Question

use the references to access important values

$k_{a}$ for nitrous acid, $hno_{2}$, is $4.50 \times 10^{-4}$.

$k_{a}$ for phenol (a weak acid), $c_{6}h_{5}oh$, is $1.00 \times 10^{-10}$.

$k_{a}$ for benzoic acid, $c_{6}h_{5}cooh$, is $6.30 \times 10^{-5}$.

what is the formula for the weakest conjugate base?

Explanation:

Step1: Recall the relationship between acid strength and conjugate base strength

The stronger the acid, the weaker its conjugate base. Mathematically, \(K_a\times K_b = K_w=1.0\times10^{-14}\). So, a larger \(K_a\) value for an acid means a smaller \(K_b\) value (weaker base) for its conjugate base.

Step2: Compare the \(K_a\) values of the given acids

Given \(K_a(HNO_2)=4.50\times 10^{-4}\), \(K_a(C_6H_5OH) = 1.00\times 10^{-10}\), \(K_a(C_6H_5COOH)=6.30\times 10^{-5}\).
Since \(4.50\times 10^{-4}>6.30\times 10^{-5}>1.00\times 10^{-10}\), \(HNO_2\) is the strongest acid among the three.

Step3: Determine the formula of the conjugate base of the strongest acid

The conjugate - base of \(HNO_2\) is formed by the loss of \(H^+\) from \(HNO_2\). Using the formula \(HA
ightleftharpoons H^++A^-\), for \(HNO_2\), the conjugate base is \(NO_2^-\).

Answer:

\(NO_2^-\)