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##### Acid equilibria and alpha plots

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**Acid equilibria and alpha plots**Chemistry 321, Summer 2014**In this lecture**• Alpha plots show dynamic changes in species concentration during a titration • For weak acids, alpha plots mirror the behavior seen on titration plots and yield further information**Formal concentration**Given: Let CHA = formal concentration of the acid = [HA] + [A–] = sum of all forms of the acid at equilibrium CHA = [HA]0 if only the weak acid is added = [A–]0if only the conjugate base is added = [HA]0 + [A–]0 if both are added**Alpha is the mole fraction of a species relative to the**solution’s formal concentration So, symbolically, For instance, We can rewrite this like: [HA] = αHA CHAor [A–] = = αA– CHA The constraint is that Σ αi = 1 For a monoprotic acid, αHA + αA– = 1**The equation of the alpha plot**Start with the definitions of CHA and αHA:**The equation of the alpha plot**Start with the definitions of CHA and αHA: Invert the expression:**The equation of the alpha plot**Start with the definitions of CHA and αHA: Invert the expression: Recalling the equilibrium expression: so**The equation of the alpha plot (continued)**Re-invert the equation: Similarly, we can derive an expression for αA–: Note that both expressions for alpha depend on [H+] (and, by extension, pH) only! So this can be plotted.**The alpha plot**pKa Where the two curves cross (each α = 0.5), the x-coordinate is the pKaof the weak acid.**Limiting behavior on the graph**For acetic acid, Ka = 1.8 × 10–5. Consider an acetic acid solution at pH 8.74 (meaning [H+] = 1.8 × 10–9). The point is that even at a really high pH, there is still someundissociated acid left (i.e., not zero). When you are dealing with a polyproticacid or base, then there are pHs at which some species have zero concentration…this is also important when dealing with ligands.**Polyprotic acid alpha plots**Polyprotic acid dissociation occurs in a stepwise manner; that is, the different H+ ions on each molecule dissociate at different pHs, rather than all at once. Note the definitions of the equilibrium constants Ka1 and Ka2 N.B.: pKa1 = 6.37, and pKa2 = 10.25**Setting up the alpha plot equations for a diprotic acid**Let CH2A = [H2A] + [HA–] + [A2–] ( = formal concentration of H2A) Expanding the previous definition of αi: [H2A] = αH2A CH2A and [HA–] = αHA– CH2A and [A2–] = αA2- CH2A Note that αH2A + αHA– + αA2- = 1**Setting up the alpha plot equations for a diprotic acid**Let CH2A = [H2A] + [HA–] + [A2–] ( = formal concentration of H2A) Expanding the previous definition of αi: [H2A] = αH2A CH2A and [HA–] = αHA– CH2A and [A2–] = αA2- CH2A Note that αH2A + αHA– + αA2- = 1**Setting up the alpha plot equations for a diprotic acid**Inverting the equation yields:**Setting up the alpha plot equations for a diprotic acid**Inverting the equation yields: Recall the definitions of Ka1 and Ka2:**Setting up the alpha plot equations for a diprotic acid**Inverting the equation yields: Recall the definitions of Ka1 and Ka2: multiply to get:**Setting up the alpha plot equations for a diprotic acid**Substitute into the original expression:**Setting up the alpha plot equations for a diprotic acid**Substitute into the original expression: Put it all over a common denominator: Limiting behavior: at low pH (acidic), the [H+]2 term dominates the other terms, so αH2A ≈ 1; at high pH (alkaline), [H+]2 0, so αH2A ≈ 0.**Setting up the alpha plot equations for a diprotic acid**The other αi expressions (αHA– and αA2–) are derived similarly.**The alpha plot for carbonic acid**What are the pKas for carbonic acid?**The alpha plot for carbonic acid**At pH 4, αCO3 2- ≈ 0, according to the graph**The alpha plot for carbonic acid**not zero, but basically negligible! At pH 4, the only two species that matter are HCO3–and H2CO3**The titration curve for carbonic acid reflects the stepwise**dissociation behavior**Challenge problem**Consider the stepwise dissociation of phosphoric acid:**Challenge problem (continued)**• Derive the equations to calculate αi for all phosphate-containing species. • Draw the alpha plot for all phosphate-containing species; make sure the axes are labeled and the pKas are sensible. • Calculate the mole fraction (αi) for all phosphate-containing species at blood pH (7.40). • Assume all phosphate-containing species have a soluble sodium salt (i.e., if you need PO43–, you will use Na3PO4). Which two salts will you use to create pH 7.40 phosphate buffer?