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Chapter 14: Problem 1

Why is using the Gibbs function advantageous when studying chemical and phase equilibrium?

Short Answer

Expert verified
The Gibbs function is advantageous because it helps predict chemical and phase equilibrium and determine stability under constant temperature and pressure.

Step by step solution

01

Introduction to Gibbs Function

The Gibbs function, also known as Gibbs free energy (G), is a thermodynamic potential that measures the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure.
02

Derivation and Formula

The Gibbs free energy is given by the equation: \[ G = H - TS \] where H is enthalpy, T is temperature, and S is entropy.
03

Chemical Equilibrium

At chemical equilibrium, the Gibbs free energy of a system is at its minimum value for the given conditions of temperature and pressure. This property helps predict the direction of chemical reactions and the position of equilibrium.
04

Phase Equilibrium

For phase equilibrium, the Gibbs free energy helps determine which phase (solid, liquid, or gas) is the most stable under given conditions. The phase with the lowest Gibbs free energy will be the stable phase.
05

Practical Use

Using the Gibbs function allows scientists and engineers to determine equilibrium compositions of reactions, decide on feasible reactions, and optimize thermal processes without needing to consider detailed internal energy changes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Equilibrium
Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, leading to no net change in the concentration of reactants and products. The Gibbs free energy (G) plays a crucial role in understanding chemical equilibrium because it can indicate the spontaneity of a reaction. At equilibrium, the Gibbs free energy is at its minimum value for the given temperature and pressure, meaning that any deviation from this point will increase the system's free energy.
Therefore, the system naturally tends to move towards this minimum energy state. The equation that defines the Gibbs free energy is: Agllers Cheves Solution: When Bravo V=

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Most popular questions from this chapter

Methane gas at \(25^{\circ} \mathrm{C}, 1 \mathrm{~atm}\) enters a reactor operating at steady state and burns with \(90 \%\) of theoretical air entering at \(217^{\circ} \mathrm{C}, 1 \mathrm{~atm}\). An equilibrium mixture of \(\mathrm{CO}_{2}, \mathrm{CO}\), \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{H}_{2}\), and \(\mathrm{N}_{2}\) exits at \(1527^{\circ} \mathrm{C}, 1 \mathrm{~atm}\). Determine, per kmol of methane entering, (a) the composition of the exiting mixture. (b) the heat transfer between the reactor and its surroundings, in \(\mathrm{kJ}\). Neglect kinetic and potential energy effects.

An isolated system has two phases, denoted by A and B, each of which consists of the same two substances, denoted by 1 and 2 . Show that necessary conditions for equilibrium are 1\. the temperature of each phase is the same, \(T_{\mathrm{A}}=T_{\mathrm{B}}\). 2\. the pressure of each phase is the same, \(p_{\mathrm{A}}=p_{\mathrm{B}}\). 3\. the chemical potential of each component has the same value in each phase, \(\mu_{1}^{\mathrm{A}}=\mu_{1}^{\mathrm{B}}, \mu_{2}^{\mathrm{A}}=\mu_{2}^{\mathrm{B}}\).

Spark-ignition engine exhaust gases contain several air pollutants including the oxides of nitrogen, \(\mathrm{NO}\), and \(\mathrm{NO}_{2}\), collectively known as \(\mathrm{NO}_{x}\). Additionally, the exhaust gases may contain carbon monoxide (CO) and unburned or partially burned hydrocarbons (HC). (a) The pollutant amounts actually present depend on engine design and operating conditions, and typically differ significantly from values calculated on the basis of chemical equilibrium. Discuss both the reasons for these discrepancies and possible mechanisms by which such pollutants are formed in an actual engine. (b) For spark-ignition engines, the average production of pollutants upstream of the catalyst, in \(\mathrm{g}\) per mile of vehicle travel, are nitric oxides, \(1.5\); hydrocarbons, 2 ; and carbon monoxide, 20 . For a city in your locale having a population of 100,000 or more, estimate the annual amount, in \(\mathrm{kg}\), of each pollutant that would be discharged if automobiles had no emission control devices. Repeat if the vehicles adhere to current U.S. government emissions standards.

If the ionization-equilibrium constants for \(\mathrm{Cs} \rightleftarrows\) \(\mathrm{Cs}^{+}+\mathrm{e}^{-}\)at 1800 and \(2200 \mathrm{~K}\) are \(K=8.21\) and \(K=23.06\), respectively, estimate the enthalpy of ionization, in \(\mathrm{kJ} / \mathrm{kmol}\), at \(2000 \mathrm{~K}\) using the van't Hoff equation.

Gaseous propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) at \(25^{\circ} \mathrm{C}, 1 \mathrm{~atm}\) enters a reactor operating at steady state and burns with \(80 \%\) of theoretical air entering separately at \(25^{\circ} \mathrm{C}, 1 \mathrm{~atm}\). An equilibrium mixture of \(\mathrm{CO}_{2}, \mathrm{CO}, \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{H}_{2}\), and \(\mathrm{N}_{2}\) exits at \(1227^{\circ} \mathrm{C}\), \(1 \mathrm{~atm}\). Determine the heat transfer between the reactor and its surroundings, in \(\mathrm{kJ}\) per \(\mathrm{kmol}\) of propane entering. Neglect kinetic and potential energy effects.
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