Question

Rank the following acids in order of increasing acidity: ${\mathrm{CH}}_3\mathrm{COOH},{\mathrm{CH}}_2\mathrm{ClCOOH},{\mathrm{CHCl}}_2\mathrm{COOH},{\mathrm{CCl}}_3\mathrm{COOH}$, ${\mathrm{CF}}_3\mathrm{COOH}$. [Section 16.10]

Short answer

The ranking of the given acids in order of increasing acidity is: $C{H}_{3}COOH<C{H}_{2}ClCOOH<CHC{l}_{2}COOH<CC{l}_{3}COOH<C{F}_{3}COOH$. This is based on the stability of their conjugate bases, which is influenced by the electronegativity and inductive effect of the halogen atoms in the functional groups.

Step-by-step solution

Identify the conjugate base of each acid

Lose a proton (H+) from each carboxylic acid to obtain its conjugate base: - $C{H}_{3}CO{O}^{-}$: conjugate base of CH_3COOH - $C{H}_{2}ClCO{O}^{-}$: conjugate base of CH_2ClCOOH - $CHC{l}_{2}CO{O}^{-}$: conjugate base of CHCl_2COOH - $CC{l}_{3}CO{O}^{-}$: conjugate base of CCl_3COOH - $C{F}_{3}CO{O}^{-}$: conjugate base of CF_3COOH

Analyze the effect of electronegativity and inductive effect on the stability of the conjugate bases

A more stable conjugate base results in a stronger acid. The impact of the different functional groups on the stability of the conjugate bases can be understood through the electronegativity and inductive effect of the halogen atoms. - Halogens (Cl or F) are more electronegative than carbon and thus pull electron density towards themselves. This effect, known as the inductive effect, increases with the number of halogen atoms. - The electronegativity of fluorine is greater than that of chlorine. Therefore, the trifluoromethyl group has a stronger inductive effect than the trichloromethyl group.

Rank the conjugate bases according to stability

Based on the inductive effect discussed above, we can rank the stability of the conjugate bases as follows: Least stable: $C{H}_{3}CO{O}^{-}$ (alkyl group, no inductive effect) < $C{H}_{2}ClCO{O}^{-}$ < $CHC{l}_{2}CO{O}^{-}$ < $CC{l}_{3}CO{O}^{-}$ (trichloromethyl group, strong inductive effect) < $C{F}_{3}CO{O}^{-}$ (trifluoromethyl group, strongest inductive effect) Most stable

Determine the ranking of the acids according to acidity

Since the stability of the conjugate base is directly proportional to the acidity of their corresponding acid, the final ranking of the acids according to increasing acidity is: Least acidic: CH_3COOH (corresponding to least stable conjugate base) < CH_2ClCOOH < CHCl_2COOH < CCl_3COOH < CF_3COOH (corresponding to most stable conjugate base) Most acidic

Key concepts

Conjugate Base Stability

The stability of a conjugate base is crucial in determining the strength of its parent acid. When an acid loses a proton, it forms its conjugate base. If this base is stable, it means that the acid is stronger since the equilibrium favors the dissociation into its ions. Factors that affect conjugate base stability include the presence of electronegative atoms and groups that can stabilize negative charges. For example, atoms like fluorine or chlorine, due to their high electronegativity, help stabilize the negative charge by drawing electron density towards themselves through an inductive effect. This overall stability directly implies that the parent acid is strong. In the examples given, the more halogen atoms present, the more stable the conjugate base, which correlates to a more robust acid.

Electronegativity

Electronegativity is a measure of an atom's ability to attract electron density towards itself. It plays a pivotal role in the strength of an acid because it affects the stability of the conjugate base. As seen in the example acids, atoms like fluorine (F) and chlorine (Cl) are very electronegative. This property allows them to pull electrons towards themselves, which can stabilize the conjugate base's negative charge. The higher the electronegativity of a substituent atom within the molecule, the more stable the resulting conjugate base becomes. Consequently, the acid becomes stronger. This is why molecules such as trifluoroacetic acid ( CF_3COOH ) are very strong acids; the electronegativity of the fluorine atoms strongly stabilizes the conjugate base.

Inductive Effect

The inductive effect refers to the transmission of charge through a chain of atoms in a molecule, primarily influencing the molecule's reactivity and stability. This effect is a key factor in acid strength. Atoms like chlorine and fluorine induce a strong pulling effect on electrons through sigma bonds, thereby stabilizing negative charges on the conjugate base. In the provided examples, each additional halogen atom enhances the inductive effect, leading to increased stability of the conjugate base and thus stronger acids. For instance, CCl_3COOH displays a notably strong inductive effect due to the presence of three chlorine atoms pulling electron density away from the conjugate base, effectively stabilizing it and increasing the acid's overall strength.

Carboxylic Acids

Carboxylic acids are a category of organic acids characterized by the presence of a carboxyl group ( -COOH ). They are versatile and common in both nature and industrial applications. The acidity of carboxylic acids varies based on the substituents attached to its carbon chain. When electron-withdrawing groups such as halogens are attached, they increase the acid strength by stabilizing the conjugate base via the inductive effect. In the given examples, each additional electronegative halogen attached to the carboxylic acid increases its acidity. For example, trifluoroacetic acid, with three highly electronegative fluorine atoms, has significant inductive stabilization of its conjugate base, making it much more acidic than acetic acid, which has no such stabilizing groups.