Problem 113 - Chemistry and Chemical Reactivity

Question

The halogens form three stable, weak acids, HOX. $$\begin{array}{ll}\text { Acid } & \mathrm{pK}_{\mathrm{a}} \\\\\hline \mathrm{HOCl} & 7.46 \\\\\mathrm{HOBr} & 8.7 \\ \mathrm{HOI} & 10.6 \\\\\hline\end{array}$$ (a) Which is the strongest of these acids? (b) Explain why the acid strength changes as the halogen atom is changed.

Step-by-Step Solution

Answer

(a) HOCl is the strongest acid. (b) The acid strength changes due to differences in electronegativity, with more electronegative halogens stabilizing the conjugate base more effectively.

Step 1: Understanding Acid Strength and pKa Values

The acid dissociation constant (\( K_a \)) measures an acid's strength; the smaller the \( pK_a \) value, the stronger the acid. This is because \( pK_a \) is the negative logarithm of \( K_a \), so a lower \( pK_a \) indicates a higher \( K_a \), meaning the acid ionizes more completely in water.

Step 2: Compare pKa Values of HOX Acids

We are given the \( pK_a \) values: \(\mathrm{HOCl} = 7.46\), \(\mathrm{HOBr} = 8.7\), and \(\mathrm{HOI} = 10.6\). To determine which acid is the strongest, we compare the \( pK_a \) values. The acid with the lowest \( pK_a \) value is the strongest.

Step 3: Identify the Strongest Acid

Among the acids, \(\mathrm{HOCl}\) has the smallest \( pK_a \) value of 7.46. Therefore, \(\mathrm{HOCl}\) is the strongest acid of the three.

Step 4: Explain Acid Strength Differences

The strength of these acids changes with different halogen atoms due to differences in electronegativity and the stability of the conjugate base. A more electronegative central atom (halogen) stabilizes the conjugate base by drawing electron density away, thus allowing the acid to donate a proton more easily.

Key Concepts

pKa Values

The concept of pKa values is essential when discussing acid strength. A pKa value is derived from the acid dissociation constant (Ka). It represents the strength of an acid in a solution. The pKa is calculated as the negative logarithm (base 10) of the Ka, given by the formula:\[pK_a = -\log(K_a)\\]A lower pKa value indicates a stronger acid, meaning the acid more readily releases its proton in solution. In the case of the halogen acids, we observe pKa values as follows:

• HOCl: 7.46
• HOBr: 8.7
• HOI: 10.6

Among these, HOCl has the lowest pKa value, making it the strongest acid. This is because it dissociates more in water, releasing more hydrogen ions.

Halogen Acids

Halogen acids are a group of binary acids composed of hydrogen, oxygen, and a halogen from Group 17 of the periodic table. In the case of the described acids, HOX (where X represents Cl, Br, or I), the strength varies notably. As we move down the halogen group in the periodic table — from chlorine to bromine to iodine — we observe changes in acid behavior.

• HOCl is the strongest, reflecting chlorine's high electronegativity.
• HOBr is weaker, followed by HOI, the weakest.

The variation in acid strength among halogen acids is partly due to the varying electronegativities of the halogen atoms. Chlorine's greater electronegativity helps stabilize the conjugate base after proton donation, making HOCl a stronger acid compared to the others. This behavior shows how the nature of halogen acids is influenced by their respective halogen components.

Acid Dissociation Constant

The acid dissociation constant, denoted Ka, is a vital measure describing an acid's ability to donate protons in a given environment or solution. It represents the equilibrium constant for the dissociation of an acid into its ions. The larger the value of Ka, the more an acid dissociates completely, which demonstrates its strength.In mathematical terms:\[K_a = \frac{[H^+][A^-]}{[HA]}\\]Here, \([H^+]\) and \([A^-]\) are the concentrations of the hydrogen ion and conjugate base, while \([HA]\) is the concentration of the undissociated acid. Therefore, a higher Ka value translates to a stronger acid. When comparing halogen acids like HOCl, HOBr, and HOI, analyzing their Ka and thus their pKa values helps predict which will dissociate more readily in water, which is a significant factor in understanding acid strength.