Find the value of Ka for the conjugate acid of the following...

Find the value of $K_{\mathrm{a}}$ for the conjugate acid of the following bases.
(a) pyridine, a pesticide; $K_{\mathrm{b}}=1.5 \times 10^{-9}$
(b) aniline, an important dye intermediate; $K_{\mathrm{b}}=3.8 \times 10^{-10}$

Key Concepts

Ionization Constant of Water (Kw)

Kw is the equilibrium constant for the self-ionization of water, representing the product of the concentrations of hydrogen ions and hydroxide ions in water. At 25°C, Kw is typically 1.0 × 10?¹?. This constant is essential in acid–base equilibrium calculations, particularly in relating Ka and Kb for conjugate acid-base pairs.

Conjugate Acid-Base Pairs

This concept refers to a pair of chemical species that differ by a proton (H?). When a base accepts a proton, it becomes its conjugate acid, and when an acid donates a proton, it becomes its conjugate base. Understanding this relationship is crucial in acid–base chemistry as it allows one to relate the strengths of acids and bases in a reversible reaction.

Relationship between Ka and Kb

For any conjugate acid–base pair, the acid dissociation constant (Ka) of the conjugate acid and the base dissociation constant (Kb) of the base are related by the equation Ka × Kb = Kw. This relationship is fundamental because it provides a method to calculate one equilibrium constant if the other is known, using the ionization constant of water.

Transcript

00:01 For this problem, we're given four compounds, four different portions of a question, and we're given information about those compounds, and we want to determine the values that we're being asked for.

00:13 So, for example, in the first one, we want to find the kb of the lactate ion, given the ka of lactic acid is 1 .4 times 10 to the negative 4.

00:23 So we know that ka times kb equals kw.

00:32 And we know that kw equals 1 times 10 to the negative 14th.

00:37 So now we have two pieces of information.

00:40 So far we have kw and we have the ka of lactic acid.

00:46 And we're asked to find the kb.

00:48 So we can just plug in values for this problem.

00:51 So we're solving for kb.

00:52 We have the ka of 1 .4 times 10 to the negative 4th, and then we have our kw, which is 1 times 10 to the negative 14th.

01:05 So all we need to do is get kb by itself.

01:08 So we divide both sides by 1 .4 times 10 to the negative 4th.

01:13 Same thing for this value.