Acid equilibria and alpha plots
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Transcript of Acid equilibria and alpha plots
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Acid equilibria and alpha plots
Chemistry 321, Summer 2014
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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
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Formal concentrationGiven:
Let CHA = formal concentration of the acid= [HA] + [A–] = sum of all forms of the
acid at equilibriumCHA = [HA]0 if only the weak acid is added
= [A–]0 if only the conjugate base is added= [HA]0 + [A–]0 if both are added
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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 CHA or [A–] = = αA– CHA
The constraint is that Σ αi = 1
For a monoprotic acid, αHA + αA– = 1
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The equation of the alpha plot
Start with the definitions of CHA and αHA:
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The equation of the alpha plot
Start with the definitions of CHA and αHA:
Invert the expression:
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The equation of the alpha plot
Start with the definitions of CHA and αHA:
Invert the expression:
Recalling the equilibrium expression:
so
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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.
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-1 1 3 5 7 9 11 13 150
0.10.20.30.40.50.60.70.80.91
Alpha Fractions
HAA-
pH
Alph
a
The alpha plot
Where the two curves cross (each α = 0.5), the x-coordinate is the pKa of the weak acid.
pKa
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Limiting behavior on the graphFor 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 some undissociated acid left (i.e., not zero).
When you are dealing with a polyprotic acid or base, then there are pHs at which some species have zero concentration…this is also important when dealing with ligands.
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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
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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
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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
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Setting up the alpha plot equations for a diprotic acid
Inverting the equation yields:
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Setting up the alpha plot equations for a diprotic acid
Inverting the equation yields:
Recall the definitions of Ka1 and Ka2:
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Setting up the alpha plot equations for a diprotic acid
Inverting the equation yields:
Recall the definitions of Ka1 and Ka2:
multiply to get:
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Setting up the alpha plot equations for a diprotic acidSubstitute into the original expression:
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Setting up the alpha plot equations for a diprotic acidSubstitute 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.
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The other αi expressions (αHA– and αA2–) are derived similarly.
Setting up the alpha plot equations for a diprotic acid
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The alpha plot for carbonic acid
What are the pKas for carbonic acid?
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The alpha plot for carbonic acid
At pH 4, αCO3 2- ≈ 0, according to the graph
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The alpha plot for carbonic acid
not zero, but basically negligible!
At pH 4, the only two species that matter are HCO3– and H2CO3
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The titration curve for carbonic acid reflects the stepwise dissociation behavior
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Challenge problemConsider the stepwise dissociation of phosphoric acid:
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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 PO4
3–, you will use Na3PO4). Which two salts will you use to create pH 7.40 phosphate buffer?