$pK_a$ та $pK_b$

When we studied equilibrium, we calculated the equilibrium constants. We derived them from the reaction rate and the forward and reverse reactions' rate laws. We used them both qualitatively and quantitatively. Qualitatively, we interpreted the magnitude of $K_{eq}$ and predicted the direction of chemical reactions. Quantitatively, we calculated the solution concentrations at equilibrium.

Now we've started learning about acids and bases. We can distinguish between strong and weak acids and bases. Strong ones fully dissociate. So, the pH of strong acids is typically low. In contrast, the weak ones are in equilibrium. Because we have equilibrium reactions, the pH of weak acids is typically higher. Remember, chemists are unbelievably creative. So, for acids, we call it the acid dissociation constant. And for bases, we call it the base dissociation constant. We denote them with $pK_{a}$ and $pK_{b}$.

Why "p" ?

The first thing you probably noticed is that we have a "p" in front of the constant. Remember, the "p" notation means "take the negative logarithm." For example, pH is the negative log of hydrogen ion concentration, $-log{[H^{+}]}$. But why do we use it for dissociation constants? Because chemists are lazy. Let's look at an example.

Consider carbonic acid. Remember, its a polyprotic acid. The balanced chemical equation is $H_{2}CO_{3} \rightleftharpoons H^{+} + HCO_{3}^{-} \rightleftharpoons H^{+} + CO_{3}^{2-}$. For the first dissociation, $K_{a1}=4.3\times10^{-7}$ and $pK_{a1}=6.35$. For the second dissociation, $K_{a2}=4.7\times10^{-11}$ and $pK_{a2}=10.33$. Now we have to answer a couple questions. Which is easier to write? The $pK_{a}$. Which is easier to compare? Again, $pK_{a}$.

Interpreting and Comparing $pK_{a}$

Just like we interpreted the equilibrium constant, we can interpret dissociations constants. The first thing to notice is if $pK_{a}$ is positive or negative. Positive tells us we have a weak acid or base. So, we know we have an equilibrium reaction. A negative number indicates a strong acid or base. It fully dissociates. So, the product concentration is much larger than the reactant. For example, the $pK_{a}$ of hydrochloric acid is -6.3. Let's converted that to $K_{a}$. $K_{a}=10^{-pK_{a}}=10^{-(-6.3)}=1,995,262.31$. The $K_{a}$ values of the strong acids are essentially meaningless because they're so large. They only tell you that it fully dissociates.

For the weak acids, the magnitude of the $pK_{a}$ tells us about strength. For example, let's compare acetic acid ($CH_{3}COOH$) and chloroacetic acid ($ClCH_{2}COOH$). For acetic acid, $pK_{a}=4.76$. For chloroacetic acid, $pK_{a}=2.87$. Which will dissociate more? A larger $pK_{a}$ equals less dissociation. So, chloroacetic acid dissociates more. Do you know why replacing hydrogen with chlorine increases acidity? The halogens are all very electronegative. The chlorine pulls oxygen's electron density towards it. Because chlorine draws the electrons, the electrostatic attraction between oxygen and hydrogen diminishes. The oxygen-hydrogen bond breaks more easily!

The size of the $pK_{a}$ also tells us about direction. Remember, acid dissociations are just equilibrium constants. So, they are still, $\frac{[Products]}{[Reactants]}$. But now we've added the negative logarithm. What does that do? Unfortunately, it makes us have to think for half a second. Earlier, I said that a more positive $pK_{a}$ means the acid dissociates less. It's weaker! So, the reaction leans more towards the products. Let's look at the math.

Let's say we had an acid with $K_{a}=\frac{1}{1000}=0.001$. So, the reactant concentration is 1000 times larger than the product concentration. What's the $pK_{a}$? It's $pK_{a}=-log{(K_{a})}=-log{(0.001)}=3$. Here, we could also convert to scientific notation ($0.001\rightarrow 1.0\times10^{-3}$). So, we see that the larger the positive number, the more the reaction favors the reactants.

(Video) 18.2 Ka, pKa, Kb, pKb, Kw, pKw (HL)

by Mike Sugiyama Jones

In this short video, Mike Jones explains acid and base dissociation constants. You'll learn the relationships between the equilibrium constants and the dissociation constants. You'll also learn to compare the magnitude of the constants. This is an excellent short video for understanding acid-base equilibrium constants.