Question

Place the species in each of the following groups in order of increasing acid strength. Explain the order you chose for each group. a. \(\mathrm{HIO}_{3}, \mathrm{HBrO}_{3}\) b. \(\mathrm{HNO}_{2}, \mathrm{HNO}_{3}\) c. HOCI, HOI d. \(\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{H}_{3} \mathrm{PO}_{3}\)

Short answer

The species in each group can be arranged in increasing acid strength as follows: a. \(\mathrm{HIO}_{3} < \mathrm{HBrO}_{3}\) - due to the difference in electronegativity between iodine and bromine. b. \(\mathrm{HNO}_{2} < \mathrm{HNO}_{3}\) - due to the difference in the number of oxygen atoms in their conjugate bases. c. \(\mathrm{HOI} < \mathrm{HOCl}\) - due to the difference in electronegativity between iodine and chlorine. d. \(\mathrm{H}_{3} \mathrm{PO}_{3} < \mathrm{H}_{3} \mathrm{PO}_{4}\) - due to the difference in the number of oxygen atoms bonded to the central phosphorous atom.

Step-by-step solution

Group a - Comparison of \(\mathrm{HIO}_{3}\) and \(\mathrm{HBrO}_{3}\)

First, we need to find the conjugate bases of \(\mathrm{HIO}_{3}\) and \(\mathrm{HBrO}_{3}\), which are \(\mathrm{IO}_{3}^{-}\) and \(\mathrm{BrO}_{3}^{-}\), respectively. Now, we compare the stability of these two conjugate bases. As iodine (I) is less electronegative than bromine (Br), the electrons in the \(\mathrm{IO}_{3}^{-}\) will experience less effective nuclear charge than the electrons in the \(\mathrm{BrO}_{3}^{-}\). This means that \(\mathrm{IO}_{3}^{-}\) is less stable compared to \(\mathrm{BrO}_{3}^{-}\). Consequently, \(\mathrm{HIO}_{3}\) is a weaker acid than \(\mathrm{HBrO}_{3}\).

Group b - Comparison of \(\mathrm{HNO}_{2}\) and \(\mathrm{HNO}_{3}\)

The conjugate bases of \(\mathrm{HNO}_{2}\) and \(\mathrm{HNO}_{3}\) are \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NO}_{3}^{-}\), respectively. Here, the difference in the acid strength is due to the difference in the number of oxygen atoms. \(\mathrm{NO}_{3}^{-}\) is more stable than \(\mathrm{NO}_{2}^{-}\) because it has more electron-donating oxygen atoms. This means that \(\mathrm{HNO}_{3}\) is a stronger acid than \(\mathrm{HNO}_{2}\).

Group c - Comparison of \(\mathrm{HOCl}\) and \(\mathrm{HOI}\)

The conjugate bases of \(\mathrm{HOCl}\) and \(\mathrm{HOI}\) are \(\mathrm{OCl}^{-}\) and \(\mathrm{OI}^{-}\), respectively. Chlorine (Cl) is more electronegative than iodine (I), so the electrons in \(\mathrm{OCl}^{-}\) experience a greater effective nuclear charge than the electrons in \(\mathrm{OI}^{-}\). This makes \(\mathrm{OCl}^{-}\) more stable, and thus \(\mathrm{HOCl}\) is a stronger acid than \(\mathrm{HOI}\).

Group d - Comparison of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{H}_{3} \mathrm{PO}_{3}\)

The conjugate bases of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{H}_{3} \mathrm{PO}_{3}\) are \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{H}_{2} \mathrm{PO}_{3}^{-}\), respectively. Here, we need to consider the number of oxygen atoms bonded to the central phosphorous (P) atom. In \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\), there are three oxygen atoms, whereas in \(\mathrm{H}_{2} \mathrm{PO}_{3}^{-}\), there are only two. This makes \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) more stable, which means \(\mathrm{H}_{3} \mathrm{PO}_{4}\) is a stronger acid than \(\mathrm{H}_{3} \mathrm{PO}_{3}\). Now, we arrange the species in each group in increasing acid strength, as follows: a. \(\mathrm{HIO}_{3} < \mathrm{HBrO}_{3}\) b. \(\mathrm{HNO}_{2} < \mathrm{HNO}_{3}\) c. \(\mathrm{HOI} < \mathrm{HOCl}\) d. \(\mathrm{H}_{3} \mathrm{PO}_{3} < \mathrm{H}_{3} \mathrm{PO}_{4}\)

Key concepts

Acid-Base Equilibrium

In the fascinating world of chemistry, understanding acid-base equilibrium is essential. It refers to a chemical equilibrium between acids and their conjugate bases in solution. The acid dissociation constant (Ka) is a quantitative measure of an acid’s strength, representing the equilibrium concentration of the components involved in the reaction.

An acid's Ka value indicates its propensity to donate protons to the base, which means a higher value corresponds to a stronger acid. The equilibrium formula is represented as:
\[\begin{equation}Ka = \frac{[A^-][H^+]}{[HA]}\end{equation}\]
where \begin{itemize} \tem [A^-] is the concentration of the conjugate base, \tem [H^+] is the concentration of the hydrogen ion, and \tem [HA] is the concentration of the acid.\end{itemize}For a strong acid, the equilibrium lies far to the right, signifying almost complete dissociation into its ions, whereas a weak acid only partially dissociates and the equilibrium favors the reactant side.

Conjugate Bases

Diving deeper, we encounter the concept of conjugate bases. When an acid donates a proton, it forms its conjugate base. The strength of the conjugate base has an inverse relationship with the strength of its parent acid - the weaker the acid, the stronger its conjugate base.

Stability and Structure are crucial factors in determining the strength of the conjugate base. A stable conjugate base results from a strong acid because the base is less likely to re-associate with a proton. Factors such as resonance stabilization, electronegativity, and inductive effects all contribute to this stability.

For instance, in the textbook solution, the iodine in \[\begin{equation}\mathrm{IO_3^-}\end{equation}\]is a less electronegative atom compared to bromine in \[\begin{equation}\mathrm{BrO_3^-}\end{equation}\]. It means the electrons in the conjugate base of \[\begin{equation}\mathrm{HIO_3}\end{equation}\] are less tightly held and this base is less stable, making \[\begin{equation}\mathrm{HIO_3}\end{equation}\] a weaker acid than \[\begin{equation}\mathrm{HBrO_3}\end{equation}\].

Electronegativity and Acid Strength

Electronegativity is a property of atoms that is intimately connected to acid strength. It measures an atom’s ability to attract and hold onto electrons. When dealing with acids, the more electronegative an atom attached to a hydroxyl group (-OH), the stronger the acid will be.

The reason ties back to the acid's ability to donate its proton. If the electronegative atom pulls electron density towards itself, the bond to the hydrogen atom weakens, facilitating the release of the proton, thereby increasing the acid's strength. This concept is evident in the comparison between \[\begin{equation}\mathrm{HOCl}\end{equation}\] and \[\begin{equation}\mathrm{HOI}\end{equation}\], where Chlorine's higher electronegativity compared to Iodine's leads to \[\begin{equation}\mathrm{HOCl}\end{equation}\] being a stronger acid.

Additionally, the number of electronegative atoms (like oxygen in oxoacids) affects stability and acid strength. The more electronegative atoms present, the greater the electron-withdrawing effect, the more stable the conjugate base, and therefore, the stronger the parental acid, as shown in \[\begin{equation}\mathrm{HNO_3}\end{equation}\] compared to \[\begin{equation}\mathrm{HNO_2}\end{equation}\].