Question

$K _{ u }$ values for acids $H _{2} SO _{3}, HNO _{2}, CH _{3} COOH$ and $HCN$ are respectively $1.3 \times 10^{-2}, 4 \times 10^{-4}, 1.8 \times 10^{-5}$ and $4 \times 10^{-10}$, which of the above acids produces stronger conjugate base in aqueous solution?

• A. $H_2SO_3$
• B. $HNO_2$
• C. $CH_3COOH$
• D. $HCN$

Answer 1

The Correct Option is D

The strength of a conjugate base is inversely related to the strength of its corresponding acid. This means that as the acid becomes weaker, its conjugate base becomes stronger. The strength of an acid is represented by its dissociation constant, \(K_a\). A lower \(K_a\) value indicates a weaker acid.

Given the \(K_a\) values: 

• \(H_2SO_3\): \(1.3 \times 10^{-2}\)
• \(HNO_2\): \(4 \times 10^{-4}\)
• \(CH_3COOH\): \(1.8 \times 10^{-5}\)
• \(HCN\): \(4 \times 10^{-10}\)

From these values, \(HCN\) has the smallest \(K_a\) value. Therefore, it is the weakest acid among the given options, making its conjugate base, \(CN^-\), the strongest.

Let's summarize why \(HCN\) is the correct answer:

• The smallest \(K_a\) value corresponds to \(HCN\), making it the weakest acid.
• The weaker the acid, the stronger its conjugate base.
• Hence, \(CN^-\), derived from \(HCN\), is the strongest conjugate base among the options.