Step 1: Understanding the relation between \( K_a \) and base strength.
- The strength of a conjugate base is inversely related to the acid's \( K_a \) value.
- A lower \( K_a \) value means a weaker acid and a stronger conjugate base. Step 2: Arranging the bases.
- \( {HCN} \) has the lowest \( K_a \), meaning \( {CN}^- \) is the strongest base.
- \( {HNO}_2 \) has a moderate \( K_a \), so \( {NO}_2^- \) is a weaker base than \( {CN}^- \).
- \( {HF} \) has the highest \( K_a \), meaning \( {F}^- \) is the weakest base.