Question

Sulfur dioxide reacts with strontium oxide as follows: $$ \mathrm{SO}_{2}(g)+\mathrm{SrO}(g) \longrightarrow \mathrm{SrSO}_{3}(s) $$ (a) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ}\). (b) If you had only standard enthalpy data for this reaction, estimate of the value of \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\), using data from Appendix \(C\) on other substances.

Short answer

Since \(\Delta G^{\circ}-\Delta H^{\circ} > 0\), the Gibbs free energy for this reaction (\(\Delta G^{\circ}\)) is less negative than the enthalpy change (\(\Delta H^{\circ}\)). To estimate \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\) using standard enthalpy data, find reactions in Appendix C that closely resemble the given reaction, apply Hess's Law to obtain the overall reaction, and use the relationship \(\Delta G^{\circ} = \Delta H^{\circ} - T(\Delta S^{\circ})\) to estimate \(\Delta G^{\circ}\).

Step-by-step solution

Use Gibbs free energy formula

To analyze the relation between \(\Delta G^{\circ}\) and \(\Delta H^{\circ}\), we should use the Gibbs free energy formula: \(\Delta G^{\circ}=\Delta H^{\circ}-T\Delta S^{\circ}\) Since we want to compare \(\Delta G^{\circ}\) and \(\Delta H^{\circ}\), we can rewrite the equation as: \(\Delta G^{\circ}-\Delta H^{\circ}=-T\Delta S^{\circ}\) Now, let's analyze the sign of \(\Delta S^{\circ}\) by analyzing the reaction more closely. ###Step 2: Analyze the entropy change###

Identify the sign of ΔS°

Entropy is a measure of disorder or randomness. In the given reaction, we can observe the following changes related to entropy: - In the reaction, we're going from two gaseous substances (\(\mathrm{SO}_{2}\) and \(\mathrm{SrO}\)) to one solid substance (\(\mathrm{SrSO}_{3}\)) - Gaseous substances generally have higher entropy than solid substances From these observations, we can conclude that the entropy of the reactants is higher than the entropy of the product. Therefore, the change in entropy, \(\Delta S^{\circ}\), is negative for this reaction. ###Step 3: Determine the sign of ΔG° - ΔH°###

Compare ΔG° and ΔH° using entropy change

From our analysis in step 1, we have the equation: \(\Delta G^{\circ}-\Delta H^{\circ}=-T\Delta S^{\circ}\) Since we determined in step 2 that \(\Delta S^{\circ}\) is negative and the temperature is always positive, we will have a positive product of (-T)(ΔS°), resulting in: \(\Delta G^{\circ}-\Delta H^{\circ} > 0\) This indicates that \(\Delta G^{\circ}\) is less negative than \(\Delta H^{\circ}\). ###Answer for part (a)### Since \(\Delta G^{\circ}-\Delta H^{\circ} > 0\), the Gibbs free energy for this reaction (\(\Delta G^{\circ}\)) is less negative than the enthalpy change (\(\Delta H^{\circ}\)). For part (b), we need to estimate the value of \(\Delta G^{\circ}\) using available standard enthalpy data and applying Hess's law. Unfortunately, we cannot provide specific values from the appendix here. However, we can explain the general approach to solve this part. ###Step 4: Find standard enthalpy data###

Check Appendix C for related reactions

Look for reactions in Appendix C that closely resemble the given reaction. Record the enthalpy change (\(\Delta H^{\circ}\)) for each selected reaction. ###Step 5: Apply Hess's Law###

Add reactions to estimate ΔH° for the given reaction

Using Hess's Law, add, subtract, or manipulate the found reactions to obtain the overall reaction. Ensure that the sum of the coefficients of the selected reactions is equal to the coefficients in the given reaction. Add the respective \(\Delta H^{\circ}\) values of the selected reactions to estimate the enthalpy change for the given reaction. ###Step 6: Estimate ΔG° using the relationship###

Use the relationship between ΔG° and ΔH° to estimate ΔG°

Now that we have an estimate of \(\Delta H^{\circ}\) for the given reaction, we can return to the relationship we derived in step 1: \(\Delta G^{\circ}-\Delta H^{\circ}=-T\Delta S^{\circ}\) Since we know that \(\Delta S^{\circ}\) is negative, we can estimate \(\Delta G^{\circ}\) using the estimated value of \(\Delta H^{\circ}\) and accounting for the temperature and entropy change: \(\Delta G^{\circ} = \Delta H^{\circ} - T(\Delta S^{\circ})\) This will give us an estimate for \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\).

Key concepts

Entropy Change

When assessing reactions in thermodynamics, understanding entropy change is crucial. Entropy (\( S \)) is essentially the measure of randomness or disorder in a system. It represents how energy within a system is dispersed. In the given reaction, as sulfur dioxide (\( \mathrm{SO}_{2}(g) \)) and strontium oxide (\( \mathrm{SrO}(g) \)) combine to form solid strontium sulfite (\( \mathrm{SrSO}_{3}(s) \)), there is a transition from gaseous to solid state.
This transformation is significant because gases have significantly higher entropy than solids due to their more disordered state and greater degrees of freedom.
Thus, moving from two gaseous reactants to a singular solid product means the overall entropy decreases, indicating a negative change in entropy (\( \Delta S^{\circ} < 0 \)).

This negative entropy change implies that the final state of the system is more ordered than the initial state, contributing to the understanding of why the reaction's free energy change (\( \Delta G^{\circ} \)) is less negative than the enthalpy change (\( \Delta H^{\circ} \)) due to the entropy term affecting the reaction's spontaneity.

Enthalpy Change

Enthalpy (\( H \)) is a representation of the total heat content of a system. It plays a pivotal role in understanding thermodynamic reactions and determining if they are energetically favorable.
In our example, to find the enthalpy change (\( \Delta H^{\circ} \)), you would usually use standard enthalpies of formation from reliable references like appendix data or tables.

Hess's Law is a fundamental principle that can help estimate the enthalpy change for reactions. This law states that the total enthalpy change for a reaction is the sum of the enthalpies of the steps into which the reaction can be divided.
By using known enthalpy values of similar reactions or forming equations directly from reactants to products, you can estimate the enthalpy change conveniently.

• Check whether the products or reactants release more energy, indicating exothermicity (\( \Delta H^{\circ} < 0 \)) or gain energy (endothermicity).
• This step aids in understanding the tendency of the system to release or absorb heat.

Evaluating this change is integral in predicting the behavior of a reaction when combined with entropy considerations.

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It’s fundamental in predicting the direction and feasibility of chemical reactions.
Key concepts include:

• **First Law of Thermodynamics**: Energy cannot be created or destroyed, only transformed from one form to another. This law introduces the concept of internal energy and highlights conservation of energy.
• **Second Law of Thermodynamics**: Entropy of an isolated system always increases over time. It defines phenomena that occur naturally toward disorder.
• **Gibbs Free Energy (\( G \))**: Combines enthalpy and entropy into a single value to predict reaction spontaneity. This energy is expressed in the formula \( \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} \), indicating both enthalpy and entropy changes' contributions.

This specific formula is crucial because it helps predict whether a reaction is spontaneous under constant temperature and pressure conditions. A negative \( \Delta G^{\circ} \) indicates a spontaneous reaction, while a positive value suggests non-spontaneity.
By understanding the interplay of these core elements, we gain insights into the energy transformations and predict how reactions evolve within these constraints. Thermodynamics provides the framework to balance these elements and assess systems effectively.