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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
All textbooksMcMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblem 16
Chapter 18, Problem 16

Consider the following graph of total free energy of reactants and products versus reaction progress for the general reaction, Reactants -> Products. At which of the four points (labeled a, b, c, and d) is Q < K? Graph showing total free energy vs reaction progress with points a, b, c, d labeled.
(a) Point a(b) Point c and d(c) Point a, c, and d(d) Point b

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1
Identify the points on the graph where the reaction is not at equilibrium. These points are where the reaction quotient Q is not equal to the equilibrium constant K.
Understand that at equilibrium, Q = K, and the system is at its lowest free energy state.
Recognize that points a, b, c, and d are not at equilibrium because they are not at the lowest free energy state (point e).
Determine the direction of the reaction progress. If the reaction proceeds towards products, Q < K; if it proceeds towards reactants, Q > K.
Since points a, c, and d are on the path towards the products (lower free energy), Q < K at these points.

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Key Concepts

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

Gibbs Free Energy (G)

Gibbs Free Energy is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is a crucial factor in determining the spontaneity of a reaction; if the change in Gibbs Free Energy (ΔG) is negative, the reaction is spontaneous in the forward direction.
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Gibbs Free Energy of Reactions

Reaction Quotient (Q) and Equilibrium Constant (K)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in a reaction, while the equilibrium constant (K) is the value of Q when the reaction is at equilibrium. When Q < K, it indicates that the reaction will proceed in the forward direction to reach equilibrium, favoring the formation of products.
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Reaction Quotient Q

Free Energy Diagram

A free energy diagram visually represents the change in Gibbs Free Energy as a reaction progresses from reactants to products. It typically shows the energy levels of reactants and products, along with transition states, and helps identify points of interest, such as where Q is less than K, indicating the direction in which the reaction will favorably proceed.
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Related Practice
Textbook Question
Nitrogen reacts with fluorine to form nitrogen trifluoride: Calculate ∆G°, and determine whether the equilibrium composition should favor reactions or products at 25 °C(a) ∆G° = -6.7 kJ; the equilibrium composition should favor products. (b) ∆G° = -332 kJ; the equilibrium composition should favor reactants (c) ∆G° = -166 kJ; the equilibrium composition should favor products (d) ∆G° = +82.6 kJ; the equilbirum composiiton should favor reactants.
Textbook Question
Ammonium hydrogen sulfide, a stink bomb ingredient, decomposes to ammonia and hydrogen sulfide: Calculate the standard free-energy change for the rection at 25 °C if the total pressure resulting from the solid NH4S placed in an evacuated container is 0.658 atm at 25 °C.(a) -43.8 kJ(b) +1.04 kJ(c) -462 kJ(d) +5.51 kJ
Textbook Question

Spinach contains a lot of iron but is not a good source of dietary iron because nearly all the iron is tied up in the oxalate complex [Fe(C2O4)3]3-.

(b) Under the acidic conditions in the stomach, the Fe3+ concentration should be greater because of the reaction

[Fe(C2O4)3]3-(aq) + 6 H3O+(aq) ⇌ Fe3+(aq) + 3 H2C2O4(aq) + 6 H2O(l)

Show, however, that this reaction is nonspontaneous under standard-state conditions. (For H2C2O4, Ka1 = 5.9 × 10-2 and Ka2 = 6.4 × 10-5.)

Textbook Question

Formation constants for the ammonia and ethylenediamine complexes of nickel(II) indicate that Ni(en)32+ is much more

stable than Ni(NH3)62+:

(1) <REACTION>

(2) <REACTION>

The enthalpy changes for the two reactions, ΔH°1 and ΔH°2, should be about the same because both complexes have six Ni﹣N bonds. 

(c) Assuming that ΔH°2 - ΔH°1 is zero, calculate the value of ΔS°2 - ΔS°1.

Textbook Question
Consider the gas-phase reaction of AB3 and A2 molecules:

(a) Write a balanced equation for the reaction.(b) What is the sign of the entropy change for the reaction?