To determine which [tex]\( K_a \)[/tex] value represents the weakest acid, we need to understand the relationship between the [tex]\( K_a \)[/tex] value and the strength of an acid. The [tex]\( K_a \)[/tex] value, or acid dissociation constant, measures the extent to which an acid dissociates in water. A lower [tex]\( K_a \)[/tex] value indicates a weaker acid because it dissociates less in water.
Let's compare the given [tex]\( K_a \)[/tex] values:
- [tex]\( K_a = 1.62 \times 10^{-12} \)[/tex]
- [tex]\( K_a = 3.24 \times 10^{-7} \)[/tex]
- [tex]\( K_a = 1.82 \times 10^{-1} \)[/tex]
- [tex]\( K_a = 1.29 \times 10^{-4} \)[/tex]
We are looking for the smallest [tex]\( K_a \)[/tex] value, which represents the weakest acid.
1. [tex]\( 1.62 \times 10^{-12} \)[/tex]
2. [tex]\( 3.24 \times 10^{-7} \)[/tex]
3. [tex]\( 1.82 \times 10^{-1} \)[/tex]
4. [tex]\( 1.29 \times 10^{-4} \)[/tex]
Among these values, [tex]\( 1.62 \times 10^{-12} \)[/tex] is the smallest.
Therefore, the [tex]\( K_a \)[/tex] value that represents the weakest acid is [tex]\( 1.62 \times 10^{-12} \)[/tex]. This corresponds to option A.
So, the answer is:
A. [tex]\( K_a = 1.62 \times 10^{-12} \)[/tex]
