To recognize the relationship in between acid or base toughness and also the magnitude of (K_a), (K_b), (pK_a), and (pK_b). To understand also the leveling effect.

You are watching: Calculate the acid ionization constant ka for the acid

The magnitude of the equilibrium consistent for an ionization reactivity deserve to be provided to identify the loved one toughness of acids and bases. For example, the general equation for the ionization of a weak acid in water, where HA is the parent acid and also A− is its conjugate base, is as follows:

The equilibrium continuous for this dissociation is as follows:

label16.5.2>

As we listed previously, the concentration of water is essentially constant for all reactions in aqueous solution, so () in Equation ( ef16.5.2) have the right to be included into a new amount, the acid ionization continuous ((K_a)), also referred to as the acid dissociation constant:

=dfrac label16.5.3>

Hence the numerical values of K and (K_a) differ by the concentration of water (55.3 M). Aacquire, for simplicity, (H_3O^+) have the right to be created as (H^+) in Equation ( ef16.5.3). Keep in mind, though, that free (H^+) does not exist in aqueous options and that a proton is moved to (H_2O) in all acid ionization reactions to create hydronium ions, (H_3O^+). The larger the (K_a), the stronger the acid and also the higher the (H^+) concentration at equilibrium. Like all equilibrium constants, acid–base ionization constants are actually measured in terms of the tasks of (H^+) or (OH^−), hence making them unitmuch less. The worths of (K_a) for a number of common acids are offered in Table (PageIndex1).

Table (PageIndex1): Values of (K_a), (pK_a), (K_b), and (pK_b) for Selected Acids ((HA) and also Their Conjugate Bases ((A^−)) Acid(HA)(K_a)(pK_a)(A^−)(K_b)(pK_b) *The number in parentheses indicates 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 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 through water to develop the hydroxide ion, as shown in the complying with basic equation, wbelow B is the parent base and also BH+ is its conjugate acid:

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

= frac label16.5.5>

Once aacquire, the concentration of water is consistent, so it does not show up in the equilibrium consistent expression; instead, it is contained in the (K_b). The bigger the (K_b), the stronger the base and also the greater the (OH^−) concentration at equilibrium. The values of (K_b) for a variety of prevalent weak bases are provided in Table (PageIndex2).

Table (PageIndex2): Values of (K_b), (pK_b), (K_a), and also (pK_a) for Schosen Weak Bases (B) and 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 connection between the magnitude of (K_a) for an acid and also (K_b) for its conjugate base. Consider, for example, the ionization of hydrocyanic acid ((HCN)) in water to produce an acidic solution, and also the reactivity of (CN^−) with water to create an easy solution:

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

label16.5.8>

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

label16.5.9>

If we include Equations ( ef16.5.6) and also ( ef16.5.7), we obtain 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 situation, the amount of the reactions described by (K_a) and also (K_b) is the equation for the autoionization of water, and the product of the two equilibrium constants is (K_w):

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

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Just as with (pH), (pOH), and also pKw, we can usage negative logarithms to stop exponential notation in composing acid and base ionization constants, by defining (pK_a) as follows:

and (pK_b) as

Similarly, Equation ( ef16.5.10), which expresses the relationship between (K_a) and (K_b), can be created in logarithmic form as follows:

At 25 °C, this becomes

The worths of (pK_a) and also (pK_b) are given for numerous common acids and bases in Tables (PageIndex1) and (PageIndex2), respectively, and an extra extensive collection of data is gave in Tables E1 and E2. Because of the use of negative logarithms, smaller sized worths of (pK_a) correspond to bigger acid ionization constants and thus stronger acids. For instance, nitrous acid ((HNO_2)), through a (pK_a) of 3.25, is around a million times stronger acid than hydrocyanic acid (HCN), via a (pK_a) of 9.21. Conversely, smaller sized worths of (pK_b) correspond to larger base ionization constants and hence stronger bases.