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

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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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Textbook Question

Indicate whether each statement is true or false. (a) A reaction that is spontaneous in one direction will be nonspontaneous in the reverse direction under the same reaction conditions. (b) All spontaneous processes are fast. (c) Most spontaneous processes are reversible. (d) An isothermal process is one in which the system loses no heat. (e) The maximum amount of work can be accomplished by an irreversible process rather than a reversible one.

Textbook Question

(d) Does the amount of work that a system can do on its surroundings depend on the path of the process?

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Textbook Question

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic?

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Textbook Question

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

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Textbook Question

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (d) At what temperature are the two phases in equilibrium?

Textbook Question

The normal freezing point of n-octane (C₈H₁₈) is -57 °C. (b) In what temperature range is the freezing of n-octane a spontaneous process?