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Weak Base Solutions

Weak Base Solutions

Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...

Weak Acid Solutions

Weak Acid Solutions

Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a...

Titration of a Weak Acid with a Weak Base

Titration of a Weak Acid with a Weak Base

Weak acids and bases do not undergo dissociation completely, and titrations between these two are rarely studied. When such studies are performed, say, for the titration of a weak acid with a weak base, the titration curve plots the change in pH as a function of the volume of base added. Take the titration of acetic acid with ammonia, for instance. During the titration, these two species form ammonium acetate and water, but the pH change is slow and gradual.
As a result, there is no simple...

Titration Calculations: Weak Acid - Strong Base

Titration Calculations: Weak Acid - Strong Base

Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:

Crossed Aldol Reaction Using Weak Bases

Crossed Aldol Reaction Using Weak Bases

This lesson deals with the crossed aldol reaction using weak bases. The self-condensation of an aldehyde having α hydrogen is prevented by adding it slowly to a mixture of formaldehyde and weak bases like hydroxide and alkoxide. Upon slow addition of the aldehyde, the base deprotonates the α carbon of the aldehyde to form the corresponding enolate. The enolate subsequently attacks the formaldehyde to form a single crossed product. Figure 1 depicts the aforementioned reaction.

Titration of a Weak Base with a Strong Acid

Titration of a Weak Base with a Strong Acid

The titration curve of a weak base like ammonia with a strong acid like hydrochloric acid is the mirror image of the titration curve of a weak acid with a strong base.
Using the ICE table and substituting the Kb value, we calculate the initial pH of 50 mL of 0.1 M ammonia to be 11.11. Addition of 25 mL of 0.1 M hydrochloric acid to this solution of ammonia results in a buffer with an equal concentration of ammonia and ammonium ions. The pH of this buffer can be calculated by substituting these...

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Kibble-Zurek Scaling from Linear Response Theory.

Entropy (Basel, Switzerland)·2022

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Unifying Kibble-Zurek Mechanism in Weakly Driven Processes.

¹Instituto de Ciências Exatas e Naturais, Faculdade de Física, Universidade Federal do Pará, Av. Augusto Correa, 1, Guamá, Belém 66075-110, PA, Brazil.

Entropy (Basel, Switzerland)

|January 28, 2026

Summary

This study introduces a new framework for the Kibble-Zurek mechanism, eliminating previous ad hoc hypotheses. The new model accurately describes the phenomenon, yielding excess work scaling close to 2/5 for various systems.

Keywords:

Kibble-Zurek mechanism linear response theory

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Area of Science:

Physics
Non-equilibrium thermodynamics
Quantum mechanics

Background:

The Kibble-Zurek mechanism describes defect formation during phase transitions.
Previous models relied on ad hoc hypotheses, limiting their applicability.
Linear response theory has been applied, but with simplifying assumptions.

Purpose of the Study:

To develop a new theoretical framework for the Kibble-Zurek mechanism.
To eliminate unnecessary ad hoc hypotheses in describing the phenomenon.
To obtain accurate scaling relations for excess work.

Main Methods:

Development of a new theoretical framework.
Application of linear response theory without ad hoc assumptions.
Analysis of systems with diverging relaxation times at critical points.

Main Results:

A new framework is presented that preserves all characteristics of the Kibble-Zurek mechanism.
The Kibble-Zurek scaling for excess work is found to be approximately 2/5.
This result is valid for both open and thermally isolated systems.

Conclusions:

The new framework provides a more rigorous description of the Kibble-Zurek mechanism.
The 2/5 scaling for excess work is a robust prediction of the model.
The framework is exemplified using four distinct scaling functions.