Without doing any calculations, determine the signs of ΔS_sys and ΔS surr for each chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous. a. C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(g) ΔH°_rxn = -2044 kJ

Verified step by step guidance

1. Determine the sign of \( \Delta S_{sys} \): Consider the change in the number of moles of gas. The reaction goes from 6 moles of gas (1 mole of \( \text{C}_3\text{H}_8 \) and 5 moles of \( \text{O}_2 \)) to 7 moles of gas (3 moles of \( \text{CO}_2 \) and 4 moles of \( \text{H}_2\text{O} \)). Since the number of moles of gas increases, \( \Delta S_{sys} \) is positive.
2. Determine the sign of \( \Delta S_{surr} \): Since \( \Delta H^\circ_{rxn} = -2044 \text{ kJ} \), the reaction is exothermic. An exothermic reaction releases heat to the surroundings, increasing the entropy of the surroundings, so \( \Delta S_{surr} \) is positive.
3. Predict the spontaneity of the reaction: For a reaction to be spontaneous, the total entropy change (\( \Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr} \)) must be positive. Since both \( \Delta S_{sys} \) and \( \Delta S_{surr} \) are positive, \( \Delta S_{univ} \) is positive at all temperatures.
4. Conclude the spontaneity: The reaction is spontaneous at all temperatures because both the system and the surroundings experience an increase in entropy.
5. Summarize: The reaction \( \text{C}_3\text{H}_8(g) + 5 \text{O}_2(g) \rightarrow 3 \text{CO}_2(g) + 4 \text{H}_2\text{O}(g) \) has \( \Delta S_{sys} > 0 \), \( \Delta S_{surr} > 0 \), and is spontaneous at all temperatures.

Key Concepts

Entropy (ΔS)

Entropy, represented as ΔS, is a measure of the disorder or randomness in a system. In chemical reactions, an increase in the number of gas molecules or a transition from solid to liquid or gas typically results in a positive ΔS, indicating greater disorder. Conversely, reactions that produce fewer gas molecules or transition to a more ordered state usually have a negative ΔS.

Enthalpy (ΔH) and Spontaneity

Enthalpy change (ΔH) reflects the heat absorbed or released during a reaction. A negative ΔH indicates an exothermic reaction, which tends to favor spontaneity. The spontaneity of a reaction is also influenced by temperature, as described by the Gibbs free energy equation (ΔG = ΔH - TΔS), where a negative ΔG indicates a spontaneous process.

Gibbs Free Energy (ΔG)

Gibbs free energy (ΔG) combines enthalpy and entropy to determine the spontaneity of a reaction. A reaction is spontaneous when ΔG is negative, which can occur under specific temperature conditions depending on the signs of ΔH and ΔS. For reactions with a negative ΔH and positive ΔS, spontaneity is favored at all temperatures, while the opposite conditions may require high temperatures for spontaneity.