Write the equation for dissocation of acetic acid in water:

Question

My Answer:
CH2COOH + H2O <=> H3O+ + CH3COO-

Equation for hydrolysis of acetate anion in water:
My Answer:
CH3COO- + H2O <=> CH3COOH + OH-

Now, using the above formulas, I have to show how a buffer works when:

a. Some dilute NaOH is added to buffer containing both CH3COOH and CH3COO-
My answer:
CH3COOH + CH3COO- + NaOH <=> CH3COONa + CH3COO- + H2O

b. Some dilute hydrochloric acid is added to buffer containing both CH3COOH and CH3COO-
My answer:
CH3COOH + CH3COO- + HCl <=> CH3COOH + CH3COOH + Cl-

Can my answers please be checked? (I believe (b) is wrong). Thanks ahead of time!

They look ok to me except for the first equation in which you made a typo. It should be CH3COOH and not CH2COOH.
Your answer to a shows that CH3COOH is neutralized by the added NaOH and the CH3COO- is unaffected. Your answer to b shows that the HCl reacts with the CH3COO^- ion to produce CH3COOH leaving the CH3COOH already there unaffected. This would pass my grading standards.

Thanks for looking it over and for the explanation!