# pH, pKa, Ka, pKb, Kb

## Key Questions

• $\text{p"K_"a}$ and $\text{p"K_"b}$ are measures of the strengths of acids and bases, respectively

Acids

When you dissolve an acid in water, it undergoes an equilibrium reaction with the water in an.

HA + H₂O ⇌ H₃O⁺ + A⁻

The value of the equilibrium constant is given by

K_"a" = (["H"_3"O"^+]["A"^-]]/["HA"]

The greater the value of ${K}_{\text{a}}$, the stronger the acid.

For most weak acids, ${K}_{\text{a}}$ ranges from ${10}^{-} 2$ to ${10}^{-} 14$.

We convert these exponential numbers into a normal range by taking their negative logarithm.

The operator $\text{p}$ means "take the negative logarithm of".

So $\text{p"K_"a" = -logK_"a}$.

For most weak acids, $\text{p"K_"a}$ ranges from 2 to 14.

Thus, the smaller the value of $\text{p"K_"a}$ , the stronger the acid.

Bases

When you dissolve a base in water, it reacts with the water in an equilibrium reaction.

B + H₂O ⇌ BH⁺ + OH⁻

The value of the equilibrium constant is given by

K_"b" = (["BH"^+]["OH"^-]]/["B"]

The greater the value of ${K}_{\text{b}}$, the stronger the base.

For most weak acids, ${K}_{\text{b}}$ ranges from ${10}^{-} 2$ to ${10}^{-} 13$.

$\text{p"K_"b" = -logK_"b}$.

For most weak acids, $\text{p"K_"a}$ ranges from 2 to 13.

The smaller the value of $\text{p"K_"b}$ , the stronger the base.

Here's a video on $\text{p"K_"a}$ and $\text{p"K_"b}$.

These are measures of acidity and basicity...

#### Explanation:

And acid in aqueous solution is conceived to undergo a protonolysis reaction...

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

And as for any equilibrium, we can measure and quantify it in the usual way...

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

Note that ${H}_{2} O$ DOES NOT appear in the equilibrium expression because it is present in such high concentration that it is effectively constant..

For strong acids, i.e. $H I$, $H B r$, $H C l$, ${H}_{2} S {O}_{4}$ protonolysis is effectively quantitative: the given equilibrium lies entirely to the right as we face the page, and the acid solution is quantitative in ${H}_{3} {O}^{+}$. For weaker acids, $H F$, ${H}_{3} C - C {O}_{2} H$, the equilibrium lies somewhat to the left...and concentrations of the parent acid remain at equilibrium.

And likewise, we can formalize the performance of a base by an equivalent equilibrium...we use ammonia, because this is a WEAK base in aqueous solution...

$N {H}_{3} \left(a q\right) + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s N {H}_{4}^{+} + H {O}^{-}$

And ${K}_{b}$ is defined in an equivalent way to ${K}_{a}$...

${K}_{b} = \frac{\left[N {H}_{4}^{+}\right] \left[H {O}^{-}\right]}{\left[N {H}_{3} \left(a q\right)\right]}$, ${K}_{b} \text{(ammonia)} = 1.74 \times {10}^{-} 5$...

Confused yet....?

Well, note that NECESSARILY....for a given acid/conjugate pair, say $N {H}_{4}^{+} \text{/} N {H}_{3}$...

${K}_{a} {K}_{b} = {10}^{-} 14$...or perhaps more usefully...

$p {K}_{a} + p {K}_{b} = 14$...

• The pH scale provides a way of measuring how acidic or basic solutions are. The scale ranges from 0-14. A pH of 0 is the most acidic, 7 is neutral and 14 is the most basic.

Here is a video of a lab which looks at a number of different solutions and measures their pH levels using a pH meter and an indicator.

video from: Noel Pauller