# step three.4: Acid-base ionization constants (Ka and you will Kb relationship)

step three.4: Acid-base ionization constants (Ka and you will Kb relationship)

Brand new magnitude of your equilibrium lingering to own an enthusiastic ionization effect is also be used to determine the newest cousin advantages out-of acids and angles. Such, the entire formula towards the ionization from a faltering acid from inside the liquids, in which HA ‘s the moms and dad acid and you may A? is actually their conjugate legs, is as uses:

As we noted earlier, the concentration of water is essentially constant for all reactions in aqueous solution, so $$[H_2O]$$ in Equation $$\ref<16.5.2>$$ can be incorporated into a new quantity, the Lesbian dating only acid ionization constant ($$K_a$$), also called the acid dissociation constant:

## Discover an easy matchmaking between the magnitude out-of $$K_a$$ getting an acidic and you can $$K_b$$ because of its conjugate foot

Thus the numerical values of K and $$K_a$$ differ by the concentration of water (55.3 M). Again, for simplicity, $$H_3O^+$$ can be written as $$H^+$$ in Equation $$\ref<16.5.3>$$. Keep in mind, though, that free $$H^+$$ does not exist in aqueous solutions and that a proton is transferred to $$H_2O$$ in all acid ionization reactions to form hydronium ions, $$H_3O^+$$. The larger the $$K_a$$, the stronger the acid and the higher the $$H^+$$ concentration at equilibrium. Like all equilibrium constants, acidbase ionization constants are actually measured in terms of the activities of $$H^+$$ or $$OH^?$$, thus making them unitless. The values of $$K_a$$ for a number of common acids are given in Table $$\PageIndex<1>$$.

Weak bases react having water to create the newest hydroxide ion, because shown regarding following standard equation, in which B ‘s the mother base and BH+ is the conjugate acid:

## Notice the inverse matchmaking between the stamina of father or mother acidic and the power of your conjugate ft

Once again, the concentration of water is constant, so it does not appear in the equilibrium constant expression; instead, it is included in the $$K_b$$. The larger the $$K_b$$, the stronger the base and the higher the $$OH^?$$ concentration at equilibrium. The values of $$K_b$$ for a number of common weak bases are given in Table $$\PageIndex<2>$$.

Imagine, such, the ionization out-of hydrocyanic acidic ($$HCN$$) in water to produce an acidic solution, and also the result of $$CN^?$$ which have h2o to manufacture a basic service:

In such a case, the total reactions described because of the $$K_a$$ and you will $$K_b$$ is the picture to your autoionization off h2o, as well as the unit of these two equilibrium constants was $$K_w$$:

Thus if we know often $$K_a$$ having an acid or $$K_b$$ for the conjugate base, we are able to assess one other equilibrium ongoing your conjugate acidbase partners.

Just like $$pH$$, $$pOH$$, and you will pKw, we could use negative logarithms to eliminate exponential notation in writing acidic and base ionization constants, by determining $$pK_a$$ as follows:

The values of $$pK_a$$ and $$pK_b$$ are given for several common acids and bases in Tables $$\PageIndex<1>$$ and $$\PageIndex<2>$$, respectively, and a more extensive set of data is provided in Tables E1 and E2. Because of the use of negative logarithms, smaller values of $$pK_a$$ correspond to larger acid ionization constants and hence stronger acids. For example, nitrous acid ($$HNO_2$$), with a $$pK_a$$ of 3.25, is about a million times stronger acid than hydrocyanic acid (HCN), with a $$pK_a$$ of 9.21. Conversely, smaller values of $$pK_b$$ correspond to larger base ionization constants and hence stronger bases.

Figure $$\PageIndex<1>$$: The Relative Strengths of Some Common Conjugate AcidBase Pairs. The strongest acids are at the bottom left, and the strongest bases are at the top right. The conjugate base of a strong acid is a very weak base, and, conversely, the conjugate acid of a strong base is a very weak acid.

The relative strengths of some common acids and their conjugate bases are shown graphically in Figure $$\PageIndex<1>$$. The conjugate acidbase pairs are listed in order (from top to bottom) of increasing acid strength, which corresponds to decreasing values of $$pK_a$$. This order corresponds to decreasing strength of the conjugate base or increasing values of $$pK_b$$. At the bottom left of Figure $$\PageIndex<2>$$ are the common strong acids; at the top right are the most common strong bases. Thus the conjugate base of a strong acid is a very weak base, and the conjugate base of a very weak acid is a strong base.