To determine which of the species is the strongest base given the acid strength series [tex]\( HCN < HF < HSO_4^- \)[/tex], we need to examine the conjugate bases of each acid. Remember, the strength of a conjugate base is inversely proportional to the strength of its acid; that is, a weaker acid has a stronger conjugate base.
Here are the acids and their corresponding conjugate bases:
1. [tex]\( HCN \)[/tex] (weakest acid) -> [tex]\( CN^- \)[/tex] (conjugate base)
2. [tex]\( HF \)[/tex] -> [tex]\( F^- \)[/tex] (conjugate base)
3. [tex]\( HSO_4^- \)[/tex] (strongest acid) -> [tex]\( SO_4^{2-} \)[/tex] (conjugate base)
The strength of the conjugate bases correlates inversely with acid strength:
- Since [tex]\( HCN \)[/tex] is the weakest acid, its conjugate base [tex]\( CN^- \)[/tex] will be the strongest base.
- [tex]\( HF \)[/tex], being a stronger acid than [tex]\( HCN \)[/tex] but weaker than [tex]\( HSO_4^- \)[/tex], has [tex]\( F^- \)[/tex] as its conjugate base which is less basic than [tex]\( CN^- \)[/tex] but more basic than [tex]\( SO_4^{2-} \)[/tex].
- [tex]\( HSO_4^- \)[/tex], the strongest acid among the three, has [tex]\( SO_4^{2-} \)[/tex] as a very weak conjugate base.
Given these points, the strongest base among the conjugate bases ([tex]\( CN^- \)[/tex], [tex]\( F^- \)[/tex], [tex]\( SO_4^{2-} \)[/tex]) is [tex]\( CN^- \)[/tex].
Therefore, the correct answer is:
D. [tex]\( CN^- \)[/tex]
