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Chapter 16: Problem 90

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 \(\mathrm{NO}_{2}^{-},(\mathbf{b}) \mathrm{PO}_{4}^{3-}\) or \(\mathrm{AsO}_{4}^{3-}\) \((\mathbf{c}) \mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}.\)

Short Answer

Expert verified
The stronger bases in each pair are: (a) \(\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{PO}_{4}^{3-}\) (c) \(\mathrm{CO}_{3}^{2-}\)

Step by step solution

01

Identify the conjugate acids

For each anion, identify its conjugate acid by adding one proton (H+). The conjugate acids for each anion are as follows: (a) For \(\mathrm{NO}_{3}^{-}\), the conjugate acid is \(\mathrm{HNO}_{3}\) (Nitric acid). For \(\mathrm{NO}_{2}^{-}\), the conjugate acid is \(\mathrm{HNO}_{2}\) (Nitrous acid). (b) For \(\mathrm{PO}_{4}^{3-}\), the conjugate acid is \(\mathrm{HPO}_{4}^{2-}\) (Dihydrogen phosphate ion). For \(\mathrm{AsO}_{4}^{3-}\), the conjugate acid is \(\mathrm{HAsO}_{4}^{2-}\) (Dihydrogen arsenate ion). (c) For \(\mathrm{HCO}_{3}^{-}\), the conjugate acid is \(\mathrm{H}_{2}\mathrm{CO}_{3}\) (Carbonic acid). For \(\mathrm{CO}_{3}^{2-}\), the conjugate acid is \(\mathrm{HCO}_{3}^{-}\) (Bicarbonate ion). ##Step 2: Compare the strength of conjugate acids##
02

Compare the strength of conjugate acids

Analyze the strength of the conjugate acids identified in step 1: (a) Nitric acid (\(\mathrm{HNO}_{3}\)) is a strong acid, whereas nitrous acid (\(\mathrm{HNO}_{2}\)) is a weak acid. Therefore, \(\mathrm{NO}_{3}^{-}\) is a weaker base compared to \(\mathrm{NO}_{2}^{-}\). (b) Both \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{HAsO}_{4}^{2-}\) are weak acids. However, As(arsenic) is below P(phosphorus) in the periodic table, making \(\mathrm{HAsO}_4^{2-}\) more acidic than \(\mathrm{HPO}_4^{2-}\). As a result, \(\mathrm{AsO}_{4}^{3-}\) is a weaker base compared to \(\mathrm{PO}_{4}^{3-}\). (c) Carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\)) is a weak acid, and bicarbonate ion (\(\mathrm{HCO}_{3}^{-}\)) is also a weak acid. However, carbonic acid has two acidic protons, while bicarbonate ion has only one. So, carbonic acid is stronger than bicarbonate ion, making \(\mathrm{CO}_{3}^{2-}\) a stronger base compared to \(\mathrm{HCO}_{3}^{-}\). ##Step 3: Determine the stronger base in each pair##
03

