How to Calculate Buffers

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In chemistry, a "buffer" is a solution you add to another solution in order to balance its pH, its relative acidity or its alkalinity. You make a buffer using a "weak" acid or base and its "conjugate" base or acid, respectively. To determine a buffer's pH--or extrapolate from its pH the concentration of any one of its components--you can make a series of calculations based on the Henderson-Hasselbalch equation, which is also known as the "buffer equation."

    Use the buffer equation to determine the pH of an acidic buffer solution, given certain acid-base concentrations. The Henderson-Hasselbalch equation is as follows: pH = pKa + log ([A-]/[HA]), where "pKa" is the dissociation constant, a number unique to each acid, "[A-]" represents the concentration of conjugate base in moles per liter (M) and "[HA]" represents the concentration of the acid itself. For example, consider a buffer that combines 2.3 M carbonic acid (H2CO3) with .78 M hydrogen carbonate ion (HCO3-). Consult a pKa table to see that carbonic acid has a pKa of 6.37. Plugging these values into the equation, you see that pH = 6.37 + log (.78/2.3) = 6.37 + log (.339) = 6.37 + (-0.470) = 5.9.

    Calculate the pH of an alkaline (or basic) buffer solution. You can rewrite the Henderson-Hasselbalch equation for bases: pOH = pKb + log ([B+]/[BOH]), where "pKb" is the base's dissociation constant, "[B+]" stands for the concentration of a base's conjugate acid and "[BOH]" is the concentration of the base. Consider a buffer that combines 4.0 M ammonia (NH3) with 1.3 M ammonium ion (NH4+), Consult a pKb table to locate ammonia's pKb, 4.75. Using the buffer equation, determine that pOH = 4.75 + log (1.3/4.0) = 4.75 + log (.325) = 4.75 + (-.488) = 4.6. Remember that pOH = 14 - pH, so pH = 14 -pOH = 14 - 4.6 = 9.4.

    Determine the concentration of a weak acid (or its conjugate base), given its pH, pKa and the concentration of the weak acid (or its conjugate base). Keeping in mind that you can rewrite a "quotient" of logarithms--i.e. log (x/y)--as log x - log y, rewrite the Henderson Hasselbalch equation as pH = pKa + log [A-] - log [HA]. If you have a carbonic acid buffer with a pH of 6.2 that you know is made with 1.37 M hydrogen carbonate, compute its [HA] as follows: 6.2 = 6.37 + log(1.37) - log[HA] = 6.37 + .137 - log[HA]. In other words log[HA] = 6.37 - 6.2 + .137 = .307. Calculate [HA] by taking the "inverse log" (10^x on your calculator) of .307. The concentration of carbonic acid is thus 2.03 M.

    Calculate the concentration of a weak base (or its conjugate acid), given its pH, pKb and the concentration of the weak acid (or its conjugate base). Determine the concentration of ammonia in an ammonia buffer with pH of 10.1 and ammonium ion concentration of .98 M, keeping in mind that the Henderson Hasselbalch equation also works for bases--so long as you use pOH instead of pH. Convert your pH to pOH as follows: pOH = 14 - pH = 14 - 10.1 = 3.9. Then, plug in your values to the alkaline buffer equation "pOH = pKb + log[B+] - log [BOH]" as follows: 3.9 = 4.75 + log[.98] - log[BOH] = 4.75 + (-0.009) - log[BOH]. Since log[BOH] = 4.75 - 3.9 - .009 = .841, the concentration of ammonia is the inverse log (10^x) or .841, or 6.93 M.

    Tips

    • You may see two values for carbonic acid when you consult your pKa table. This is because H2CO3 has two hydrogens--and therefore two "protons"--and can dissociate twice, according to the equations H2CO3 + H2O --> HCO3 - + H3O + and HCO3 - + H2O --> CO3 (2-) + H3O. For the purposes of the calculation, you need only consider the first value.

References

About the Author

Robert Schrader is a writer, photographer, world traveler and creator of the award-winning blog Leave Your Daily Hell. When he's not out globetrotting, you can find him in beautiful Austin, TX, where he lives with his partner.

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