# what is another name for the acid dissociation constant?

The magnitude of the equilibrium fixed for an ionization response can be utilized to find out the relative strengths of acids and bases. For instance, the overall equation for the ionization of a weak acid in water, the place HA is the guardian acid and A− is its conjugate base, is as follows:

[HA_{(aq)}+H_2O_{(l)} rightleftharpoons H_3O^+_{(aq)}+A^−_{(aq)} label{16.5.1}]

You're reading: what is another name for the acid dissociation constant?

The equilibrium fixed for this dissociation is as follows:

[K=dfrac{[H_3O^+][A^−]}{[H_2O][HA]} label{16.5.2}]

As we famous earlier, the focus of water is basically fixed for all reactions in aqueous answer, so ([H_2O]) in Equation (ref{16.5.2}) might be integrated into a brand new amount, the acid ionization fixed ((K_a)), additionally referred to as the acid dissociation fixed:

[K_a=K[H_2O]=dfrac{[H_3O^+][A^−]}{[HA]} label{16.5.3}]

Thus the numerical values of Ok and (K_a) differ by the focus of water (55.3 M). Once more, for simplicity, (H_3O^+) might be written as (H^+) in Equation (ref{16.5.3}). Be mindful, although, that free (H^+) doesn’t exist in aqueous options and {that a} proton is transferred to (H_2O) in all acid ionization reactions to type hydronium ions, (H_3O^+). The bigger the (K_a), the stronger the acid and the upper the (H^+) focus at equilibrium. Like all equilibrium constants, acid-base ionization constants are literally measured by way of the actions of (H^+) or (OH^−), thus making them unitless. The values of (K_a) for plenty of widespread acids are given in Desk (PageIndex{1}).

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

Weak bases react with water to supply the hydroxide ion, as proven within the following basic equation, the place B is the guardian base and BH+ is its conjugate acid:

[B_{(aq)}+H_2O_{(l)} rightleftharpoons BH^+_{(aq)}+OH^−_{(aq)} label{16.5.4}]

The equilibrium fixed for this response is the bottom ionization fixed (Kb), additionally referred to as the bottom dissociation fixed:

[K_b=K[H_2O]= frac{[BH^+][OH^−]}{[B]} label{16.5.5}]

As soon as once more, the focus of water is fixed, so it doesn’t seem within the equilibrium fixed expression; as an alternative, it’s included within the (K_b). The bigger the (K_b), the stronger the bottom and the upper the (OH^−) focus at equilibrium. The values of (K_b) for plenty of widespread weak bases are given in Desk (PageIndex{2}).

Desk (PageIndex{2}): Values of (K_b), (pK_b), (K_a), and (pK_a) for Chosen Weak Bases (B) and Their Conjugate Acids (BH+) Base (B) (K_b) (pK_b) (BH^+) (K_a) (pK_a) *As in Desk (PageIndex{1}). hydroxide ion (OH^−) (1.0) 0.00* (H_2O) (1.0 instances 10^{−14}) 14.00 phosphate ion (PO_4^{3−}) (2.1 instances 10^{−2}) 1.68 (HPO_4^{2−}) (4.8 instances 10^{−13}) 12.32 dimethylamine ((CH_3)_2NH) (5.4 instances 10^{−4}) 3.27 ((CH_3)_2NH_2^+) (1.9 instances 10^{−11}) 10.73 methylamine (CH_3NH_2) (4.6 instances 10^{−4}) 3.34 (CH_3NH_3^+) (2.2 instances 10^{−11}) 10.66 trimethylamine ((CH_3)_3N) (6.3 instances 10^{−5}) 4.20 ((CH_3)_3NH^+) (1.6 instances 10^{−10}) 9.80 ammonia (NH_3) (1.8 instances 10^{−5}) 4.75 (NH_4^+) (5.6 instances 10^{−10}) 9.25 pyridine (C_5H_5N) (1.7 instances 10^{−9}) 8.77 (C_5H_5NH^+) (5.9 instances 10^{−6}) 5.23 aniline (C_6H_5NH_2) (7.4 instances 10^{−10}) 9.13 (C_6H_5NH_3^+) (1.3 instances 10^{−5}) 4.87 water (H_2O) (1.0 instances 10^{−14}) 14.00 (H_3O^+) (1.0^*) 0.00

There’s a easy relationship between the magnitude of (K_a) for an acid and (K_b) for its conjugate base. Contemplate, for instance, the ionization of hydrocyanic acid ((HCN)) in water to supply an acidic answer, and the response of (CN^−) with water to supply a primary answer:

[HCN_{(aq)} rightleftharpoons H^+_{(aq)}+CN^−_{(aq)} label{16.5.6}]

[CN^−_{(aq)}+H_2O_{(l)} rightleftharpoons OH^−_{(aq)}+HCN_{(aq)} label{16.5.7}]

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

[K_a=dfrac{[H^+][CN^−]}{[HCN]} label{16.5.8}]

The corresponding expression for the response of cyanide with water is as follows:

