To determine which of the given [tex]\( K_a \)[/tex] values represents the weakest acid, we need to understand what the [tex]\( K_a \)[/tex] value indicates. The [tex]\( K_a \)[/tex] value is the acid dissociation constant, which measures the strength of an acid in solution. Specifically, it quantifies the extent to which an acid can donate protons (H[tex]\(^+\)[/tex]) in water. The smaller the [tex]\( K_a \)[/tex] value, the weaker the acid, because it only partially dissociates in water.
Let's compare the given [tex]\( K_a \)[/tex] values:
- A. [tex]\( K_a = 1.82 \times 10^{-1} \)[/tex]
- B. [tex]\( K_a = 3.24 \times 10^{-7} \)[/tex]
- C. [tex]\( K_a = 1.29 \times 10^{-4} \)[/tex]
- D. [tex]\( K_a = 1.62 \times 10^{-12} \)[/tex]
From the list, we observe the following:
1. [tex]\( K_a \)[/tex] value of [tex]\( 1.82 \times 10^{-1} \)[/tex] (Option A) is relatively large.
2. [tex]\( K_a \)[/tex] value of [tex]\( 3.24 \times 10^{-7} \)[/tex] (Option B) is significantly smaller than Option A but larger than the others.
3. [tex]\( K_a \)[/tex] value of [tex]\( 1.29 \times 10^{-4} \)[/tex] (Option C) is larger than Option B.
4. [tex]\( K_a \)[/tex] value of [tex]\( 1.62 \times 10^{-12} \)[/tex] (Option D) is extremely small, much smaller than all the other options.
So, the smallest [tex]\( K_a \)[/tex] value in the given options is [tex]\( 1.62 \times 10^{-12} \)[/tex].
The smallest [tex]\( K_a \)[/tex] value corresponds to the weakest acid because it shows the least tendency to donate protons. Therefore, the weakest acid among the given options corresponds to:
D. [tex]\( K_a = 1.62 \times 10^{-12} \)[/tex]
So, the correct answer is Option D.
