Homoleptic Lanthanide Amides as Homogeneous Catalysts for the Tishchenko Reaction

Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...

Amides are synthesized by treating carboxylic acids with amines in the presence of dehydrating agents like dicyclohexylcarbodiimide (DCC).
The DCC-promoted synthesis of amides begins with the protonation of DCC by carboxylic acid. The protonation makes it a better acceptor. Next, the addition of carboxylate to the protonated carbodiimide gives a reactive acylating agent.
Subsequently, the amine acts as a nucleophile that attacks the acylating agent to form a tetrahedral intermediate. In the...

The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure.
The mathematical representation of the change in the concentration of reactants and products, over time, is the rate...

Amides can undergo either acid-catalyzed hydrolysis or base-promoted hydrolysis through a typical nucleophilic acyl substitution. Each hydrolysis requires severe conditions.
Acid-catalyzed hydrolysis:
Hydrolysis of amides under acidic conditions yields carboxylic acids. Since the reaction occurs slowly, hydrolysis requires the conditions of heat.
The mechanism begins with the protonation of the carbonyl oxygen by the acid catalyst. The protonation makes the amide carbonyl carbon more...

Various carboxylic acid derivatives (such as acid chlorides, esters, and anhydrides) can be used for the acylation of amines to yield amides. The reaction requires two equivalents of amines. The first amine molecule functions as a nucleophile and attacks the carbonyl carbon to produce a tetrahedral intermediate. This is followed by the loss of the leaving group and restoration of the C=O bond.
Next, the second equivalent of amine serves as a Brønsted base and deprotonates the quaternary...