Ch.19 - Chemical Thermodynamics

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.19 - Chemical Thermodynamics

Problem 15b

Chapter 19, Problem 15b

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (b) In what temperature range is it a spontaneous process?

Verified step by step guidance

insert step 1> Identify the process: The vaporization of liquid water to steam is an endothermic process, meaning it requires heat input.

insert step 2> Understand spontaneity: A process is spontaneous if the change in Gibbs free energy (\( \Delta G \)) is negative.

insert step 3> Use the Gibbs free energy equation: \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is the enthalpy change, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the entropy change.

insert step 4> Determine the conditions for spontaneity: For the process to be spontaneous, \( \Delta G < 0 \). This implies \( T\Delta S > \Delta H \).

insert step 5> Calculate the temperature range: Rearrange the inequality to find the temperature range where the process is spontaneous: \( T > \frac{\Delta H}{\Delta S} \). Use the known values of \( \Delta H \) and \( \Delta S \) for water vaporization at 1 atm to find the temperature range.

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Key Concepts

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

Vaporization

Vaporization is the process by which a liquid turns into a gas. For water, this occurs when molecules gain enough energy to overcome intermolecular forces. At 1 atm pressure, water vaporizes at 100°C, but the spontaneity of this process depends on temperature and the Gibbs free energy change.

Gibbs Free Energy

Gibbs free energy (G) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. A process is spontaneous when the change in Gibbs free energy (ΔG) is negative. For vaporization, ΔG can be influenced by temperature, pressure, and the enthalpy and entropy changes associated with the phase transition.

Phase Equilibrium

Phase equilibrium occurs when the rates of vaporization and condensation are equal, resulting in a stable state. At 1 atm, water and steam coexist at 100°C. Above this temperature, vaporization becomes spontaneous as the system favors the gaseous phase, while below it, condensation is favored, indicating the importance of temperature in determining the spontaneity of vaporization.

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