By Sunil Bhardwaj

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Consider a buffer solution containing an acid, HA and its salt $${ Na }^{ + }$$ and $${ A }^{ - }$$. Ionization of weak acid may be represented as, $$HA + { H }_{ 2 }O \rightleftharpoons { H }_{ 3 }{ O }^{ + } + { A }^{ - }\qquad ...(1)$$ The ionization constant is given by, $${ K }_{ a } = \frac { \left[ { H }_{ 3 }{ O }^{ + } \right] \left[ { A }^{ - } \right] }{ \left[ HA \right] } \qquad ...(2)$$ or $$\left[ { H }_{ 3 }{ O }^{ + } \right] = { K }_{ a }\frac { \left[ HA \right] }{ \left[ { A }^{ - } \right] }$$ lets take negative log, $$-log \left[ { H }_{ 3 }{ O }^{ + } \right] = -log { K }_{ a } - log\frac { \left[ HA \right] }{ \left[ { A }^{ - } \right] }$$ $$pH = p{ K }_{ a } + log\frac { \left[ { A }^{ - } \right] }{ \left[ HA \right] }$$ $$or pH = p{ K }_{ a } + log\frac { \left[ Salt \right] }{ \left[ Acid \right] } \qquad ...(3)$$ This is handersons equation. Similarly for bases we can write,$$pH = p{ K }_{ b } + log\frac { \left[ Salt \right] }{ \left[ Base \right] } \qquad ...(4)$$

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