Final answer:
CN⁻ is the stronger base when compared to F⁻ because the stronger acid (HF) has the weaker conjugate base (F⁻), and HCN is a weaker acid than HF.
Step-by-step explanation:
The question asks which is the stronger base between the conjugate bases of HF and HCN, which are F⁻ and CN⁻, respectively. When considering the acidity of the corresponding acids (HF and HCN), we can refer to their ionization constants.
HF is a stronger acid than HCN, meaning that the conjugate base of HF, which is F⁻, is a weaker base than CN⁻. The stronger acid has the weaker conjugate base, so the answer is that CN⁻ is the stronger base compared to F⁻.
This is because the ability of an atom to stabilize a negative charge is related to its electronegativity, and while fluorine is highly electronegative and can stabilize the negative charge well (making F⁻ a relatively weak base), CN⁻ does not have such a highly electronegative atom to stabilize the charge (making it a relatively stronger base).