rate_laws - Derivation of Kinetic Rate Laws Consider a...

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Derivation of Kinetic Rate Laws Consider a general chemical reaction whose balanced equation is a A + b B + ... e E + f F + where a, b, e, and f are the stoichiometric coefficients. Introduce a variable w which is a measure of the difference in concentration from the initial value: w = 1 a ([A] 0 [A]) = 1 b ([B] 0 [B]) = ... (1) = 1 e ([E] [E] 0 ) = 1 f ([F] [F] 0 ) = where the zero subscript denotes the initial concentration. The rate of the reaction can often be written in as many equivalent forms as there are species in the stoichiometric equation. Let the volume be constant. As the rate is the change in concentration, Δ w , per change in time, Δ t , take the change in the variable w in Eq. (1) per change in time remembering that the initial concentra- tions are constant. One obtains for the rate Rate = Δ w Δ t =− 1 a Δ [A] Δ t 1 b Δ [B] Δ t = = 1 e Δ [E] Δ t = 1 f Δ [F] Δ t = Many reactions are found experimentally to have rates that can be expressed in terms of a simple rate law Rate = k [A] x [B] y (2) = k ([A] 0 aw ) x ([B] 0 bw ) y where Eq. (1) was used to solve for the concentrations (in the first line of Eq. (2)) in terms of the
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rate_laws - Derivation of Kinetic Rate Laws Consider a...

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