How to Calculate Buffering Capacity
Buffers are solutions that resist change in pH. They are important in chemical and biological systems. The capacity of a buffer, B, is defined as the ability of buffer to resist pH change when hydroxide (OH-) ions. B varies with a number of factors, including temperature, concentration of the buffer, the pH of the solution and the dissociation constant of the acid component of the buffer: B=dn/d(pH)=2.303[(Kw/[H+])+[H+]+((Ca*Ka*[H+])/((Ka*[H+])^2))].
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Things You'll Need
- The self-ionization constant of water, Kw, at the temperature and pressure of the reaction
- The concentration of protons, [H+]
- The analytical concentration of the weak acid making up the buffer, Ca, where Ca=[H+]+[HA]
- The dissociation constant of the weak acid making up the buffer, Ka
Instructions
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1
Divide the self-ionization constant of water, Kw, by the concentration of protons in solution. This term of the equation, Kw/[H+], is independent of the buffer and is instead a property of water. It becomes significant near pH 11.5.
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2
Add the concentration of protons, [H+]. This term of the equation, [H+], is also independent of the buffer. It becomes significant near pH 2. Put this number aside, and label it "A."
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3
Multiply the analytical concentration of the acid, Ca, by the dissociation constant of the acid, Ka, and by the concentration of protons, [H+]. Put this number aside, and label it "B."
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4
Multiply Ka by [H+], and square the result. Label this "C."
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5
Divide B by C. Label the result "D." This term is where the type and amount of buffer used influence B.
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6
Add A to D, and multiply the result by 2.303. This result is B.
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Tips & Warnings
The easiest way to find [H<+] if you don't have it is to use the pH of the solution and the definition of pH: pH = - log [H+]. Be sure to use log base 10, not log base e (i.e. ln) when making this calculation. For example, if the pH of the solution is 5, then 5 = -log [H+], and [H+] =10^-5.
B is maximized when the pH of the solution is equal to the pKa of the acid in the buffer. When the pH of the solution moves 1 pH unit from the pKa in either direction, the buffer efficacy drops to 33% of the maximal capacity. At these pHs, there is a tenfold difference in the concentration of the acid and the base. This follows from the Henderson--Hasselbalch equation, pH=pKa+log([A-]/log[HA]).
Kw varies with the temperature and pressure of the reaction. At standard atmospheric pressure and temperature, Kw=1*10^-14. When finding buffer capacity, use this number for Kw unless you know that the temperature or pressure will be different, or if you're solving a problem for a chemistry class that describes different conditions.
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Comments
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Not very clear. It is not said when the protons derive from the ionization of water (before the stoichiometry) or when they derive from the ionization of the buffer salt (after the stoichiometry). You should give a real example if you want someone to understand what you mean there. Yours sincerely, Rodrigo
