Exercises: Models and conjugate pairs

Understanding of the behaviour of acids and bases developed decisively in the late 19th and early 20th centuries. Consider the substances $\mathrm{HCl}$ and $\mathrm{NH}_3$ at $25\,^{\circ}\mathrm{C}$.

1. a) Justify why hydrogen chloride behaves as an acid according to both Arrhenius's theory and the Brønsted-Lowry theory, writing the corresponding chemical equation in aqueous solution.
2. b) Explain, with reasoning, why a strict historical interpretation based only on the dissociation of hydroxides does not directly describe ammonia. Write its reaction with water and explain how proton transfer produces hydroxide ions, consistent with the extended aqueous definition of a base.

In the Brønsted-Lowry framework, two chemical species form a conjugate acid-base pair if they are related by the transfer of exactly one proton ($\mathrm{H}^+$), which involves a change of one unit in their net electric charge.

1. a) Write the molecular or ionic formula of the conjugate base of each of the following acidic chemical species: hydrogensulfate ion, $\mathrm{HSO}_4^-$, and oxonium ion, $\mathrm{H}_3\mathrm{O}^+$.
2. b) Write the molecular or ionic formula of the conjugate acid corresponding to each of the following bases: hydrogenphosphate ion, $\mathrm{HPO}_4^{2-}$, and methylamine, $\mathrm{CH}_3\mathrm{NH}_2$.

Amphiprotic substances are those that can donate or accept protons depending on the chemical species they react with. The hydrogencarbonate ion, $\mathrm{HCO}_3^-$, is an amphiprotic species of great importance in aqueous solution at $25\,^{\circ}\mathrm{C}$.

1. a) Write the balanced reaction in which the hydrogencarbonate ion acts as a Brønsted-Lowry acid towards the hydroxide anion, $\mathrm{OH}^-$, identifying the two conjugate acid-base pairs.
2. b) Write the balanced reaction in which the hydrogencarbonate ion acts as a Brønsted-Lowry base towards the oxonium ion, $\mathrm{H}_3\mathrm{O}^+$, likewise identifying the two conjugate pairs.

Two independent aqueous solutions of two monoprotic acids, $\mathrm{HA}$ and $\mathrm{HB}$, are prepared at the same initial analytical concentration $c_0 = 0.10\,\mathrm{mol\times L^{-1}}$ and at $25\,^{\circ}\mathrm{C}$. The diagram shows a microscopic sample of identical volume for both containers, in which a total equivalent of $6$ acid molecules was initially introduced into each solution. Observe the distribution of particles at equilibrium illustrated below:

1. a) From the count of species present at equilibrium (undissociated molecules and ions produced), determine the percentage or degree of dissociation of each acid.
2. b) Deduce, with reasoning, which of the two acids is stronger, justifying whether two solutions with exactly the same initial molar concentration of solute necessarily have the same acidity. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.

The terms "strong" and "concentrated" are often confused when describing an acidic solution. Consider at $25\,^{\circ}\mathrm{C}$ the following two solutions: solution 1 of hydrochloric acid, $\mathrm{HCl}$, with concentration $c_1 = 1.0\times 10^{-4}\,\mathrm{mol\times L^{-1}}$ (a strong, fully ionised acid), and solution 2 of acetic acid, $\mathrm{CH}_3\mathrm{COOH}$, with concentration $c_2 = 2.0\,\mathrm{mol\times L^{-1}}$ ($K_a = 1.8\times 10^{-5}$).

1. a) Calculate the concentration of $\mathrm{H}_3\mathrm{O}^+$ ions in both solutions, neglecting the autoprotolysis of water.
2. b) Classify each solution according to its intrinsic acid strength and according to its concentration, and explain why the weak acid solution can have a higher concentration of $\mathrm{H}_3\mathrm{O}^+$ ions than the strong acid. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.

The concept of neutralisation has complementary interpretations depending on the theoretical framework used.

