Problem 272 - A Complete Resource Book in Chemistry for JEE Main

Question

Four species are listed below \([\mathbf{2 0 0 8}]\) (I) \(\mathrm{HCO}_{3}^{-}\) (II) \(\mathrm{H}_{3} \mathrm{O}^{+}\) (III) \(\mathrm{HSO}_{4}^{-}\) (IV) \(\mathrm{HSO}_{3} \mathrm{~F}\) Which one of the following is the correct sequence of their acid strength? (a) IV \(<\mathrm{II}<\mathrm{III}<\mathrm{I}\) (b) \(\mathrm{II}<\mathrm{III}<\mathrm{I}<\mathrm{IV}\) (c) \(\mathrm{I}<\mathrm{III}<\mathrm{II}<\mathrm{IV}\) (d) III \(<\mathrm{I}<\mathrm{IV}<\mathrm{II}\)

Step-by-Step Solution

Answer

The correct sequence of acid strength is (c): I < III < II < IV.

Step 1: Identify the Acids

We need to recognize that all these species can act as acids by donating a proton. Therefore, we have: - (I) \(\text{HCO}_{3}^{-}\) can donate a proton to become \(\text{CO}_3^{2-}\).- (II) \(\text{H}_3\text{O}^+\) is the hydronium ion and can donate a proton to become \(\text{H}_2\text{O}\).- (III) \(\text{HSO}_{4}^{-}\) can donate a proton to become \(\text{SO}_4^{2-}\).- (IV) \(\text{HSO}_{3}\text{F}\) can donate a proton to become \(\text{SO}_3\text{F}^-\).Next, we need to compare their abilities to donate a proton.

Step 2: Determine Relative Acid Strengths

The acid strengths are generally considered in terms of their readiness to donate a proton (H+). Some important points to consider:- Fluoro derivatives of sulfuric acids like \(\text{HSO}_3\text{F}\) (IV) are strong acids owing to the presence of electronegative fluorine and the overall stability of the conjugate base.- Hydronium ion \(\text{H}_3\text{O}^+\) (II) is a strong acid since it readily donates a proton to form water.- \(\text{HSO}_4^-\) (III) is a strong acid that is slightly weaker than the hydronium ion because its conjugate base, \(\text{SO}_4^{2-}\), is more stable than water.- \(\text{HCO}_3^-\) (I) is significantly weaker, as it exists in equilibrium with carbonate ion \(\text{CO}_3^{2-}\).Based on these considerations, the ranking from weakest to strongest acid is: \(\text{HCO}_3^-\) < \(\text{HSO}_4^-\) < \(\text{H}_3\text{O}^+\) < \(\text{HSO}_3\text{F}\).

Step 3: Select the Correct Sequence

From our analysis, we have identified the correct sequence from weakest to strongest acid as: I < III < II < IV, which matches option (c). Therefore, the correct sequence of acid strength is \(\text{HCO}_3^- < \text{HSO}_4^- < \text{H}_3\text{O}^+ < \text{HSO}_3\text{F}\).

Key Concepts

Proton Donation

Proton donation is a fundamental concept when discussing acids. An acid's strength is largely determined by its ability to donate a proton, which is represented by the hydrogen ion (H⁺). When an acid donates a proton, it transforms into its conjugate base. For instance, bicarbonate ( HCO₃⁻ ) donates a proton to become carbonate ( CO₃^{2-} ), and the hydronium ion ( H₃O⁺ ) donates a proton to become water ( H₂O ).

• An effective proton donor will more readily lose its H⁺ ion, indicating a stronger acid.
• Variations in proton donation ability can significantly affect a compound’s acid strength.

By understanding proton donation processes, we can better evaluate the relative strengths of different acids.

Conjugate Base Stability

The stability of a conjugate base significantly influences the strength of its corresponding acid. The more stable the conjugate base, the stronger the acid because it is more willing to give up its proton. Here are some crucial points:

• For an acid to be strong, the resulting conjugate base after donation should require minimal energy to stabilize.
• The sulfate ion ( SO₄^{2-} ), derived from HSO₄^{-} , is highly stable due to resonance, which contributes to the strong acidity of bisulfate.
• On the other hand, CO₃^{2-} from HCO₃^{-} lacks extensive resonance, resulting in a weaker acid due to less conjugate base stability.

The concept of conjugate base stability provides insights into why some acids are more potent than others, guiding us in predicting reactions involving acids and bases.

Acid Strength Comparison

The comparison of acid strengths involves evaluating how readily an acid can donate a proton. This ability is linked to several factors, including electronegativity, the structure of the molecule, and the stability of the conjugate base. Let's look at these factors:

• Electronegative atoms (like fluorine) can increase an acid's strength by stabilizing the conjugate base through electron-withdrawing effects, as seen in HSO₃F.
• The individual geometry of a molecule also plays a role; for example, HSO₄^- is stronger than HCO₃^- owing to its resonance-stabilized base.
• The culmination of these influences results in the observed strength order: HCO₃^- < HSO₄^- < H₃O⁺ < HSO₃F.

Understanding these comparisons helps us predict which acids will react more vigorously in different chemical scenarios.

Fluoro Derivatives of Sulfuric Acids

Fluoro derivatives of sulfuric acids exhibit very strong acidity. The presence of a fluorine atom, a highly electronegative element, greatly enhances acid strength. Here's why fluorine influences acidity:

• Fluorine's electronegativity makes it an electron-withdrawing group, stabilizing the conjugate base through an inductive effect.
• This stabilization makes it easier for the acid to donate its proton, as seen with HSO₃F, which can donate its proton more readily compared to acids lacking such electronegativity effects.
• In summary, the unique properties imparted by the fluoro substitution lead to significant increases in acid strength and make these compounds a critical study area in advanced acid-base chemistry.

Grasping the impact of fluoro derivatives expands one's understanding of how molecular changes alter chemical behavior.