To know the connection in between acid or base strength and the magnitude of (K_a), (K_b), (pK_a), and (pK_b). To understand also the leveling result.

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The magnitude of the equilibrium consistent for an ionization reaction have the right to be supplied to identify the family member staminas of acids and bases. For instance, the basic equation for the ionization of a weak acid in water, wright here HA is the parent acid and also A− is its conjugate base, is as follows:

The equilibrium consistent for this dissociation is as follows:


As we detailed previously, the concentration of water is essentially consistent for all reactions in aqueous solution, so () in Equation ( ef16.5.2) deserve to be included right into a brand-new amount, the acid ionization constant ((K_a)), additionally called the acid dissociation constant:

=dfrac label16.5.3>

Therefore the numerical worths of K and (K_a) differ by the concentration of water (55.3 M). Aacquire, for simplicity, (H_3O^+) can be written as (H^+) in Equation ( ef16.5.3). Keep in mind, though, that cost-free (H^+) does not exist in aqueous options and also that a proton is moved to (H_2O) in all acid ionization reactions to form hydronium ions, (H_3O^+). The bigger the (K_a), the more powerful the acid and the greater the (H^+) concentration at equilibrium. Like all equilibrium constants, acid–base ionization constants are actually measured in terms of the activities of (H^+) or (OH^−), hence making them unitmuch less. The worths of (K_a) for a variety of widespread acids are offered in Table (PageIndex1).

Table (PageIndex1): Values of (K_a), (pK_a), (K_b), and (pK_b) for Selected Acids ((HA) and Their Conjugate Bases ((A^−)) Acid(HA)(K_a)(pK_a)(A^−)(K_b)(pK_b) *The number in parentheses indicates the ionization step referred to for a polyprotic acid.
hydroiodic acid (HI) (2 imes 10^9) −9.3 (I^−) (5.5 imes 10^−24) 23.26
sulfuric acid (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 acid (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 with water to develop the hydroxide ion, as presented in the adhering to general equation, wbelow B is the parent base and also BH+ is its conjugate acid:

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

= frac label16.5.5>

Once again, the concentration of water is constant, so it does not show up in the equilibrium continuous expression; instead, it is had in the (K_b). The bigger the (K_b), the more powerful the base and also the higher the (OH^−) concentration at equilibrium. The worths of (K_b) for a number of prevalent weak bases are offered in Table (PageIndex2).

Table (PageIndex2): Values of (K_b), (pK_b), (K_a), and (pK_a) for Schosen Weak Bases (B) and also Their Conjugate Acids (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 straightforward relationship in between the magnitude of (K_a) for an acid and (K_b) for its conjugate base. Consider, for instance, the ionization of hydrocyanic acid ((HCN)) in water to produce an acidic solution, and the reaction of (CN^−) through water to develop an easy solution:

The equilibrium continuous expression for the ionization of HCN is as follows:


The equivalent expression for the reactivity of cyanide through water is as follows:


If we add Equations ( ef16.5.6) and also ( ef16.5.7), we obtain the following:

Reactivity 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 situation, the amount of the reactions explained by (K_a) and (K_b) is the equation for the autoionization of water, and the product of the two equilibrium constants is (K_w):

Thus if we know either (K_a) for an acid or (K_b) for its conjugate base, we can calculate the other equilibrium consistent for any conjugate acid–base pair.

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Just as through (pH), (pOH), and also pKw, we can usage negative logarithms to prevent exponential notation in writing acid and base ionization constants, by specifying (pK_a) as follows:

and (pK_b) as

Similarly, Equation ( ef16.5.10), which expresses the relationship between (K_a) and also (K_b), deserve to be created in logarithmic create as follows:

At 25 °C, this becomes

The values of (pK_a) and also (pK_b) are given for a number of widespread acids and bases in Tables (PageIndex1) and (PageIndex2), respectively, and also an extra comprehensive set of data is gave in Tables E1 and E2. Due to the fact that of the usage of negative logarithms, smaller sized values of (pK_a) correspond to bigger acid ionization constants and hence more powerful acids. For example, nitrous acid ((HNO_2)), via a (pK_a) of 3.25, is about a million times more powerful acid than hydrocyanic acid (HCN), through a (pK_a) of 9.21. Conversely, smaller sized values of (pK_b) correspond to larger base ionization constants and also thus more powerful bases.