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
To find the equilibrium concentrations of H2SO3, H+, HSO3−, and SO32− in a 0.050 M solution of sulfurous acid (H2SO3) at 25 oC, we need to use the given equilibrium constants (Ka1 and Ka2) and the initial concentration of H2SO3.
Step 1: Write the balanced chemical equation representing the dissociation of H2SO3.
H2SO3 ⇌ H+ + HSO3−
Step 2: Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of the species involved in the equilibrium.
H2SO3 ⇌ H+ + HSO3−
Initial: 0.050 M 0 M 0 M
Change: -x M +x M +x M
Equilibrium: 0.050 - x M x M x M
Step 3: Write the expressions for equilibrium constants (Ka1 and Ka2) using the equilibrium concentrations (x) of the species.
Ka1 = [H+][HSO3−] / [H2SO3]
Ka2 = [SO32−][H+] / [HSO3−]
Step 4: Substitute the equilibrium concentrations into the equilibrium constant expressions.
Ka1 = x * x / (0.050 - x)
Ka2 = x * (0.050 - x) / x
Step 5: Plug in the given equilibrium constants (Ka1 = 1.5×10^−2 and Ka2 = 1.0×10^−7) into the respective equations for Ka1 and Ka2.
1.5×10^−2 = x * x / (0.050 - x)
1.0×10^−7 = x * (0.050 - x) / x
Step 6: Solve the above equations for x using algebraic manipulation or numerical methods. Once you find the value of x, substitute it back into the equilibrium expressions to calculate the equilibrium concentrations of H2SO3, H+, HSO3−, and SO32−.
This process may involve rearranging and solving quadratic equations or using numerical methods such as calculators or computer programs.
Note: The process described above is a simplified explanation. In practice, the calculations might be more involved due to the presence of the second equilibrium constant (Ka2) and possible additional dissociation reactions.