>CO<sub>3</sub> molecule per 590 dissolved CO<sub>2</sub> molecules [REF, CRC handbook?]. Carbonic acid has pKas of ~3.49 and ~10.32 [PINES 2016], where | ||
pKa = -log(Ka), | |||
which are defined as: | |||
Ka<sub>1</sub> = [H<sup>+</sup>][HCO<sub>3</sub><sup>-</sup>]/[H<sub>2</sub>CO<sub>3</sub>] = 10<sup>~-3.49</sup> | Ka<sub>1</sub> = [H<sup>+</sup>][HCO<sub>3</sub><sup>-</sup>]/[H<sub>2</sub>CO<sub>3</sub>] = 10<sup>~-3.49</sup> | ||
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Ka<sub>2</sub> = [H<sup>+</sup>][CO<sub>3</sub><sup>2-</sup>]/[HCO<sub>3</sub><sup>-</sup>] = 10<sup>~-10.32</sup>, | Ka<sub>2</sub> = [H<sup>+</sup>][CO<sub>3</sub><sup>2-</sup>]/[HCO<sub>3</sub><sup>-</sup>] = 10<sup>~-10.32</sup>, | ||
and in addition, | |||
Ka<sub>0</sub> = [H<sub>2</sub>CO<sub>3</sub>]/[CO<sub>2</sub> (aq)], | |||
Where the brackets, [], indicate the molar concentration of the species they contain. | |||
Thus, we can see that the first deprotonation completely dominates the acidity of carbonic acid at low pH, being seven orders of magnitude larger than the second, and we are justified in ignoring the second deprotonation's contribution henceforth. Combining the coefficient of hydration from above with the first deprotonation gives an overall equilibrium constant defined as: | Thus, we can see that the first deprotonation completely dominates the acidity of carbonic acid at low pH, being seven orders of magnitude larger than the second, and we are justified in ignoring the second deprotonation's contribution henceforth. Combining the coefficient of hydration from above with the first deprotonation gives an overall equilibrium constant defined as: | ||
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[CO<sub>3</sub><sup>2-</sup>] = Ka<sub>0</sub> * Ka<sub>1</sub> * Ka<sub>2</sub> * 4.3 * V<sub>CO<sub>2</sub></sub> * 10<sup>2pH</sup> | [CO<sub>3</sub><sup>2-</sup>] = Ka<sub>0</sub> * Ka<sub>1</sub> * Ka<sub>2</sub> * 4.3 * V<sub>CO<sub>2</sub></sub> * 10<sup>2pH</sup> | ||
which uses numbers a brewer is likely to know, pH and volumes of CO<sub>2</sub> as independent variables. | which uses numbers a brewer is likely to know, pH and volumes of CO<sub>2</sub> as independent variables. | ||