Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problem 134

Chapter 18, Problem 134

Suppose that a reaction has ΔH = - 33 kJ and ΔS = - 58 J>K. At what temperature will it change from spontaneous to nonspontaneous?

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Identify the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \).

Recognize that a reaction is spontaneous when \( \Delta G < 0 \) and nonspontaneous when \( \Delta G > 0 \). The transition point is when \( \Delta G = 0 \).

Set \( \Delta G = 0 \) and substitute the given values into the equation: \( 0 = -33 \text{ kJ} - T(-58 \text{ J/K}) \).

Convert \( \Delta H \) from kJ to J to match the units of \( \Delta S \): \( -33 \text{ kJ} = -33000 \text{ J} \).

Solve for the temperature \( T \) by rearranging the equation: \( T = \frac{-33000 \text{ J}}{-58 \text{ J/K}} \).

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Key Concepts

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

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction. It is defined by the equation ΔG = ΔH - TΔS, where ΔG is the change in Gibbs Free Energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A reaction is spontaneous when ΔG is negative.

Spontaneity of Reactions

The spontaneity of a reaction refers to its ability to occur without external intervention. A reaction is spontaneous at a given temperature if the Gibbs Free Energy change (ΔG) is negative. The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) determines whether a reaction will be spontaneous or nonspontaneous.

Temperature and Entropy

Temperature plays a crucial role in determining the spontaneity of a reaction, particularly when considering entropy changes. The term TΔS in the Gibbs Free Energy equation indicates that as temperature increases, the impact of entropy on spontaneity becomes more significant. If ΔS is negative, increasing temperature can lead to a positive ΔG, making the reaction nonspontaneous.

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Textbook Question

The normal boiling point of bromine is 58.8 °C, and the standard entropies of the liquid and vapor are S°[Br2(l) = 152.2 J/(K*mol); S°[Br2(g) = 245.4 J/(K*mol). At what temperature does bromine have a vapor pressure of 227 mmHg?

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Textbook Question

Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = - 48 kJ; ΔS = + 135 J>K at 400 K (b) ΔH = - 48 kJ; ΔS = - 135 J>K at 400 K (c) ΔH = + 48 kJ; ΔS = + 135 J>K at 400 K (d) ΔH = + 48 kJ; ΔS = - 135 J>K at 400 K

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Textbook Question

The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has ∆G° = -224.4 kJ/mol at 25°C:

Use the following additional data at 25 °C to calculate the standard molar entropy S° of O2 at 25°C: ∆H°f(KClO3) = -397.7 kJ/mol, ∆H°f(KCl) = -436.5 kJ/mol, S°(KClO3) = 143.1 J/(K*mol), and S°(KCl) = 82.6 J/(K*mol).

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Textbook Question

A mixture of 14.0 g of N2 and 3.024 g of H2 in a 5.00 L container is heated to 400 °C. Use the data in Appendix B to calculate the molar concentrations of N2, H2, and NH3 at equilibrium. Assume that ∆H° and ∆S° are independent of temperature, and remember that the standard state of a gas is defined in terms of pressure.

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Textbook Question

The lead storage battery uses the reaction: (b) Calculate ∆G for this reaction on a cold winter's day (10 °F) in a battery that has run down to the point where the sulfuric acid concentration is only 0.100 M.

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Textbook Question

Chloroform has ΔHvaporization = 29.2 kJ>mol and boils at 61.2 °C. What is the value of ΔSvaporization for chloroform?

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