Question

What are the equilibrium concentrations of H2SO3, H+, HSO3−, and SO32−in a 0.050 M solution of sulfurous acid H2SO3 at 25 oC? For H2SO3 at 25 oC, Ka1 = 1.5×10−2 and Ka2 = 1.0×10−7

Answer 1

What are the equilibrium concentrations of H2SO3, H+, HSO3-, and SO32-in a 0.050 M solution of sulfurous acid H2SO3 at 25 oC? For H2SO3 at 25 oC, Ka1 = 1.5×10-2 and Ka2 = 1.0×10-7.

**Solution:**

$$\mathrm{H_2SO_3} \leftrightarrow \mathrm{H^+} + \mathrm{HSO_3^-}$$ $$K_{a1} = \frac{[\mathrm{H^+}][\mathrm{HSO_3^-}]}{[\mathrm{H_2SO_3}]}$$

From this equation $[\mathrm{H^+}][\mathrm{HSO_3^-}] = K_{a1} \cdot [\mathrm{H_2SO_3}] = 1.5 \cdot 10^{-2} \cdot 0.050 = 7.5 \cdot 10^{-4}$.

The concentration of $\mathrm{H^+} = \mathrm{HSO_3^-} = \sqrt{7.5 \cdot 10^{-4}} = 2.738 \cdot 10^{-2} \, \mathrm{M}$.

$$\mathrm{HSO_3^-} \leftrightarrow \mathrm{H^+} + \mathrm{SO_3^{2-}}$$ $$K_{a2} = \frac{[\mathrm{H^+}][\mathrm{SO_3^{2-}}]}{[\mathrm{HSO_3^-}]}.$$

So, $[\mathrm{H^+}][\mathrm{SO_3^{2-}}] = K_{a2} \cdot [\mathrm{HSO_3^-}] = 1.0 \cdot 10^{-2} \cdot 2.738 \cdot 10^{-2} = 2.738 \cdot 10^{-9}$.

The concentration of $\mathrm{H^+} = \mathrm{SO_3^{2-}} = \sqrt{2.738 \cdot 10^{-9}} = 5.23 \cdot 10^{-5} \, \mathrm{M}$.

**Answer:**

The equilibrium concentrations in 0.050 M solution are:

$$[\mathrm{H_2SO_3}] = 5 \cdot 10^{-2} - 2.738 \cdot 10^{-2} = 2.262 \cdot 10^{-2} \, \mathrm{M};$$ $$[\mathrm{H^+}] = 2.738 \cdot 10^{-2} + 5.23 \cdot 10^{-5} = 2.743 \cdot 10^{-2} \, \mathrm{M},$$ $$[\mathrm{HSO_3^-}] = 2.738 \cdot 10^{-2} - 5.23 \cdot 10^{-5} = 2.733 \cdot 10^{-2} \, \mathrm{M}, \text{ and}$$ $$[\mathrm{SO_3^{2-}}] = 5.23 \cdot 10^{-5} \, \mathrm{M}.$$