I cannot for the life of me figure this out. Please help and show the steps if p

Question

I cannot for the life of me figure this out. Please help and show the steps if possible. Thank you in advance.

For a 0.50 M H2SO3, which in aqueous solutions gives H2SO3, HSO3-, and SO32-, it can be said that [H2SO3]o = F (formal concentration) = 0.50 M = [H2SO3]aq + [HSO3-]aq + [SO32-]aq. The fraction of each species is given by   ao = [H2SO3] / F, a1 = HSO3-] / F, and a2 = [SO32-] / F respectively. Write down all possible fractions of CH3COOH given the formal concentration of acetic acid F = 0.550 M.

Explanation / Answer

H2SO3 <------------> H+ + HSO3- , Ka= 0.0139 ( value taken from wikipedia)

initially [H2SO3]=0.5, [H+]=[HSO3-] =0, at equi [H2SO3] = 0.5-x , [H+]=[HSO3-] = x,

Ka =[H+[SO3-]/[H2SO3]

0.0139 = x^2/( 0.5-x)

solving we get x = 0.0767 =[H+]

now fractions [H2SO3] = ( 0.5-0.0767)/0.5 = 0.8466 ,

fraction H+ = (0.767/0.5 = 0.1534 = fraction of HSO3-

2) CH3COOH <------> CH3COO -   + H+

at eqi [CH3COOH] = 0.55-x , [H+][=CH3COO-] = x,   Ka = 1.738 x10^ -5 ( from wiki)

Ka = 1.73 x10^ -5 = x^2/(0.55-x)

x = 0.00308 ,

now fraction of CH3COOH = ( 0.55-0.00308)/0.5 = 0.9944

Fraction of H+=fraction of CH3COO- =0.00308/0.55 = 0.0056

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