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In mathematics and other formal sciences, first-order or first order most often means either: " linear " (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
A common form for the rate equation is a power law: [6] = [] [] The constant is called the rate constant.The exponents, which can be fractional, [6] are called partial orders of reaction and their sum is the overall order of reaction.
[A] can provide intuitive insight about the order of each of the reagents. If plots of v / [A] vs. [B] overlay for multiple experiments with different-excess, the data are consistent with a first-order dependence on [A]. The same could be said for a plot of v / [B] vs. [A]; overlay is consistent with a first-order dependence on [B].
Using the Eyring equation, there is a straightforward relationship between ΔG ‡, first-order rate constants, and reaction half-life at a given temperature. At 298 K, a reaction with ΔG ‡ = 23 kcal/mol has a rate constant of k ≈ 8.4 × 10 −5 s −1 and a half life of t 1/2 ≈ 2.3 hours, figures that are often rounded to k ~ 10 −4 s ...
For a first-order reaction, it has units of s −1. For that reason, it is often called frequency factor . According to collision theory , the frequency factor, A, depends on how often molecules collide when all concentrations are 1 mol/L and on whether the molecules are properly oriented when they collide.
In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
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Generally, as the temperature increases so does the rate at which the reaction occurs. Residence time, , is the average amount of time a discrete quantity of reagent spends inside the tank. Assume: isothermal conditions, or constant temperature (k is constant) single, irreversible reaction (ν A = -1) first-order reaction (r = k C A)