Determine the stronger base in each pair

Based on the comparison of conjugate acid strengths, we can conclude the stronger base in each pair: (a) \(\mathrm{NO}_{2}^{-}\) is a stronger base compared to \(\mathrm{NO}_{3}^{-}\). (b) \(\mathrm{PO}_{4}^{3-}\) is a stronger base compared to \(\mathrm{AsO}_{4}^{3-}\). (c) \(\mathrm{CO}_{3}^{2-}\) is a stronger base compared to \(\mathrm{HCO}_{3}^{-}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conjugate Acid-Base Pairs
In acid-base chemistry, understanding conjugate acid-base pairs is crucial for analyzing reactions. A conjugate acid-base pair consists of two species that transform into each other by gaining or losing a proton (\(H^+\)). For example, when a base gains a proton, it turns into its conjugate acid, and when an acid loses a proton, it becomes its conjugate base.
Consider the pair \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{HNO}_{2}\): \(\mathrm{NO}_{2}^{-}\) is a base because it can accept a proton to form \(\mathrm{HNO}_{2}\), its conjugate acid. Conversely, \(\mathrm{HNO}_{2}\) can donate a proton, thus behaving as an acid in this pair.
Understanding these relationships helps us predict reactivity and the nature of solutions:
  • A strong acid will have a weak conjugate base because it easily loses protons.
  • Conversely, a weak acid will have a stronger conjugate base since it holds on to its protons more firmly.
  • These pairs are pivotal in predicting the direction of acid-base reactions and equilibria.
Strong and Weak Acids
Acids are categorized based on their ability to donate protons (\(H^+\)) in solution. This ability determines whether an acid is strong or weak.
Strong acids, like nitric acid (\(\mathrm{HNO}_{3}\)), dissociate completely in water, meaning they fully donate their available protons. This makes their conjugate bases very weak. In the case of \(\mathrm{HNO}_{3}\), \(\mathrm{NO}_{3}^{-}\) barely acts as a base because it's very stable and has little tendency to gain a proton back. On the other hand, weak acids, such as nitrous acid (\(\mathrm{HNO}_{2}\)), only partially dissociate in solution. This incomplete dissociation means that the conjugate base is more reactive or stronger compared to that of a strong acid.
When comparing the strengths of acids, consider:
  • Complete dissociation indicates a strong acid. Examples include hydroiodic acid (\(\mathrm{HI}\)) and \(\mathrm{HNO}_{3}\).
  • Partial dissociation points to a weak acid. Examples include acetic acid (\(\mathrm{CH}_3\mathrm{COOH}\)) and \(\mathrm{HNO}_{2}\).
  • Strong acids tend to lead to very weak, often inert, conjugate bases.
  • Weak acids have conjugate bases that can readily accept protons and act as bases in solution.
Anions
Anions play a vital role in acid-base chemistry. These are negatively charged ions that often form the base part of a conjugate acid-base pair. Understanding the behavior of different anions can help predict the basicity of the compound.
Anions like \(\mathrm{NO}_{3}^{-}\), \(\mathrm{PO}_{4}^{3-}\), and \(\mathrm{CO}_{3}^{2-}\) typically arise from the dissociation of their corresponding acids. The nature of these anions鈥攁s determined by their conjugate acid鈥攊ndicates their ability to participate in acid-base reactions.
Key points about anions include:
  • An anion derived from a strong acid, such as \(\mathrm{NO}_{3}^{-}\), is a weak base because it has minimal tendency to accept a proton.
  • An anion from a weak acid, such as \(\mathrm{CO}_{3}^{2-}\), can act as a stronger base.
  • The position of the element in periodic table affects anion behavior; elements lower in the same group often result in weaker bases due to their larger size and lower charge density.
  • Anion stability is crucial; more stable anions are typically weaker bases.
By understanding these properties, one can better predict and explain the acid-base behavior of different compounds in chemical reactions.

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Most popular questions from this chapter

Butyric acid is responsible for the foul smell of rancid butter. The \(\mathrm{pK}_{a}\) of butyric acid is 4.84 (a) Calculate the pK \(_{b}\) for the butyrate ion. (b) Calculate the pH of a 0.050 \(M\) solution of butyric acid. (c) Calculate the pH of a 0.050\(M\) solution of sodium butyrate.

Predict whether aqueous solutions of the following compounds are acidic, basic, or neutral: \((\mathbf{a})\mathrm{NH}_{4} \mathrm{Br},(\mathbf{b}) \mathrm{FeCl}_{3}\) \((\mathbf{c}) \mathrm{Na}_{2} \mathrm{CO}_{3},(\mathbf{d}) \mathrm{KClO}_{4},(\mathbf{e}) \mathrm{NaHC}_{2} \mathrm{O}_{4}\)

Phenol, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH},\) has a \(K_{a}\) of \(1.3 \times 10^{-10}.\) (a) Write out the \(K_{a}\) reaction for phenol. (b) Calculate \(K_{b}\) for phenol's conjugate base. (c) Is phenol a stronger or weaker acid than water?

Lactic acid \(\left(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right)\) has one acidic hydrogen. A 0.10 \(\mathrm{M}\) solution of lactic acid has a pH of \(2.44 .\) Calculate \(K_{a} .\)

In many reactions, the addition of \(\mathrm{AlCl}_{3}\) produces the same effect as the addition of \(\mathrm{H}^{+} .\) (a) Draw a Lewis structure for \(\mathrm{AlCl}_{3}\) in which no atoms carry formal charges, and determine its structure using the VSEPR method. (b) What characteristic is notable about the structure in part (a) that helps us understand the acidic character of AlCl \(_{3} ?\) (c) Predict the result of the reaction between \(\mathrm{AlCl}_{3}\) and \(\mathrm{NH}_{3}\) in a solvent that does not participate as a reactant. (d) Which acid-base theory is most suitable for discussing the similarities between \(\mathrm{AlCl}_{3}\) and \(\mathrm{H}^{+}\) ?
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