To determine which of the given acids is the weakest, we need to compare their acid dissociation constants ([tex]\( K_a \)[/tex] values). The weaker the acid, the smaller its [tex]\( K_a \)[/tex] value.
Here are the [tex]\( K_a \)[/tex] values for the acids:
- [tex]\( HCN \)[/tex]: [tex]\( K_a = 6.3 \times 10^{-10} \)[/tex]
- [tex]\( HF \)[/tex]: [tex]\( K_a = 6.5 \times 10^{-4} \)[/tex]
- [tex]\( HNO_2 \)[/tex]: [tex]\( K_a = 4.5 \times 10^{-4} \)[/tex]
- [tex]\( HClO \)[/tex]: [tex]\( K_a = 3.0 \times 10^{-8} \)[/tex]
We need to identify the smallest [tex]\( K_a \)[/tex] value among these to find the weakest acid.
1. [tex]\( K_a \)[/tex] of [tex]\( HCN \)[/tex] is [tex]\( 6.3 \times 10^{-10} \)[/tex].
2. [tex]\( K_a \)[/tex] of [tex]\( HF \)[/tex] is [tex]\( 6.5 \times 10^{-4} \)[/tex].
3. [tex]\( K_a \)[/tex] of [tex]\( HNO_2 \)[/tex] is [tex]\( 4.5 \times 10^{-4} \)[/tex].
4. [tex]\( K_a \)[/tex] of [tex]\( HClO \)[/tex] is [tex]\( 3.0 \times 10^{-8} \)[/tex].
Comparing these values:
- [tex]\( 6.3 \times 10^{-10} \)[/tex] is the smallest among [tex]\( 6.3 \times 10^{-10} \)[/tex], [tex]\( 6.5 \times 10^{-4} \)[/tex], [tex]\( 4.5 \times 10^{-4} \)[/tex], and [tex]\( 3.0 \times 10^{-8} \)[/tex].
Therefore, the weakest acid, which corresponds to the smallest [tex]\( K_a \)[/tex] value, is [tex]\( HCN \)[/tex].
Thus, HCN is the weakest acid among the given options.
