Derivation of buffer capacity

The reaction is:

$\ce{HA <=> H+ + A-}$

They have given that:

But shouldn't $C_{buf}=[HA]+[A^-]+[H^+]$ ?

The total concentration at equilibrium is $c(1-\alpha)+2c\alpha=c(1+\alpha)\neq c$. Hence the initial concentration of buffer is different from that at equilibrium.

• you asked a question, then you replied correctly. The quantity of matter is conserved. – Yomen Atassi Sep 4 '15 at 18:55
• I don't understand. Does that mean they have given wrong equation? I have proved that its different in the last line. – Aditya Dev Sep 4 '15 at 19:15
• At the equilibrium, [HA]=c(1−α) and [A-]=cα. The quantity of matter of the specie A is conserved. So, the total amount of all species having A is c. So, c=[HA]+[A-]=c(1−α)+cα – Yomen Atassi Sep 4 '15 at 21:23