Question

Based on their compositions and structures and on conjugate acid-base relationships, select the stronger base in each of the following pairs: (a) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{NO}_{2}^{-}\), (b) \(\mathrm{PO}_{4}{ }^{3-}\) or \(\mathrm{AsO}_{4}{ }^{3-}\), (c) \(\mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}{ }^{2-}\)

Short answer

In summary, the stronger bases in each given pair are: (a) NO2-, (b) AsO4^3-, and (c) CO3^2-.

Step-by-step solution

(a) Compare NO3- and NO2-

First, let's write the conjugate acids for each species: \( \mathrm{NO}_{3}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{HNO}_{3} \) \( \mathrm{NO}_{2}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{HNO}_{2} \) Now, let's compare the stability of HNO3 and HNO2. HNO3 is a stronger acid, which means that its conjugate base (NO3-) is a weaker base. On the other hand, HNO2 is a weaker acid, which means that its conjugate base (NO2-) is a stronger base. Therefore, NO2- is the stronger base.

(b) Compare PO4^3- and AsO4^3-

Similarly, let's write the conjugate acids for each species: \( \mathrm{PO}_{4}^{3-} + \mathrm{H}^{+} \rightarrow \mathrm{HPO}_{4}^{2-} \) \( \mathrm{AsO}_{4}^{3-} + \mathrm{H}^{+} \rightarrow \mathrm{HAsO}_{4}^{2-} \) Now we need to compare the stability of HPO4^2- and HAsO4^2-. Due to the higher size of the As atom than the P atom, the negative charge is less localized (more dispersed) in AsO4^3- compared to PO4^3-. This means that the conjugate acid HAsO4^2- is more stable than HPO4^2-. Consequently, AsO4^3- is a stronger base than PO4^3-.

(c) Compare HCO3- and CO3^2-

First, let's write the conjugate acids for each species: \( \mathrm{HCO}_{3}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2}\mathrm{CO}_{3} \) \( \mathrm{CO}_{3}^{2-} + \mathrm{H}^{+} \rightarrow \mathrm{HCO}_{3}^{-} \) In this case, CO3^2- already ionizes to form HCO3-, which is a weaker acid than H2CO3 (also HCO3- is part of the conjugate pair with H2CO3). Since H2CO3 is a stronger acid than HCO3-, its conjugate base (HCO3-) is a weaker base. This means, CO3^2- is a stronger base compared to HCO3-. To summarize, the stronger bases in each given pair are: (a) NO2- (b) AsO4^3- (c) CO3^2-

Key concepts

Conjugate Acids and Bases

In acid-base chemistry, understanding the concept of conjugate acids and bases is crucial. A conjugate pair is formed when an acid donates a proton ( H^+ ) to a base. For example, when NO_2^- accepts a proton, it becomes its conjugate acid, HNO_2 .
Knowing the relative strength of acids and bases can help us predict which species is stronger in different pairs. The strength of an acid is inversely related to the strength of its conjugate base. This means, if an acid is strong, its conjugate base is weak and vice versa. For instance, since HNO_3 is a strong acid, its conjugate base, NO_3^- , is a weak base. Conversely, the weaker acid HNO_2 makes NO_2^- a stronger base.
The concept of conjugate bases and acids helps us understand why some substances are more reactive in solutions and provides insight into their behavior in chemical reactions. This is a foundational concept that applies broadly across many areas of chemistry.

Base Strength Comparison

Comparing base strengths involves evaluating which base has a higher affinity for protons. A stronger base is better at accepting H^+ ions. Several factors determine base strength, including the stability of the conjugate acid and the charge delocalization in the base itself.
When faced with a choice between NO_3^- and NO_2^- , analyzing the conjugate acids helps: since HNO_3 is stronger than HNO_2 , NO_2^- is the stronger base. Similarly, for PO_4^{3-} and AsO_4^{3-} , although both are polyatomic ions, AsO_4^{3-} 's larger size results in a greater ability to disperse its negative charge, making it the stronger base.
Thus, by understanding these underlying principles, we can more easily determine the stronger base in any given pair.

Molecular Stability and Charge Delocalization

The stability of a molecule plays a significant role in its acid-base characteristics. Stability often comes from the ability to delocalize charge across the molecule. This is particularly important in conjugate bases where dispersing negative charge can stabilize the molecule.
Consider PO_4^{3-} and AsO_4^{3-} . AsO_4^{3-} is predicted to have greater base strength due to its larger size and ability to delocalize negative charge more effectively than PO_4^{3-} . Although both ions share a similar structure, the larger radius of arsenate allows the negative charge to spread over the ion more efficiently, leading to increased stability of its conjugate acid, HAsO_4^{2-} .
Charge delocalization is a key concept in determining molecular stability and thus influences the outcome of acid-base reactions. Recognizing how structures can disperse charge sets a firm foundation in evaluating whether a substance is a strong or weak base.