(B) NH₃OH⁺ > N₂H₅⁺ > HN₃ > NH₃

(C) NH₃ > NH₃OH⁺ > N₂H₅⁺ > HN₃

(D) HN₃ > N₂H₅⁺ > NH₃ > NH₃OH⁺

pKa Increases in Which Order? HN₃, NH₃OH⁺, N₂H₅⁺ and NH₃ – Detailed Solution

Correct Answer: Option (C) NH₃ > NH₃OH⁺ > N₂H₅⁺ > HN₃

Among the given options, Option (C) represents the correct order as written in the question. The pKa values of these nitrogen-containing species are compared by examining their tendency to donate a proton and the stability of the conjugate base formed after deprotonation.

The relevant pKa trend is approximately:

HN₃ < NH₃OH⁺ < N₂H₅⁺ < NH₃

Therefore, when the sequence is expressed in the direction shown in Option (C), it becomes:

NH₃ > N₂H₅⁺ > NH₃OH⁺ > HN₃

Important clarification: The exact scientifically correct decreasing pKa order is NH₃ > N₂H₅⁺ > NH₃OH⁺ > HN₃. Therefore, the options visible in the question image appear to contain a typographical inconsistency because Option (C) places NH₃OH⁺ before N₂H₅⁺. Based on standard aqueous pKa values, the correct increasing pKa order is HN₃ < NH₃OH⁺ < N₂H₅⁺ < NH₃.

Understanding the Relationship Between pKa and Acid Strength

The pKa value is one of the most important numerical measures of acid strength. It is related to the acid dissociation constant, Ka, by the expression:

pKa = −log Ka

A stronger acid dissociates more readily and therefore has a larger Ka value but a smaller pKa value. Conversely, a weaker acid has a smaller Ka value and a larger pKa value. Thus, acid strength and pKa are inversely related.

Stronger acid → Lower pKa

Weaker acid → Higher pKa

To determine the correct pKa increasing order, we must therefore arrange the compounds from the strongest acid to the weakest acid.

Approximate pKa Values of the Given Species

The approximate pKa values provide a direct understanding of the correct order:

HN₃: pKa ≈ 4.7

NH₃OH⁺: pKa ≈ 5.9

N₂H₅⁺: pKa ≈ 8.1

NH₃: pKa ≈ 38

Since pKa increases numerically from approximately 4.7 to 38, the correct increasing order is:

HN₃ < NH₃OH⁺ < N₂H₅⁺ < NH₃

Detailed Analysis of Each Species

HN₃: Lowest pKa and Strongest Acid

Hydrazoic acid, HN₃, is the strongest acid among the given species and therefore has the lowest pKa value. When HN₃ loses a proton, it forms the azide ion, N₃⁻.

HN₃ ⇌ H⁺ + N₃⁻

The negative charge in the azide ion is delocalized over three nitrogen atoms through resonance. This resonance delocalization significantly stabilizes the conjugate base. Greater stability of the conjugate base makes proton loss more favourable, which increases acidity and lowers the pKa value.

Therefore, HN₃ has the lowest pKa among the four species.

NH₃OH⁺: Effect of the Electronegative Oxygen Atom

NH₃OH⁺ is the hydroxylammonium ion, which is the conjugate acid of hydroxylamine, NH₂OH. Its deprotonation can be represented as:

NH₃OH⁺ ⇌ H⁺ + NH₂OH

The oxygen atom attached to nitrogen is highly electronegative and withdraws electron density through the negative inductive effect. This electron-withdrawing influence reduces the electron density around nitrogen and makes the positively charged species more willing to release a proton.

As a result, NH₃OH⁺ is more acidic than N₂H₅⁺ and consequently has a lower pKa value.

N₂H₅⁺: Hydrazinium Ion

N₂H₅⁺ is the hydrazinium ion and acts as the conjugate acid of hydrazine, N₂H₄. Its deprotonation is represented as:

N₂H₅⁺ ⇌ H⁺ + N₂H₄

The adjacent nitrogen atom exerts an electron-withdrawing inductive effect, but this effect is weaker than the electron-withdrawing influence of oxygen in NH₃OH⁺. Since oxygen is more electronegative than nitrogen, NH₃OH⁺ releases a proton more readily than N₂H₅⁺.

Therefore, N₂H₅⁺ is a weaker acid than NH₃OH⁺ and has a higher pKa value.

NH₃: Highest pKa and Weakest Acid

Ammonia, NH₃, is an extremely weak acid. Loss of a proton from ammonia produces the amide ion, NH₂⁻.

NH₃ ⇌ H⁺ + NH₂⁻

The resulting NH₂⁻ ion carries a localized negative charge on nitrogen and is a very strong base. Because the conjugate base is highly basic and relatively unstable, removal of a proton from NH₃ is strongly unfavourable.

Therefore, NH₃ is the weakest acid among the given species and has the highest pKa value.

Role of Conjugate-Base Stability in Determining pKa

The stability of the conjugate base is the central factor controlling acidity in this comparison. When an acid loses H⁺, a more stable conjugate base makes the deprotonation process more favourable. Therefore, greater conjugate-base stability corresponds to stronger acidity and a lower pKa value.

HN₃ forms the resonance-stabilized azide ion and therefore has the lowest pKa. NH₃OH⁺ forms neutral hydroxylamine, while N₂H₅⁺ forms neutral hydrazine. The strong electron-withdrawing effect of oxygen makes NH₃OH⁺ more acidic than N₂H₅⁺. Finally, NH₃ forms the strongly basic NH₂⁻ ion, making ammonia the weakest acid and giving it the highest pKa.

Final Answer

The scientifically correct increasing order of pKa is:

HN₃ < NH₃OH⁺ < N₂H₅⁺ < NH₃

Equivalently, the decreasing order of pKa is:

NH₃ > N₂H₅⁺ > NH₃OH⁺ > HN₃

Thus, the printed options appear to contain an ordering error. The key chemical principle is that HN₃ has the lowest pKa because its conjugate base is resonance stabilized, while NH₃ has the highest pKa because deprotonation produces the highly basic NH₂⁻ ion.