Question

the value of ( k_{a} ) for formic acid is ( 1.80\times10^{-4} ). what is the value of ( k_{b} ), for its conjugate base, ( \text{hcoo}^- )?

Explanation:

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

The relationship is \(K_w = K_a\times K_b\), where \(K_w = 1.0\times10^{-14}\) at \(25^{\circ}C\).

Step2: Solve for \(K_b\)

Rearrange the formula to \(K_b=\frac{K_w}{K_a}\). Substitute \(K_w = 1.0\times 10^{-14}\) and \(K_a=1.80\times 10^{-4}\) into the formula:
\(K_b=\frac{1.0\times 10^{-14}}{1.80\times 10^{-4}}\)
\(K_b=\frac{1.0}{1.80}\times10^{-14 + 4}\)
\(K_b\approx5.56\times 10^{-11}\)

Answer:

\(5.56\times 10^{-11}\)