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6.3.6: The Acidity of an Oxoacid is Determined by the Electronegativity and Oxidation State of the Oxoacid's Central Atom*

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    157377
  • Oxyacids (also known as oxoacids) are compounds of the general formula \(\ce{H_{n}EO_{m}}\), where \(\ce{E}\) is a nonmetal or early transition metal and the acidic hydrogens are attached directly to oxygen (not \(\ce{E}\)). This class of compounds includes such well-know acids as nitric acid (\(\ce{HNO_2}\)) and phosphoric acid, (\(\ce{H_3PO_4}\)).

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    The acidity of oxyacids follows three trends:

    Trend 1: In a homologous series the acidity increases with the electronegativity of the central atom

    Elements in the same group frequently form oxyacids of the same general formula. For example, chlorine, bromine, and iodine all form oxyacids of formula \(\ce{HOE}\): hypochlorous, hypobromous and hypoiodous acids. In the case of these homologous oxyacids the acidity is largely determined by the electronegativity of the central element. Central atoms which are better able to inductively pull electron density towards themselves make the oxygen-hydrogen bond that is to be ionized more polar and stablilze the conjugate base, \(OE^-\). Thus the acid strength in such homologous series increases with the electronegativity of the central atom. This may be seen from the data for the hypohalous acids in Table \(\PageIndex{1}\), in which the acid stength increases with the electronegativity of the halogen so that the order of acidity is:

    \[\ce{HClO>HBrO>HIO}\]

    Table \(\PageIndex{1}\): Relationship of central atoms electronegativity to acid ionization constant in the hypohalous acids.
    HOX Electronegativity of X Ka
    HOCl 3.0 4.0 × 10−8
    HOBr 2.8 2.8 × 10−9
    HOI 2.5 3.2 × 10−11

    Note this the influence of central atom electronegativity on the strength of oxyacids is exactly the opposite to that observed for the binary hydrides in Table \(PageIndex{5}\), for which acidity increased down a group giving the order of acidity:

    \[\ce{HI>HBr>HCl \gg HF}\]

    The reason for this is that in the hydrogen halides the bond to be broken (H-E bond) decreased in strength down the group while in oxyacids the bond to be broken is always an O-H bond and so varies much less in strength with the electronegativity of central atom.

    Trend 2: For oxoacids of a given central atom the acidity increases with the central element's oxidation state or, in other words, the number of oxygens bound to the central atom.

    Here we are looking at the trend for acids in which there are variable numbers of oxygen bound to a given central atom. An examples is the perchloric (\(\ce{ClO_4^{-}}\)), chloric (\(\ce{ClO_3^{-}}\)), chlorous (\(\ce{ClO_2^{-}}\)), and hypochlous (\(\ce{ClO^{-}}\)) acid series. In such series the greater the number of oxygens the stronger the acid. This can be explained in several ways. From the viewpoint of the acid itself the key factor is again the inductive effect, in this case involving the ability of the oxygens attached to the central atom to pull on electron density across the OH bond. This is seen from the charge density diagram for the chlorine oxoacids shown in Figure \(\PageIndex{1}\), in which the partial positive charge on the acidic hydrogen increases with the number of oxygens present.

    Figure \(\PageIndex{1}\): Increasing number of oxygens increases Ka as evidenced by the decreased electron density on the acidic hydrogen (which is most blue in HClO4 ). Note, Ka =10-pKa, and so the larger pKa, the smaller Ka. (CC BY-SA-NC; anonymous)

    The increase in oxoacid acidity with the number of oxygens bound to the central atom may also be seen by considering the stability of the conjugate oxyanion. That the stability of the conjugate base increases with the number of oxygens may be seen from the charge distribution diagrams and Lewis bonding models for the chlorine oxyanions shown in figure \(\PageIndex{2}\). As the negative charge is spread over more oxygen atoms it becomes increasingly diffuse.

    99db2ab846ba9253de6cfe75d12abf9c.jpg
    Figure \(\PageIndex{2}\): Increased diffusion of charge in chlorine oxyanions with increasing number of oxygens. The larger the ion the more dispersed the charge and thus the less the charge density, making the perchlorate the most stable anion in the series. Even the simplistic treatment of bonding depicted in the resonance structures correctly show an increased dispersion of the charge density. (CC BY-SA-NC 3.0; anonymous)

    Exercise \(\PageIndex{1}\)

    Sulfur and selenium both forms oxoacids of formula \(\ce{H_2EO_4}\) where E is either S or Se. These are called sulfurous and selenous acid, respectively. Which oxoacid would you expect to be more acidic: selenous acid or sulfurous acid?

