Problem 26 - Chemistry and Chemical Reactivity

Question

Using values of \(\Delta G_{f}^{\circ},\) calculate \(\Delta G_{\text {rem }}^{\circ}\) for each of the following reactions. Which are product-favored? (a) \(\mathrm{HgS}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{Hg}(\ell)+\mathrm{SO}_{2}(\mathrm{g})\) (b) \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{SO}_{2}(\mathrm{g})\) (c) \(\operatorname{sic} \mathrm{l}_{4}(\mathrm{g})+2 \mathrm{Mg}(\mathrm{s}) \longrightarrow 2 \mathrm{MgCl}_{2}(\mathrm{s})+\mathrm{Si}(\mathrm{s})\)

Step-by-Step Solution

Answer

Calculate \( \Delta G_{\text{rem}}^{\circ} \) for each reaction; reactions with \( \Delta G_{\text{rem}}^{\circ} < 0 \) are product-favored.

Step 1: Identify the Values Needed

First, you need the standard Gibbs free energy of formation values, \( \Delta G_{f}^{\circ} \), for each reactant and product involved in the reactions. These values are typically provided in tables in your textbook or other chemistry resources.

Step 2: Write the Formula for ΔG°

For each reaction, the standard Gibbs free energy change \( \Delta G_{\text{rem}}^{\circ} \) is calculated using: \[ \Delta G_{\text{rem}}^{\circ} = \sum \Delta G_{f}^{\circ} \text{(products)} - \sum \Delta G_{f}^{\circ} \text{(reactants)} \] where \( \sum \) denotes the summation of the \( \Delta G_{f}^{\circ} \) values, each multiplied by their stoichiometric coefficients in the balanced equation.

Step 3: Apply the Formula to Reaction (a)

For reaction (a): \[ \mathrm{HgS}( ext{s}) + \mathrm{O}_2 ( ext{g}) \rightarrow \mathrm{Hg}( ext{l}) + \mathrm{SO}_2 ( ext{g}) \]Calculate \( \Delta G_{\text{rem}}^{\circ} \) as follows: \( \Delta G_{\text{rem}}^{\circ} = [\Delta G_{f}^{\circ}(\mathrm{Hg}) + \Delta G_{f}^{\circ}(\mathrm{SO}_2)] - [\Delta G_{f}^{\circ}(\mathrm{HgS}) + \Delta G_{f}^{\circ}(\mathrm{O}_2)] \). Insert known values to find the result.

Step 4: Apply the Formula to Reaction (b)

For reaction (b): \[ 2\mathrm{H}_2\mathrm{S}( ext{g}) + 3\mathrm{O}_2( ext{g}) \rightarrow 2\mathrm{H}_2\mathrm{O}( ext{g}) + 2\mathrm{SO}_2( ext{g}) \]Calculate \( \Delta G_{\text{rem}}^{\circ} \) as follows:\( \Delta G_{\text{rem}}^{\circ} = [2\cdot\Delta G_{f}^{\circ}(\mathrm{H}_2\mathrm{O}) + 2\cdot\Delta G_{f}^{\circ}(\mathrm{SO}_2)] - [2\cdot\Delta G_{f}^{\circ}(\mathrm{H}_2\mathrm{S}) + 3\cdot\Delta G_{f}^{\circ}(\mathrm{O}_2)] \). Insert known values to find the result.

Step 5: Apply the Formula to Reaction (c)

For reaction (c): \[ \text{SiCl}_4(\text{g}) + 2\text{Mg}(\text{s}) \rightarrow 2\text{MgCl}_2(\text{s}) + \text{Si}(\text{s}) \]Calculate \( \Delta G_{\text{rem}}^{\circ} \) as follows:\( \Delta G_{\text{rem}}^{\circ} = [2\cdot\Delta G_{f}^{\circ}(\text{MgCl}_2)+\Delta G_{f}^{\circ}(\text{Si})] - [\Delta G_{f}^{\circ}(\text{SiCl}_4)+2\cdot\Delta G_{f}^{\circ}(\text{Mg})] \). Insert known values to find the result.

Step 6: Determine If Reactions Are Product-Favored

After calculating \( \Delta G_{\text{rem}}^{\circ} \) for each reaction:- If \( \Delta G_{\text{rem}}^{\circ} < 0 \), the reaction is product-favored.- If \( \Delta G_{\text{rem}}^{\circ} > 0 \), the reaction is reactant-favored.Compare the results for all three reactions to decide their favorability.

Key Concepts

Standard Gibbs Free Energy of Formation

The standard Gibbs free energy of formation, denoted as \( \Delta G_{f}^{\circ} \), is a crucial concept in thermochemistry. It refers to the change in Gibbs energy when one mole of a compound is formed from its elements in their standard states. These values are essential for predicting reaction favorability. By using \( \Delta G_{f}^{\circ} \) values, we can calculate the Gibbs free energy change for an entire reaction.In essence, \( \Delta G_{f}^{\circ} \) values provide a snapshot of the energy required or released during the formation process of compounds from their elemental forms. These values are typically listed in tables and serve as reference points for calculating the energies involved in chemical reactions.
Understanding and utilizing \( \Delta G_{f}^{\circ} \) values allows chemists to predict how much energy is required to form a substance under standard conditions—usually at 1 bar pressure and a specified temperature (commonly 298 K or 25°C).

Calculating Reaction Favorability

Calculating whether a chemical reaction is favored to proceed in the direction of forming products involves determining the overall Gibbs free energy change of the reaction, denoted as \( \Delta G_{\text{rem}}^{\circ} \). The formula used for this calculation is:\[ \Delta G_{\text{rem}}^{\circ} = \sum \Delta G_{f}^{\circ} \text{(products)} - \sum \Delta G_{f}^{\circ} \text{(reactants)} \]This formula entails summing the \( \Delta G_{f}^{\circ} \) values of the products and subtracting the sum of \( \Delta G_{f}^{\circ} \) values of the reactants. Each term in the summations is also multiplied by its respective stoichiometric coefficient from the balanced chemical equation.
The outcome of this calculation lets us know if the reaction is spontaneous under standard conditions:

• If \( \Delta G_{\text{rem}}^{\circ} < 0 \), the reaction is product-favored, meaning it is likely to occur as written, releasing energy.
• If \( \Delta G_{\text{rem}}^{\circ} > 0 \), the reaction is reactant-favored, and the reverse reaction is more spontaneous.

This method of calculating reaction favorability provides insight into whether a reaction will proceed on its own or if it requires additional energy input.

Thermochemistry Concepts

Thermochemistry is the branch of chemistry that examines the relationship between chemical reactions and energy changes, particularly heat changes. Understanding thermochemistry is fundamental to predicting how reactions behave in terms of energy.Central to thermochemistry is the understanding of enthalpy, entropy, and Gibbs free energy.

• Enthalpy (\( H \)): A measure of total heat content within a system, it reflects the energy needed to create the system and the energy needed to allow the system to pressure/volume changes.
• Entropy (\( S \)): This reflects the degree of disorder or randomness in a system. Higher entropy indicates a more disordered system.
• Gibbs Free Energy (\( G \)): Combines enthalpy and entropy into a single value to predict the direction of chemical processes. The equation \( G = H - TS \), where \( T \) is temperature, shows how these energies are interlinked.

By understanding these concepts, students can grasp how energy changes influence reaction pathways. This understanding is key for both theoretical predictions and practical applications in fields like chemical engineering and environmental science.