# Consider of the following two acids and their ionization constants. Which conjugate base (HCOO^- or CN^-) is stronger?

## $H C O O H$ ${K}_{a} = 1.7 x {10}^{-} 4$ $H C N$ ${K}_{a} = 4.9 x {10}^{-} 10$

Jan 1, 2017

The stronger the acid, the weaker the conjugate base..........

#### Explanation:

Formic acid is clearly a stronger acid than prussic acid. That is the given equilibrium lies farther to the right:

$H X \left(a q\right) + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + {X}^{-}$

And ${K}_{a} = \frac{\left[{H}_{3} {O}^{+}\right] \left[{X}^{-}\right]}{\left[H X \left(a q\right)\right]}$

SInce ${K}_{a}$ for formic acid is five orders of magnitude greater than $H C \equiv N$, it follows that cyanide ion is a MUCH stronger base than formate.

Given the figures, we could even calculate ${K}_{b}$ for the following reaction:

${A}^{-} + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s H A \left(a q\right) + H {O}^{-}$

We know that in water $p {K}_{a} + p {K}_{b} = 14$. And $p {K}_{b}$ for $N \equiv {C}^{-}$ will THUS BE SMALLER than that for $\text{formate ion}$.