Question

Consider the following Bronstead acid-base reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{HF}(a q)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{HCl}(a q)+\mathrm{F}^{-}(a q) $$. (a) Predict whether \(K\) will be greater or smaller than unity, (b) Does \(\Delta S^{\circ}\) or \(\Delta H^{\circ}\) make a greater contribution to \(\Delta G^{\circ} ?\) (c) Is \(\Delta H^{\circ}\) likely to be positive or negative?

Short answer

The predicted values are as follows: \(K<1\), indicating the Reaction favors the Reactants; ΔH° makes a greater contribution to ΔG°; ΔH° is likely to be positive, indicating it is an Endothermic Reaction.

Step-by-step solution

Predict whether K will be greater or smaller than unity

The reaction given is a Bronsted Acid-Base Reaction. In Acid-Base Reactions, the Acid donates a proton (H+) and the Base accepts it. In this case, HF is the Acid, because it’s donating an H+. The Cl- is the Base because it’s accepting the H+ to form HCl. On the other hand, we have HCl and F- as the Products. Comparing the Reactants and the Products, HF is a Stronger Acid than HCl, and Cl- is a Weaker Base than F-. This implies that the Reactants are more stable compared to the Products. Therefore, the Reaction will favor the Reactant Side, meaning that \(K<1\).

Analyze whether ΔS° or ΔH° makes a greater contribution to ΔG°

We know that Gibbs Free Energy, \(ΔG\) is given by the formula \(ΔG° = ΔH° - TΔS°\). A negative ΔG indicates a Spontaneous Reaction, while a positive ΔG indicates a non-spontaneous Reaction. From Step 1, we’ve determined \(K<1\), and because ΔG and K have a logarithmic Relationship, a smaller K corresponds to a larger (positive) ΔG. Hence, the term -TΔS must be small to give a larger ΔG. Thus, ΔH° makes a greater contribution to ΔG° than ΔS° does.

Determining whether ΔH° is likely to be positive or negative

Enthalpy Change (ΔH) is positive when Heat is absorbed (Endothermic Reaction), and negative when Heat is released (Exothermic Reaction). From Step 2, we’ve determined that ΔH° makes a greater contribution to ΔG°. Since ΔG° is positive (as determined in Step 2), to achieve this, ΔH must also be positive. Therefore, ΔH° is likely to be positive, indicating that the Reaction is Endothermic.

Key concepts

Equilibrium Constant

In chemistry, the equilibrium constant, denoted as \( K \), helps us understand the balance between reactants and products in a reversible reaction. It describes the relative concentrations of different species in the reaction at equilibrium.- For the reaction \( \text{HF}(aq) + \text{Cl}^-(aq) \rightleftharpoons \text{HCl}(aq) + \text{F}^-(aq) \), we would write the expression for the equilibrium constant as: \[ K = \frac{[\text{HCl}][\text{F}^-]}{[\text{HF}][\text{Cl}^-]} \]- **Case Analysis:** - **\( K > 1 \):** Product-favored reaction, more products at equilibrium. - **\( K < 1 \):** Reactant-favored reaction, more reactants at equilibrium.In our specific case, Hydrofluoric acid (HF) is a stronger acid compared to hydrochloric acid (HCl), which means it more readily donates a proton (\( H^+ \)) to the base \( Cl^- \). This results in equilibrium favoring the reactants (more stable), which implies \( K < 1 \). Using this understanding helps predict how a reaction might proceed and shifts in conditions influencing the position of the equilibrium.

Gibbs Free Energy

Gibbs free energy (ΔG°) is a crucial thermodynamic quantity that indicates the spontaneity of a reaction. It's defined by:\[ ΔG° = ΔH° - TΔS° \]- **ΔH°:** Change in enthalpy (heat content).- **TΔS°:** Temperature times the change in entropy (disorder).- **Understanding ΔG°'s Role:** - **Negative ΔG°:** The reaction proceeds spontaneously. - **Positive ΔG°:** The reaction doesn't naturally proceed on its own.In our analysis of the reaction \( \text{HF}(aq) + \text{Cl}^-(aq) \rightleftharpoons \text{HCl}(aq) + \text{F}^-(aq) \), we found \( K < 1 \). There's a logarithmic relation: a smaller \( K \) suggests a positive ΔG°, indicating it's non-spontaneous under standard conditions. Here, ΔH°'s influence outweighs ΔS° due to this lesser entropy term being insignificant, guiding the overall ΔG° value to reflect this non-spontaneity.

Enthalpy Change

Enthalpy change (ΔH°) reflects the heat absorbed or released during a reaction.- **Classification of Reactions Based on ΔH°:** - **Exothermic:** Releases heat, ΔH° is negative. - **Endothermic:** Absorbs heat, ΔH° is positive.- **Relating ΔH° in Our Reaction:** - Since \( ΔG° \) is positive, the underlying thermodynamics hint at the reaction being endothermic. - As determined in our step analysis, ΔH° in this context is likely positive, indicating that the reaction requires an input of energy to proceed.This concept helps us understand the energy dynamics within a chemical reaction—whether it will naturally release energy to the surroundings or require energy input to break bonds and transform into products. Managing these energy changes is vital in industrial applications and understanding chemical behavior.