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For a typical second-order reaction with rate equation = [] [], if the concentration of reactant B is constant then = [] [] = ′ [], where the pseudo–first-order rate constant ′ = []. The second-order rate equation has been reduced to a pseudo–first-order rate equation, which makes the treatment to obtain an integrated rate equation much ...
First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. [6] The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free ...
In fact, however, the observed reaction rate is second-order in NO 2 and zero-order in CO, [5] with rate equation r = k[NO 2] 2. This suggests that the rate is determined by a step in which two NO 2 molecules react, with the CO molecule entering at another, faster, step. A possible mechanism in two elementary steps that explains the rate ...
Landau theory (also known as Ginzburg–Landau theory, despite the confusing name [1]) in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. [2]
The first degree polynomial equation = + is a line with slope a. A line will connect any two points, so a first degree polynomial equation is an exact fit through any two points with distinct x coordinates. If the order of the equation is increased to a second degree polynomial, the following results:
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
The rate law depends on the first order concentration of two reactants, making it a 2nd order (bimolecular) elimination reaction. Factors that affect the rate determining step are stereochemistry, leaving groups, and base strength.
First-order approximation is the term scientists use for a slightly better answer. [3] Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has 4 × 10 3, or four thousand, residents"). In the case of a first-order approximation, at least one number given is exact.
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