Question

Calculate the standard free energy change for the ionization: \(\mathrm{HF}(\mathrm{aq}) \rightarrow \mathrm{H}^{+}(\mathrm{aq})\) \(+\mathrm{F}^{-}(\mathrm{aq})\) from the following data: \(\mathrm{HF}(\mathrm{aq}) \rightarrow \mathrm{HF}(\mathrm{g}) ; \Delta G^{\circ}=23.9 \mathrm{~kJ}\) \(\mathrm{HF}(\mathrm{g}) \rightarrow \mathrm{H}(\mathrm{g})+\mathrm{F}(\mathrm{g}) ; \Delta G^{\circ}=555.1 \mathrm{~kJ}\) \(\mathrm{H}(\mathrm{g}) \rightarrow \mathrm{H}^{+}(\mathrm{g})+\mathrm{e} ; \Delta G^{\circ}=1320.2 \mathrm{~kJ}\) \(\mathrm{F}(\mathrm{g})+\mathrm{e} \rightarrow \mathrm{F}^{-}(\mathrm{g}) ; \Delta G^{\circ}=-347.5 \mathrm{~kJ}\) \(\mathrm{H}^{+}(\mathrm{g})+\mathrm{F}^{-}(\mathrm{g}) \stackrel{\mathrm{aq} .}{\longrightarrow} \mathrm{H}^{+}(\mathrm{aq})+\mathrm{F}^{-}(\mathrm{aq})\) \(\Delta G^{\circ}=-1513.6 \mathrm{~kJ}\) (a) \(-38.1 \mathrm{~kJ}\) (b) \(+38.1 \mathrm{~kJ}\) (c) \(-1489.7 \mathrm{~kJ}\) (d) \(-1513.6 \mathrm{~kJ}\)

Short answer

\(-38.1 \mathrm{~kJ}\)

Step-by-step solution

Understand the Process

First, analyze the given reactions to understand the complete ionization process of HF(aq). We must combine them in such a way that the reactants and products cancel out appropriately to yield the net reaction, which is the ionization of HF(aq).

Write the Overall Ionization Reaction

The overall reaction we want is the ionization of HF in water: \(\mathrm{HF(aq)} \rightarrow \mathrm{H^{+}(aq)} + \mathrm{F^{-}(aq)}\).

Combine Given Reactions

Combine the given reactions in such a way that the unwanted species cancel each other out, and we are left with only the species involved in the overall reaction. Note that both directions and stoichiometry may need to be adjusted, and remember to reverse the sign of \(\Delta G^\circ\) when reversing the reaction.

Calculate the Standard Free Energy Change

Add the free energies \(\Delta G^\circ\) of each step, being careful with the signs, to determine the \(\Delta G^\circ\) for the overall reaction.

Key concepts

Ionization Reaction

An ionization reaction is a chemical process where a neutral atom or molecule gains or loses electrons, thus acquiring a net charge and becoming an ion. This reaction is fundamental in aqueous solutions where many substances dissolve to produce ions, which are essential for conductivity and chemical reactivity in biological and environmental systems. For example, when hydrogen fluoride (HF) is dissolved in water, it undergoes an ionization reaction to form hydronium (H⁺) and fluoride ions (F^-).

This chemical behavior is critical to understand because it determines the strength of acids and bases in solution, as well as the solubility and reaction mechanisms of various compounds. It is through such reactions that acids and bases interact in solutions, often resulting in significant changes in their physical and chemical properties.

Gibbs Free Energy

Gibbs free energy, denoted by \( G \), is a thermodynamic quantity that predicts the direction of chemical reactions and the point at which chemical equilibrium is reached. It combines the concepts of enthalpy (heat content), entropy (disorder), and temperature to provide information on the spontaneity of a reaction under constant pressure and temperature. A negative Gibbs free energy change (\( \Delta G^\circ < 0 \) indicates that the reaction will occur spontaneously, whereas a positive value (\( \Delta G^\circ > 0 \) suggests that the reaction is non-spontaneous under standard conditions.

For the ionization of HF, the standard free energy change tells us how the reaction will proceed. By calculating the overall \( \Delta G^\circ \) from the given data for each step in the ionization process, we can determine if the ionization will happen spontaneously. Understanding the significance of this value is crucial in predicting the behavior of chemical species in different environments.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to no net change in the concentrations of the reactants and products. It is a dynamic state where the rate of the forward reaction equals the rate of the backward reaction. Equilibrium does not mean the reactants and products are in equal concentrations, but rather that their concentrations have stabilized at a certain ratio.

At chemical equilibrium, the Gibbs free energy of the system is at its minimum, and therefore \( \Delta G \) is equal to zero. In the context of the ionization of HF, achieving equilibrium means the rate at which the HF molecules ionize to form H⁺ and F^- ions is equal to the rate at which the ions recombine to form HF. A thorough understanding of equilibrium is crucial for calculating reaction yields and for the synthesis of chemical products.

Thermodynamics

Thermodynamics is the branch of physical chemistry that deals with the relations between heat and other forms of energy such as work. It describes how thermal energy is converted to and from other forms of energy and how it affects matter. The four laws of thermodynamics lay the foundation for topics such as heat, work, energy, and the behavior of particles.

In the study of the ionization reaction of HF, thermodynamics helps us determine how the energy of the system changes during the reaction. For instance, it can predict whether heat is absorbed from or released into the surroundings during the process. By considering thermodynamic principles and calculating properties like enthalpy, entropy, and free energy, we can gain a deeper understanding of the ionization reaction and how it fits into the broader contexts of chemical and physical change.