    Answer

    Sulfurous acid should be more acidic. Since sulfur is more electronegative than selenium sulfur will polarize OH bonds to a greater extent, making them more acidic. This prediction is borne out by a comparison of the \(pK_a\) values for the acids:

    Acid \(pK_{a1}\) \(pK_{a2}\)
    sulfurous acid, \(H_2SO_3\) 1.85 7.2
    selenous acid, \(H_2SeO_3\) 2.62 8.32

    Trend 3: For polyprotic oxoacids the acidity decreases as each successive proton is removed

    Oxoacids with multiple O-H bonds are called polyprotic since they can donate more than one hydrogen ion. In this case hydrogen ions are removed in successive ionization reactions. Examples include phosphoric and carbonic acid:

    \[H_3PO_4 ⇌ H^+ + H_2PO_4^-~~~~~~~~~~~~~~~pK_{a1} = 2.2\]

    \[H_2PO_4^- ⇌ H^+ + HPO_4^{2-}~~~~~~~~~~~~~~~pK_{a2} = 7.2\]

    \[HPO_4 ⇌ H^+ + PO_4^{3-}~~~~~~~~~~~~~~~pK_{a3} = 12.4\]

    \[H_2CO_3 ⇌ H^+ + HCO_3^-~~~~~~~~~~~~~~~pK_{a1} = 3.6\]

    \[HCO_3^- ⇌ H^+ + CO_3^{2-}~~~~~~~~~~~~~~~pK_{a1} = 10.3\]

    The dissociation constants for successive ionization constants decrease by about five orders of magnitude between successive hydrogen ions. This is reflected in Linus Pauling's rule that for oxoacids and their oxyanions.

    Pauling's Rules

    1. The \(pK_a\) or an oxyacid of general formula \(\ce{E(OH)_{q}(O)_{p}}\) is given by \[pK_a = 8 - 5 \times p \label{PaulingRules}\]
    2. As an oxoaxid undergoes successive ionizations the \(pK_a\) increases by five each time.

    The central theme of Pauling's Rules is that the more oxygen there are on the central atom, the more resonance structure that can be constructed of the conjugate base, which increases it stability and increases the acidity of the acid. However, as the acids successively ionize, they have fewer resonance structure. Pauling's Rules are phenomenological (i.e., not based on a theoretical basis). However, as an empirical rules, they often works quite well, but it should be borne in mind that it is approximate.

    Exercise \(\PageIndex{2}\): How well do Pauling's rules for oxoacids work?

    Calculate the theoretical \(pK_a\) values for phosphoric and carbonic acid and their dissociation produces and compare the results with the experimental \(pK_a\) values.

    Answer

    For phosphoric acid, Pauling's rules (Equation \ref{PaulingRules}) predict the \(pK_a\) values quite well:

    • \(H_3PO_4\): \(p = 3\) and \(q =1\) and \[pK_{a1, predicted} = 8 - 5 \times 1 = 3 \nonumber\] This slightly greater than the observed value of 2.2.
    • \(H_2PO_4^-\): \[pK_{a2, predicted} = pK_{a1, experimental} + 5 = 7.2 \nonumber\] This Spot on with experiment.
    • \(HPO_4^{2-}\): \[pK_{a3, predicted} = pK_{a2, experimental} + 5 = 12.2 \nonumber\]. This is slightly less than the experimental value of 12.4.

    For carbonic acid Pauling's rules predict \(pK_{a1}\) reasonably well, but \(pK_{a2}\) less so:

    • \(H_2CO_3\): \(p = 2\), \(q =1\) and \[pK_{a1, predicted} = 8 - 5 \times 1 = 3 \nonumber\] This is slightly lower than the observed value of 3.6.
    • \(HCO_3^-\): \[pK_{a2, predicted} = pK_{a1, experimental} + 5 = 8.6 \nonumber\] This is 1.7 units less than the experimental value of 10.3.

    In some cases discrepancies between experimental \(pK_a\) values and those predicted by Pauling's rules suggest that structural rearrangements may be taking place upon ionization or else that the reported \(pK_a\) values do not really represent the ionization in question because they do not fully account for all the equilibria taking place in solution. In the case of carbonic acid, however, the reason for the discrepancy between the predicted and experimental \(pK_{a2}\) values is not entirely clear.