Acetic acid reaction sequence
Step 1: $\alpha$-bromination
$$\ce{CH3-COOH + Br2/P -&gt; Br-CH2-COOH}$$

Step 2: Nucleophilic Substitution by Sodium Cyanide
$$\ce{Br-CH2-COOH + NaCN -&gt; NaBr + NC-CH2-COOH}$$

Step 3: Acid-catalyzed Conversion of Nitrile to Amide or Acid

(1) First hydration... $$\ce{NC-CH2-COOH + H2O -&gt; H2N-CO-CH2-COOH}$$ 
(2) Further heating... $$\ce{H2N-CO-CH2-COOH -&gt; HOOC-CH2-COOH + NH4+}$$

Special Notes

Be VERY CAREFUL with Step 2 as you are potentially forming $\ce{HCN}$ which could get everyone in the lab killed if you're not careful.