1. a) Describe the neutralisation reaction in aqueous solution between solutions of sodium hydroxide, $\mathrm{NaOH}$, and nitric acid, $\mathrm{HNO}_3$, writing the net ionic equation and justifying the process according to Arrhenius's definition.
2. b) Now consider the reaction between the gases ammonia, $\mathrm{NH}_3(\mathrm{g})$, and hydrogen chloride, $\mathrm{HCl}(\mathrm{g})$, to form the white solid ammonium chloride, $\mathrm{NH}_4\mathrm{Cl}(\mathrm{s})$, in the complete absence of solvent. Explain whether this process is a neutralisation according to Arrhenius and according to Brønsted-Lowry, indicating the acid, the base and the proton transferred.

At $25\,^{\circ}\mathrm{C}$, hydrocyanic acid, $\mathrm{HCN}$, has an acidity constant $K_a = 4.9\times 10^{-10}$, while hydrofluoric acid, $\mathrm{HF}$, has $K_a = 6.8\times 10^{-4}$. Sodium fluoride, $\mathrm{NaF}$, is reacted with hydrocyanic acid in homogeneous aqueous solution.

1. a) Set out the Brønsted-Lowry proton transfer equation between the fluoride ion, $\mathrm{F}^-$, and $\mathrm{HCN}$, identify the two conjugate acid-base pairs and deduce whether the constant of this reaction will be greater or less than one.
2. b) Calculate the exact numerical value of the equilibrium constant of this reaction at $25\,^{\circ}\mathrm{C}$ and relate the result to the standard thermodynamic preference, distinguishing it from the direction in which a particular mixture will evolve, which requires knowing its reaction quotient. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.

In the laboratory there are two bottles labelled $\mathrm{X}$ and $\mathrm{Y}$. It is known that one contains formic acid, $\mathrm{HCOOH}$ ($K_a = 1.8\times 10^{-4}$ at $25\,^{\circ}\mathrm{C}$), and the other contains hypochlorous acid, $\mathrm{HClO}$ ($K_a = 3.0\times 10^{-8}$ at $25\,^{\circ}\mathrm{C}$). Two students prepare a $0.050\,\mathrm{mol\times L^{-1}}$ solution from bottle $\mathrm{X}$ and a $0.050\,\mathrm{mol\times L^{-1}}$ solution from bottle $\mathrm{Y}$. The electrical conductivity and pH are measured at $25\,^{\circ}\mathrm{C}$, finding that solution $\mathrm{X}$ has a $\mathrm{pH} = 2.53$, while solution $\mathrm{Y}$ has a $\mathrm{pH} = 4.41$.

1. a) Identify, with reasoning, which acid corresponds to each bottle by calculating the experimental acidity constant of each.
2. b) Taking the conjugate bases of both acids in aqueous solution at equal molar concentration, justify which of the two anions will undergo more pronounced basic hydrolysis and calculate its corresponding basicity constant $K_b$ at $25\,^{\circ}\mathrm{C}$, given that $K_w = 1.0\times 10^{-14}$. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.

Pure water at $25\,^{\circ}\mathrm{C}$ undergoes self-ionisation according to the equilibrium $2\,\mathrm{H}_2\mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{H}_3\mathrm{O}^+(\mathrm{aq}) + \mathrm{OH}^-(\mathrm{aq})$, with $K_w = 1.0\times 10^{-14}$ and a standard enthalpy of dissociation $\Delta H^0 > 0$.

1. a) Explain the amphiprotic behaviour of water, indicating the role played by each of the two water molecules in the autoprotolysis reaction, and state the two conjugate acid-base pairs generated.
2. b) Given that at $60\,^{\circ}\mathrm{C}$ the ionic product of water increases to $K_w = 9.6\times 10^{-14}$, justify using Le Chatelier's principle why this value increases, calculate the pH of neutral water at $60\,^{\circ}\mathrm{C}$ and explain in detail whether water at that temperature is still strictly neutral even though its pH is lower than $7.00$. Use the ideal model to relate concentrations to pH.