Thermodynamics and defect chemistry of substitutional and interstitial cation doping in layered α-V₂O₅

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...

Nucleophilic substitution in α-halocarbonyl compounds can be achieved via an SN2 pathway. The reaction in α-haloketones is generally carried out with less basic nucleophiles. The use of strong basic nucleophiles leads to the generation of α-haloenolate ions, which often participate in other side reactions.

Carbohydrates are an essential part of the diet in humans and animals. Grains, fruits, and vegetables are natural sources of carbohydrates that provide energy to the body, particularly through glucose, a simple sugar that is a component of starch and an ingredient in many staple foods. The stoichiometric formula (CH2O)n, where n is the number of carbons in the molecule represents carbohydrates. In other words, the ratio of carbon to hydrogen to oxygen is 1:2:1 in carbohydrate molecules. This...

α-Substituted ketones or aldehydes can be synthesized from enamines by the Stork enamine reaction, named after its pioneer Gilbert Stork. Enamines are useful synthetic intermediates where the lone pair on nitrogen is in conjugation with the C=C bond. They resemble enolate ions, as the resonance forms of both species have a nucleophilic α carbon.