[K_b=dfrac{[OH^−][HCN]}{[CN^−]} label{16.5.9}]

If we add Equations (ref{16.5.6}) and (ref{16.5.7}), we get hold of the next:

Response Equilibrium Constants (cancel{HCN_{(aq)}} rightleftharpoons H^+_{(aq)}+cancel{CN^−_{(aq)}} ) (K_a=[H^+]cancel{[CN^−]}/cancel{[HCN]}) (cancel{CN^−_{(aq)}}+H_2O_{(l)} rightleftharpoons OH^−_{(aq)}+cancel{HCN_{(aq)}}) (K_b=[OH^−]cancel{[HCN]}/cancel{[CN^−]}) (H_2O_{(l)} rightleftharpoons H^+_{(aq)}+OH^−_{(aq)}) (Ok=K_a instances K_b=[H^+][OH^−])

On this case, the sum of the reactions described by (K_a) and (K_b) is the equation for the autoionization of water, and the product of the 2 equilibrium constants is (K_w):

[K_aK_b = K_w label{16.5.10}]

Thus if we all know both (K_a) for an acid or (K_b) for its conjugate base, we will calculate the opposite equilibrium fixed for any conjugate acid-base pair.

Simply as with (pH), (pOH), and pKw, we will use unfavourable logarithms to keep away from exponential notation in writing acid and base ionization constants, by defining (pK_a) as follows:

[pKa = −log_{10}K_a label{16.5.11}]

[K_a=10^{−pK_a} label{16.5.12}]

and (pK_b) as

[pK_b = −log_{10}K_b label{16.5.13}]

[K_b=10^{−pK_b} label{16.5.14}]

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Equally, Equation (ref{16.5.10}), which expresses the connection between (K_a) and (K_b), might be written in logarithmic type as follows:

[pK_a + pK_b = pK_w label{16.5.15}]

At 25 °C, this turns into

[pK_a + pK_b = 14.00 label{16.5.16}]

The values of (pK_a) and (pK_b) are given for a number of widespread acids and bases in Tables (PageIndex{1}) and (PageIndex{2}), respectively, and a extra in depth set of knowledge is supplied in Tables E1 and E2. Due to the usage of unfavourable logarithms, smaller values of (pK_a) correspond to bigger acid ionization constants and therefore stronger acids. For instance, nitrous acid ((HNO_2)), with a (pK_a) of three.25, is about 1,000,000 instances stronger acid than hydrocyanic acid (HCN), with a (pK_a) of 9.21. Conversely, smaller values of (pK_b) correspond to bigger base ionization constants and therefore stronger bases.

The relative strengths of some widespread acids and their conjugate bases are proven graphically in Determine (PageIndex{1}). The conjugate acid-base pairs are listed so as (from high to backside) of accelerating acid power, which corresponds to reducing values of (pK_a). This order corresponds to reducing power of the conjugate base or growing values of (pK_b). On the backside left of Determine (PageIndex{2}) are the widespread robust acids; on the high proper are the most typical robust bases. Discover the inverse relationship between the power of the guardian acid and the power of the conjugate base. Thus the conjugate base of a robust acid is a really weak base, and the conjugate base of a really weak acid is a robust base.

The conjugate base of a robust acid is a weak base and vice versa.

We are able to use the relative strengths of acids and bases to foretell the course of an acid-base response by following a single rule: an acid-base equilibrium at all times favors the facet with the weaker acid and base, as indicated by these arrows:

[text{stronger acid + stronger base} ce{ <=>>} text{weaker acid + weaker base} ]

In an acid-base response, the proton at all times reacts with the stronger base.

For instance, hydrochloric acid is a robust acid that ionizes primarily utterly in dilute aqueous answer to supply (H_3O^+) and (Cl^−); solely negligible quantities of (HCl) molecules stay undissociated. Therefore the ionization equilibrium lies nearly all the way in which to the suitable, as represented by a single arrow:

[HCl_{(aq)} + H_2O_{(l)} rightarrow H_3O^+_{(aq)}+Cl^−_{(aq)} label{16.5.17}]

In distinction, acetic acid is a weak acid, and water is a weak base. Consequently, aqueous options of acetic acid comprise largely acetic acid molecules in equilibrium with a small focus of (H_3O^+) and acetate ions, and the ionization equilibrium lies far to the left, as represented by these arrows:

[ ce{ CH_3CO_2H_{(aq)} + H_2O_{(l)} <<=> H_3O^+_{(aq)} + CH_3CO_{2(aq)}^- }]

Equally, within the response of ammonia with water, the hydroxide ion is a robust base, and ammonia is a weak base, whereas the ammonium ion is a stronger acid than water. Therefore this equilibrium additionally lies to the left:

[H_2O_{(l)} + NH_{3(aq)} ce{ <<=>} NH^+_{4(aq)} + OH^-_{(aq)}]

All acid-base equilibria favor the facet with the weaker acid and base. Thus the proton is sure to the stronger base.