# Derive an equation similar to the Henderson–Hasselbalch equation for a buffer composed of a weak base and its conjugate acid. Instead of relating pH to pKa and the relative concentrations of an acid and its conjugate base (as the Henderson– Hasselbalch equation does), the equation should relate pOH to pKa and the relative concentrations of a base and its conjugate acid.

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Derive an equation similar to the Henderson–Hasselbalch equation for a buffer composed of a weak base and its conjugate acid. Instead of relating pH to pKa and the relative concentrations of an acid and its conjugate base (as the Henderson– Hasselbalch equation does), the equation should relate pOH to pKa and the relative concentrations of a base and its conjugate acid.

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Step 1

Henderson Hasselbalch equation is one that relates pH of buffer with ionization constants of the weak electrolyte.

For a buffer consisting of weak acid and its conjugate base, pH of buffer is expressed as :

pH = pKa + log[Conjugate base]/[Weak Acid]

Step 2

For a buffer consisting of weak base and its salt with strong acid, the pH is expressed as:

pOH = pKb + log [Conjugate acid]/[Weak base]

For a weak base, B, which forms  BH+ as its conjugate acid, the above expression can be derived as: Step 3

Now,  if Kb is ionization constant for weak base and Ka is ionization constant of its conjugate acid,

Ka *Kb = 10-14.

Taking negative logarithm both sides,

-log(Ka *Kb) = -log(10-14)

-log Ka + (-log Kb) = 14

pKa + pKb = 14

So, pKb = 14- pKa

Substituting 'pKb' by '14-pKa' in expression deri...

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