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Why do different $\ce{H}$ atoms in a polyprotic acid have different values of $\pu{K_a}$?

All $\ce{H}$ atoms (which can show acidic nature) have similar properties within the molecule. It does not matter which one reacts. For example, in $\ce{H3PO4}$, all the $\ce{H}$ atoms can be dissociated from the molecule to act as acids. All of them are attached to an $\ce{O}$ atom, which is attached to the central $\ce{P}$ atom. If all the properties are same, then why is $\pu{K_a}$ different?

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You are correct that all of the $\ce{H}$'s in $\ce{H3PO4}$ are equivalent.

However, once the first H is removed, the remaining two $\ce{H}$'s are no longer equivalent to the $\ce{H}$'s in the original $\ce{H3PO4}$. After the initial deprotination, the molecule gains an overall negative charge making it more difficult to remove the second $\ce{H}$. Then when the second $\ce{H}$ is removed the molecule gains a second negative charge making it even more difficult to remove the final $\ce{H}$. Thus, the $K_a$ values for the originally identical $\ce{H}$'s change each time the molecule is deprotinated.

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Consider $\ce{H3PO4}$. $K_{a1}$ and $K_{a2}$ for $\ce{H3PO4}$ are different because they concern different chemical species: $K_{a1}$ deals with the $\ce{H3PO4}$/$\ce{H2PO4-}$ equilibrium, whereas $K_{a2}$ deals with the $\ce{H2PO4-}$/$\ce{HPO4^2-}$ equilibrium.

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