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

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Identify the system and surroundings: The system is the chemical reaction given, and the surroundings are everything else around it.

Determine the sign of ΔS_sys (entropy change of the system) by comparing the number of moles of gaseous reactants and products. Here, reactants have 1 mole of C₃H₈ and 5 moles of O₂, totaling 6 moles of gas, while products have 3 moles of CO₂ and 4 moles of H₂O gas, totaling 7 moles of gas. Since the number of gas moles increases, ΔS_sys is positive.

Determine the sign of ΔS_surr (entropy change of the surroundings) using the sign of ΔH_rxn. Since ΔH°_rxn = -2044 kJ (negative), the reaction is exothermic, so heat is released to the surroundings, increasing their entropy. Therefore, ΔS_surr is positive.

Recall the Gibbs free energy equation:

ΔG = ΔH - T ΔS

. For spontaneity, ΔG must be negative.

Since both ΔH is negative and ΔS_sys is positive, the reaction is spontaneous at all temperatures.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy Change of the System (ΔS_sys)

Entropy (S) measures the disorder or randomness in a system. ΔS_sys refers to the change in entropy of the reacting substances. For reactions involving gases, an increase in the number of gas molecules usually means an increase in entropy, while a decrease in gas molecules leads to a decrease in entropy.

Entropy Change of the Surroundings (ΔS_surr) and Enthalpy (ΔH)

The entropy change of the surroundings is related to the heat exchanged with the surroundings, which depends on the reaction's enthalpy change (ΔH). For exothermic reactions (ΔH < 0), heat is released, increasing the surroundings' entropy (ΔS_surr > 0). For endothermic reactions (ΔH > 0), heat is absorbed, decreasing surroundings' entropy.

Temperature Dependence of Spontaneity and Gibbs Free Energy

Spontaneity depends on Gibbs free energy change (ΔG = ΔH - TΔS_sys). If ΔG < 0, the reaction is spontaneous. For exothermic reactions with negative ΔH and negative ΔS_sys, spontaneity depends on temperature: spontaneous at low temperatures when the enthalpy term dominates, but not at high temperatures where the entropy term can dominate.

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Given the values of ΔH°_rxn, ΔS°_rxn, and T, determine ΔS_univ and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. ΔH°_rxn = +135 kJ; ΔS°_rxn = -282 J/K; T = 298 K