The answer is correct. The methodology is not.You made several errors (equation, Ka expression wrong, etc and other errors in substitution but all of the errors canceled out to give you the correct answer). Use the Henderson-Hasselbalch equation.
pH = pKa + log (base/acid)
pH = 3.40 + log(0.2/0.15) = 3.52
Buffers- Common Ion effect
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Calculate the pH of a aqueous solution containing 0.15 M HNO2 and 0.20 M NaNO2 (aq). The Ka of nitrous acid is 4.0*10^-4.
HNO2 + H20 <--> NaNO2- + H30^+
Inital 0.15 0.20 X
Final 0.15 0.20
Ka= [H30+][NaNO2]/ [HNO2]
4.0*10^-4 = [H30+][0.20]/[0.15]
3.0*10^ -4 = H30+
pH= 3.52
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