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If the concentration of a reactant remains constant (because it is a catalyst, or because it is in great excess with respect to the other reactants), its concentration can be included in the rate constant, leading to a pseudo–first-order (or occasionally pseudo–second-order) rate equation. For a typical second-order reaction with rate ...
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 ...
Then the Thiele modulus for a first order reaction is: = From this relation it is evident that with large values of , the rate term dominates and the reaction is fast, while slow diffusion limits the overall rate. Smaller values of the Thiele modulus represent slow reactions with fast diffusion.
the simple first-order rate law described in introductory textbooks. Under these conditions, the concentration of the nucleophile does not affect the rate of the reaction, and changing the nucleophile (e.g. from H 2 O to MeOH) does not affect the reaction rate, though the product is, of course, different. In this regime, the first step ...
The steady-state rate equation is of mixed order and predicts that a unimolecular reaction can be of either first or second order, depending on which of the two terms in the denominator is larger. At sufficiently low pressures, k − 1 [ M ] ≪ k 2 {\displaystyle k_{-1}[{\ce {M}}]\ll k_{2}} so that d [ P ] / d t = k 1 [ A ] [ M ...
Plugging in the first CSTR equation to the second: = (+) Therefore for m identical CSTRs in series: C A m = C A o ( 1 + k τ ) m {\displaystyle C_{Am}={\frac {C_{Ao}}{(1+k\tau )^{m}}}} When the volumes of the individual CSTRs in series vary, the order of the CSTRs does not change the overall conversion for a first order reaction as long as the ...
If you've been having trouble with any of the connections or words in Wednesday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further ...
Consider , the exact solution to a differential equation in an appropriate normed space (, | | | |). Consider a numerical approximation u h {\displaystyle u_{h}} , where h {\displaystyle h} is a parameter characterizing the approximation, such as the step size in a finite difference scheme or the diameter of the cells in a finite element method .