Can you find [SO₃²⁻] with just the two acid dissociation constants Kₐ₁ and Kₐ₂?

Sulfurous acid, $\ce{H2SO3}$, is a diprotic acid.
\begin{align}
K\_{a1} &= 1.6 \cdot 10^{-2}\\
K\_{a2} &= 6.4 \cdot 10^{-8}\\
\end{align}


Is it possible to find the concentration of $\ce{SO3^2-}$ from this?


I would think you would need to know the concentration of at least one thing. It is like trying to solve for 3 unknowns with 2 equations!




No, it is not possible.


For example, as total concentration of acid approaches zero, concentration of sulfate would also approach zero.


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Here is something I found, on weak polyprotic acids, that I think answers the question:


![enter image description here](https://i.stack.imgur.com/9I2Cu.png)


So then [$\ce{SO3^{2−}}$] $= 6.4 \cdot 10^{-8}$?


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You can use approximations like $K\_\mathrm{a1}$ is much greater than $K\_\mathrm{a2}$ and that first dissociation goes to almost completion. Accurate values cannot be calculated mathematically though.


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