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. c. C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(g) ΔH°_rxn = -2044 kJ

Verified step by step guidance

Identify the type of reaction: The given reaction is a combustion reaction where propane (C_3H_8) reacts with oxygen to form carbon dioxide and water. Combustion reactions are typically exothermic.

Determine the sign of ΔS_sys: In this reaction, the number of moles of gas decreases from 6 moles (1 C_3H_8 + 5 O_2) to 7 moles (3 CO_2 + 4 H_2O). Since the number of gas molecules increases, ΔS_sys is likely positive.

Determine the sign of ΔS_surr: The reaction is exothermic (ΔH°_rxn = -2044 kJ), which means heat is released to the surroundings. This increases the entropy of the surroundings, so ΔS_surr is positive.

Predict spontaneity at different temperatures: For a reaction to be spontaneous, the total entropy change (ΔS_total = ΔS_sys + ΔS_surr) must be positive. Since both ΔS_sys and ΔS_surr are positive, the reaction is spontaneous at all temperatures.

Summarize the findings: The reaction has ΔS_sys > 0 and ΔS_surr > 0, making it spontaneous at all temperatures due to the positive total entropy change.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

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 involve the formation of solids from gases usually have a negative ΔS. Understanding the changes in entropy helps predict the spontaneity of reactions.

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 relationship between ΔH and ΔS is crucial in determining whether a reaction is spontaneous at a given temperature, as described by the Gibbs free energy equation: ΔG = ΔH - TΔS. A reaction is spontaneous when ΔG is negative, which can occur under specific temperature conditions.

Gibbs Free Energy (ΔG)

Gibbs free energy (ΔG) combines the effects of enthalpy and entropy to determine the spontaneity of a reaction. A negative ΔG indicates that a reaction can occur spontaneously, while a positive ΔG suggests non-spontaneity. The temperature at which a reaction becomes spontaneous can be found by analyzing the signs of ΔH and ΔS; for example, if ΔH is negative and ΔS is positive, the reaction is spontaneous at all temperatures.

Recommended video:

Guided course

01:51

Gibbs Free Energy of Reactions

Related Practice

Textbook Question

Without doing any calculations, determine the sign of ΔS_sys for each chemical reaction. a. 2 KClO₃(s) → 2 KCl(s) + 3 O₂(g) c. Na(s) + 2 Cl₂(g) → NaCl(s) d. N₂(g) + 3 H₂(g) → 2 NH₃(g)

views

Textbook Question

Without doing any calculations, determine the sign of ΔS_sys for each chemical reaction. b. CH₂=CH₂( g) + H₂( g) → CH₃CH₃( g)

Textbook Question

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

Textbook Question

Calculate ΔS_surrat the indicated temperature for each reaction. d. ΔH°_rxn= +114 kJ; 77 K

Textbook Question

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

Textbook Question

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.) c. ΔH°_rxn = -135 kJ; ΔS°_rxn = -282 J>K; T = 298 K