To understand the relationship in between acid or basic strength and also the magnitude of (K_a), (K_b), (pK_a), and also (pK_b). To know the leveling effect.

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The size of the equilibrium continuous for one ionization reaction have the right to be supplied to identify the family member strengths of acids and also bases. Because that example, the general equation for the ionization of a weak acid in water, whereby HA is the parental acid and also A− is its conjugate base, is as follows:

The equilibrium continuous for this dissociation is as follows:


As we noted earlier, the concentration of water is essentially continuous for all reactions in aqueous solution, so () in Equation ( ef16.5.2) can be incorporated into a brand-new quantity, the acid ionization continuous ((K_a)), also called the acid dissociation constant:

=dfrac label16.5.3>

Thus the numerical worths of K and (K_a) different by the concentration that water (55.3 M). Again, because that simplicity, (H_3O^+) have the right to be composed as (H^+) in Equation ( ef16.5.3). Keep in mind, though, that cost-free (H^+) does not exist in aqueous solutions and that a proton is moved to (H_2O) in all mountain ionization reactions to type hydronium ions, (H_3O^+). The bigger the (K_a), the stronger the acid and the greater the (H^+) concentration in ~ equilibrium. Favor all equilibrium constants, acid–base ionization constants space actually measured in terms of the tasks of (H^+) or (OH^−), hence making lock unitless. The worths of (K_a) because that a number of common acids are offered in Table (PageIndex1).

Table (PageIndex1): worths of (K_a), (pK_a), (K_b), and (pK_b) because that Selected acids ((HA) and also Their Conjugate Bases ((A^−)) Acid(HA)(K_a)(pK_a)(A^−)(K_b)(pK_b) *The number in parentheses suggests the ionization step described for a polyprotic acid.
hydroiodic acid (HI) (2 imes 10^9) −9.3 (I^−) (5.5 imes 10^−24) 23.26
sulfuric mountain (1)* (H_2SO_4) (1 imes 10^2) −2.0 (HSO_4^−) (1 imes 10^−16) 16.0
nitric acid (HNO_3) (2.3 imes 10^1) −1.37 (NO_3^−) (4.3 imes 10^−16) 15.37
hydronium ion (H_3O^+) (1.0) 0.00 (H_2O) (1.0 imes 10^−14) 14.00
sulfuric mountain (2)* (HSO_4^−) (1.0 imes 10^−2) 1.99 (SO_4^2−) (9.8 imes 10^−13) 12.01
hydrofluoric acid (HF) (6.3 imes 10^−4) 3.20 (F^−) (1.6 imes 10^−11) 10.80
nitrous acid (HNO_2) (5.6 imes 10^−4) 3.25 (NO2^−) (1.8 imes 10^−11) 10.75
formic acid (HCO_2H) (1.78 imes 10^−4) 3.750 (HCO_2−) (5.6 imes 10^−11) 10.25
benzoic acid (C_6H_5CO_2H) (6.3 imes 10^−5) 4.20 (C_6H_5CO_2^−) (1.6 imes 10^−10) 9.80
acetic acid (CH_3CO_2H) (1.7 imes 10^−5) 4.76 (CH_3CO_2^−) (5.8 imes 10^−10) 9.24
pyridinium ion (C_5H_5NH^+) (5.9 imes 10^−6) 5.23 (C_5H_5N) (1.7 imes 10^−9) 8.77
hypochlorous acid (HOCl) (4.0 imes 10^−8) 7.40 (OCl^−) (2.5 imes 10^−7) 6.60
hydrocyanic acid (HCN) (6.2 imes 10^−10) 9.21 (CN^−) (1.6 imes 10^−5) 4.79
ammonium ion (NH_4^+) (5.6 imes 10^−10) 9.25 (NH_3) (1.8 imes 10^−5) 4.75
water (H_2O) (1.0 imes 10^−14) 14.00 (OH^−) (1.00) 0.00
acetylene (C_2H_2) (1 imes 10^−26) 26.0 (HC_2^−) (1 imes 10^12) −12.0
ammonia (NH_3) (1 imes 10^−35) 35.0 (NH_2^−) (1 imes 10^21) −21.0

Weak bases react v water to produce the hydroxide ion, as displayed in the complying with general equation, whereby B is the parent base and also BH+ is that conjugate acid:

The equilibrium consistent for this reaction is the base ionization consistent (Kb), also called the base dissociation constant:

= frac label16.5.5>

Once again, the concentration the water is constant, so the does not show up in the equilibrium constant expression; instead, that is contained in the (K_b). The larger the (K_b), the stronger the base and also the higher the (OH^−) concentration in ~ equilibrium. The worths of (K_b) for a number of common weak bases are offered in Table (PageIndex2).

