Question

a solution is made by dissolving 35.5 g of ba(no₂)₂ in 500.0 ml of water.
what is the value of kb for no₂⁻? the ka of hno₂ is 4.5 × 10⁻⁴.

Explanation:

Step1: Recall the relationship between \(K_a\), \(K_b\) and \(K_w\)

For a conjugate acid - base pair, \(K_w=K_a\times K_b\), where \(K_w = 1.0\times10^{-14}\) at \(25^{\circ}C\)

Step2: Solve for \(K_b\)

We know that \(K_b=\frac{K_w}{K_a}\)
Substitute \(K_w = 1.0\times 10^{-14}\) and \(K_a=4.5\times 10^{-4}\) into the formula
\(K_b=\frac{1.0\times 10^{-14}}{4.5\times 10^{-4}}\)
\(K_b = 2.2\times10^{-11}\)

Answer:

\(2.2\times10^{-11}\)