The fresh new magnitude of one’s equilibrium ongoing to own an ionization response normally be used to determine the newest relative importance from acids and you can bases. Instance, the entire formula toward ionization out of a failure acidic during the liquids, in which HA is the moms and dad acid and you may Good? are their conjugate legs, can be as employs:
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 acid ionization constant (\(K_a\)), also called the acid dissociation constant:
There was an easy relationships involving the magnitude away from \(K_a\) to own an acid and \(K_b\) for the conjugate legs
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 angles operate which have liquid in order to make this new hydroxide ion, because shown regarding adopting the general formula, in which B is the father or mother ft and you may BH+ was their conjugate acidic:
See the inverse relationships between the electricity of the moms 
and dad acidic plus the electricity of your conjugate base
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 \(\PageIndex<2>\).
Consider, eg, the ionization of hydrocyanic acid (\(HCN\)) in the water to make an acidic service, and also the result of \(CN^?\) having liquids which will make a simple solution:
In such a case, the full total reactions described of the \(K_a\) and you will \(K_b\) is the equation toward autoionization off liquids, and the unit of these two harmony constants was \(K_w\):
Thus whenever we discover sometimes \(K_a\) getting an acidic otherwise \(K_b\) for its conjugate base, we could estimate another harmony constant the conjugate acidbase partners.
Just as with \(pH\), \(pOH\), and you can pKw, we are able to fool around with bad logarithms to eliminate rapid notation in writing acidic and you may legs ionization constants, because of the defining \(pK_a\) 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.