Problem 90 - Chemistry: The Central Science

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 \(\mathrm{CO}_{3}^{2-}\).

Step-by-Step Solution

Answer

The stronger base in each pair is: (a) \(\mathrm{NO}_{2}^{-}\), (b) \(\mathrm{PO}_{4}^{3-}\), and (c) \(\mathrm{CO}_{3}^{2-}\).

Step 1: Identify the conjugate acids

To identify the conjugate acids of each base, we simply need to add one H+ ion to each base. For the given bases, the conjugate acids are: (a) \(\mathrm{NO}_{3}^{-}\) -> HNO3 \(\mathrm{NO}_{2}^{-}\) -> HNO2 (b) \(\mathrm{PO}_{4}^{3-}\) -> \(\mathrm{HPO}_{4}^{2-}\) \(\mathrm{AsO}_{4}^{3-}\) -> \(\mathrm{HAsO}_{4}^{2-}\) (c) \(\mathrm{HCO}_{3}^{-}\) -> H2CO3 \(\mathrm{CO}_{3}^{2-}\) -> HCO3- Compare the strengths of these conjugate acids to determine the stronger base in each pair.

Step 2: Compare the conjugate acid strengths

Analyze the acid strengths based on the factors discussed in the Analysis section. (a) Nitrate vs nitrite: HNO3 and HNO2 Both have the same central atom (N) but different numbers of oxygen atoms. Since oxygen is more electronegative, adding more oxygen will make the conjugate acid stronger. Therefore, HNO3 is the stronger acid, making \(\mathrm{NO}_{3}^{-}\) the weaker base in the pair. Thus, \(\mathrm{NO}_{2}^{-}\) is the stronger base. (b) Phosphate vs arsenate: \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{HAsO}_{4}^{2-}\) The central atoms are different: P in phosphate and As in arsenate. Comparing their positions on the periodic table shows that As is below P, making it larger and less electronegative. Larger, less electronegative central atoms have stronger conjugate acids. Therefore, \(\mathrm{HAsO}_{4}^{2-}\) is the stronger acid, making \(\mathrm{AsO}_{4}^{3-}\) the weaker base in the pair. Hence, the stronger base is \(\mathrm{PO}_{4}^{3-}\). (c) Hydrogen carbonate vs carbonate: H2CO3 and HCO3- Here, the central atom is the same, but the charge is different. More negatively charged species are generally more basic. Therefore, \(\mathrm{CO}_{3}^{2-}\) is the stronger base in this pair.

Step 3: Conclusion

The stronger base in each of the given pairs are as follows: (a) \(\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{PO}_{4}^{3-}\) (c) \(\mathrm{CO}_{3}^{2-}\)

Key Concepts

Conjugate Acids

In acid-base chemistry, conjugate acids form when a base gains a proton (\(H^+\)). Imagine a seesaw: as the base gains a hydrogen ion, the acid strength increases. The concept of conjugate acids helps in understanding acid-base reactions and predicting equilibrium positions. To find a conjugate acid, simply add \(H^+\) to the base.
Every base has its own conjugate acid, and the strength of this acid is crucial for determining the base's strength:

• If a conjugate acid is strong, it means the base is weak.
• If a conjugate acid is weak, the corresponding base is strong because it readily accepts protons.

For example, in the exercise:

• For the base \(NO_3^-\), the conjugate acid is \(HNO_3\), while for \(NO_2^-\), it is \(HNO_2\).
• Recognizing these conjugate acids sets the stage for comparing their strengths and identifying the stronger base in each pair.

Base Strength Comparison

Comparing base strength involves examining the ease with which a base can accept a proton. Strong bases tend to have weaker conjugate acids:

• A base's environment, element type, and electron arrangements influence its strength.
• The stronger a conjugate acid, the weaker the base from which it forms. This inverse relationship guides comparisons.

Let's illustrate with examples:

• Between \(NO_3^-\) and \(NO_2^-\), \(HNO_3\) is a stronger conjugate acid than \(HNO_2\); therefore, \(NO_2^-\) is the stronger base.
• Now consider \(PO_4^{3-}\) and \(AsO_4^{3-}\). Since \(HAsO_4^{2-}\) is stronger than \(HPO_4^{2-}\) due to different central atoms, \(PO_4^{3-}\) emerges as the stronger base.

Grasping the concept of conjugate acid strength is pivotal when assessing which base in a pair is stronger.

Electronegativity in Acids

Electronegativity impacts acid strength by influencing how tightly electrons are held. It is a measure of an atom's ability to attract and bind electrons. This property affects both acids and bases:

• High electronegativity usually makes an acid stronger because it attracts the electrons more strongly.
• When an atom in the acid is highly electronegative, it stabilizes additional negative charge well, enhancing acid strength which weakens the corresponding base.

Take the examples given in the exercise:

• In \(NO_3^-\), oxygen is very electronegative, making \(HNO_3\) stronger due to electron withdrawing abilities.
• Consider how the position of phosphorous (P) compared to arsenic (As) in acids like \(HPO_4^{2-}\) and \(HAsO_4^{2-}\) affects their respective strengths. Arsenic is less electronegative, hence exerting lesser electron-withdrawing power than phosphorous, resulting in a weaker acid.

By understanding and applying electronegativity rules, you can better predict acid and base behavior in various chemical reactions.