Comparing acid strength of oxoacids derived from oxides

Question

Acidic strength has been compared before here and here, but the first question is about organic chemistry (and I am talking about inorganic chemistry), and the second does not discuss molecules such as $\ce{Cl2O7}$, $\ce{P4O10}$, $\ce{CO2}$, $\ce{N2O5}$, $\ce{Al2O3}$ etc. These molecules do not contain hydrogen. So what are the factors which affect their acid or base strength?

The following question brings me this doubt:

Which of the following is the correct order of acidic strength?

(A) $\ce{Cl2O7}$ > $\ce{SO2}$ > $\ce{P4O10}$

(B) $\ce{CO2}$ > $\ce{N2O5}$ > $\ce{SO3}$

(C) $\ce{Na2O}$ > $\ce{MgO}$ > $\ce{Al2O3}$

(D) $\ce{K2O}$ > $\ce{CaO}$ > $\ce{MgO}$

Answer 1

The question quoted in the OP is designed to test a periodic table trend concept.

Particularly, within a given row of the periodic table, excluding noble gases, the element oxides form increasingly acidic aqueous solutions from left to right across the row.

See the lecture by Dr. Pinkington The Acid-Base Character of Oxides and Hydroxides in Aqueous Solution for additional information.

Only answer (A) is increasingly acidic left to right across the periodic table.

Answer 2

Think about the products of each oxides reaction with water. The more electronegative elements will have a stronger attraction to the hydrogen atom's electron, making it easier to ionize. This means that the compounds with a more electronegative central atom will have stronger acidic character.

(A) $\ce{Cl2O7} (3.16) > \ce{SO2}(2.58) > \ce{P4O10}(2.19)$

(B) $\ce{CO2}(2.55) > \ce{N2O5}(3.04) > \ce{SO3}(2.58)$

(C)$\ce{Na2O}(0.93) > \ce{MgO}(1.31) > \ce{Al2O3}(1.61)$

(D) $\ce{K2O}(0.82) > \ce{CaO}(1.0) > \ce{MgO}(1.31)$

I've included the electronegativities of the central atom of each compound. The only answer that shows the compounds with decreasing central atom electronegativity is A, so it is therefore the answer. This also explains why C and D are incorrect.

Also I should note that the amount of oxygens on an oxyacid does affect its acidity. As oxygen is a very electronegative atom, the presence of additional oxygens will increase the acidity of the hydrogens in oxyacids. As a general rule though, the strongest weak oxyacid of an electronegative atom will be stronger than the strongest weak oxyacid of a less electronegative atom of the same period. This explains why B is incorrect (no oxyacid of carbon will be more acidic than an oxyacid of the more electronegative nitrogen).

Answer 3

Orthocresol is correct, $\mathrm{p}K_\mathrm{a}$ is only used for Bronsted acids. But you can use a $\mathrm{p}K_\mathrm{a}$ argument if you assume these compounds are allowed to react with water. Lets start with the covalent oxides in (A). Allowing these compounds to react with $\ce{H2O}$ produces $\ce{HClO4}$, $\ce{H2SO3}$, and $\ce{H3PO4}$. When comparing the $\mathrm{p}K_\mathrm{a}$s, remember lower numbers imply greater acidity. A qualitative explanation could be based on electronegativity (which is affected by oxidation state), and resonance stabilization of the conjugate base. The more resonance structures the conjugate base has, the more stable it is. A more stable conjugate base implies greater acidity. The same logic can be used to compounds in (B).

Mixing metal oxides with water produce metal hydroxides and aqua acids (depending on the pH of the water). The acidity of the $\ce{OH}$ fragment is dependent on the metal's ability to withdraw electron density. Typically, complexes with more electronegative metals are more acidic.