Table (PageIndex2): worths of (K_b), (pK_b), (K_a), and also (pK_a) for Selected Weak Bases (B) and also Their Conjugate mountain (BH+) Base (B) (K_b) (pK_b) (BH^+) (K_a) (pK_a) *As in Table (PageIndex1).
hydroxide ion (OH^−) (1.0) 0.00* (H_2O) (1.0 imes 10^−14) 14.00
phosphate ion (PO_4^3−) (2.1 imes 10^−2) 1.68 (HPO_4^2−) (4.8 imes 10^−13) 12.32
dimethylamine ((CH_3)_2NH) (5.4 imes 10^−4) 3.27 ((CH_3)_2NH_2^+) (1.9 imes 10^−11) 10.73
methylamine (CH_3NH_2) (4.6 imes 10^−4) 3.34 (CH_3NH_3^+) (2.2 imes 10^−11) 10.66
trimethylamine ((CH_3)_3N) (6.3 imes 10^−5) 4.20 ((CH_3)_3NH^+) (1.6 imes 10^−10) 9.80
ammonia (NH_3) (1.8 imes 10^−5) 4.75 (NH_4^+) (5.6 imes 10^−10) 9.25
pyridine (C_5H_5N) (1.7 imes 10^−9) 8.77 (C_5H_5NH^+) (5.9 imes 10^−6) 5.23
aniline (C_6H_5NH_2) (7.4 imes 10^−10) 9.13 (C_6H_5NH_3^+) (1.3 imes 10^−5) 4.87
water (H_2O) (1.0 imes 10^−14) 14.00 (H_3O^+) (1.0^*) 0.00

There is a simple relationship in between the size of (K_a) for an acid and also (K_b) because that its conjugate base. Consider, for example, the ionization the hydrocyanic acid ((HCN)) in water to produce an acidic solution, and also the reaction the (CN^−) v water to create a simple solution:

The equilibrium continuous expression because that the ionization that HCN is as follows:


The corresponding expression because that the reaction that cyanide through water is together follows:


If we include Equations ( ef16.5.6) and ( ef16.5.7), we attain the following:

Reaction Equilibrium Constants
(cancelHCN_(aq) ightleftharpoons H^+_(aq)+cancelCN^−_(aq) ) (K_a=cancel/cancel)
(cancelCN^−_(aq)+H_2O_(l) ightleftharpoons OH^−_(aq)+cancelHCN_(aq)) (K_b=cancel/cancel)
(H_2O_(l) ightleftharpoons H^+_(aq)+OH^−_(aq)) (K=K_a imes K_b=)

In this case, the sum of the reactions described by (K_a) and (K_b) is the equation for the autoionization that water, and the product the the two equilibrium constants is (K_w):

Thus if we recognize either (K_a) because that an acid or (K_b) because that its conjugate base, we have the right to calculate the other equilibrium consistent for any kind of conjugate acid–base pair.

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Just as with (pH), (pOH), and pKw, we can use an adverse logarithms to avoid exponential notation in writing acid and also base ionization constants, by specifying (pK_a) together follows:

and (pK_b) as

Similarly, Equation ( ef16.5.10), i beg your pardon expresses the relationship in between (K_a) and (K_b), have the right to be created in logarithmic kind as follows:

At 25 °C, this becomes

The worths of (pK_a) and also (pK_b) are provided for several common acids and bases in Tables (PageIndex1) and also (PageIndex2), respectively, and also a more extensive set of data is detailed in Tables E1 and E2. Due to the fact that of the usage of an adverse logarithms, smaller values of (pK_a) correspond to bigger acid ionization constants and hence more powerful acids. Because that example, nitrous mountain ((HNO_2)), through a (pK_a) that 3.25, is about a million times stronger acid than hydrocyanic mountain (HCN), with a (pK_a) the 9.21. Conversely, smaller values that (pK_b) exchange mail to bigger base ionization constants and also hence stronger bases.