Let's solve each problem in 3 steps, explaining each step and providing the final answer at the end. --- ## **First Reaction:** **2 SO₂(g) + O₂(g) → 2 SO₃(g)** ### **Step 1: Write the formula for standard entropy change (ΔS°)** \[ \Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}} \] **Explanation:** This formula means you add up the standard molar entropies (S°) of the products (multiplied by their coefficients), subtract the sum of the standard molar entropies of the reactants (also multiplied by their coefficients). --- ### **Step 2: Plug in the coefficients for each compound** \[ \Delta S^\circ = [2 \times S^\circ(\text{SO}_3)] - [2 \times S^\circ(\text{SO}_2) + 1 \times S^\circ(\text{O}_2)] \] **Explanation:** The coefficients from the balanced chemical equation are used to multiply the entropy values for each substance. --- ### **Step 3: Substitute standard entropy values (from tables) and calculate** (Standard molar entropy values at 298 K, in J/(mol·K): S°(SO₂(g)) = 248.2, S°(O₂(g)) = 205.0, S°(SO₃(g)) = 256.6) \[ \Delta S^\circ = [2 \times 256.6] - [2 \times 248.2 + 205.0] \] \[ = (513.2) - (496.4 + 205.0) \] \[ = 513.2 - 701.4 = -188.2 \ \text{J/(mol·K)} \] **Explanation:** Subtract the total entropy of reactants from that of products to find the standard entropy change. --- **Final Answer:** \[ \boxed{-188.2 \ \text{J/(mol·K)}} \] --- ## **Second Reaction:** **N₂(g) + 3 H₂(g) → 2 NH₃(g)** ### **Step 1: Write the formula for standard entropy change (ΔS°)** \[ \Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}} \] **Explanation:** Same formula as before, to find the change in entropy. --- ### **Step 2: Plug in the coefficients for each compound** \[ \Delta S^\circ = [2 \times S^\circ(\text{NH}_3)] - [1 \times S^\circ(\text{N}_2) + 3 \times S^\circ(\text{H}_2)] \] **Explanation:** Using the balanced equation, multiply each compound's entropy by its coefficient. --- ### **Step 3: Substitute standard entropy values (from tables) and calculate** (Standard molar entropy values at 298 K, in J/(mol·K): S°(N₂(g)) = 191.5, S°(H₂(g)) = 130.6, S°(NH₃(g)) = 192.5) \[ \Delta S^\circ = [2 \times 192.5] - [191.5 + 3 \times 130.6] \] \[ = (385.0) - (191.5 + 391.8) \] \[ = 385.0 - 583.3 = -198.3 \ \text{J/(mol·K)} \] **Explanation:** Again, subtract the total entropy of reactants from that of products. --- **Final Answer:** \[ \boxed{-198.3 \ \text{J/(mol·K)}} \] --- Let me know if you need the entropy values for different substances!

The concept used in answering these questions is the calculation of the standard entropy change (ΔS°) for chemical reactions, which involves summing the standard molar entropies of the products (multiplied by their coefficients) and subtracting the sum of the reactants' entropies (also weighted by their coefficients). This approach relies on standard molar entropy data from tables at 298 K and helps determine whether a reaction increases or decreases the disorder of the system during the process.

The key concept involved in answering these questions is the calculation of the standard entropy change (ΔS°) for a chemical reaction. This process is based on the principle that the entropy change of a reaction can be determined by taking the difference between the total molar entropies of the products and the reactants, each multiplied by their respective coefficients from the balanced chemical equation. The standard molar entropy values (S°) are obtained from thermodynamic tables at a specified temperature, typically 298 K. By applying the formula ΔS° = Σ (coefficients × S° of products) – Σ (coefficients × S° of reactants), we can quantify whether the reaction results in an increase or decrease in disorder within the system. This concept is fundamental in thermodynamics for understanding reaction spontaneity and energy changes related to entropy at standard conditions.