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Essay 9 RATES OF CHEMICAL REACTIONS The rate at which a chemical reaction proceeds is critical to the design of a combustion device. In particular, the relationship between this rate and the time that the gaseous mixture is in the reaction zone
(ie, the residence time) is decisive to the successful operation of the device. To explain the concept of reaction rate, it is useful to consider a particular equation, for example,
aA+bB—>cC+dD {1) This equation represents a reaction in progress, not an equilibrium state. It states thatA and B are being
depleted and C andD are being formed. The rate r at which this reaction proceeds is r: Tag]: 1[d,5,]=1[d,5c]=1[d,5,,] (2)
:1 dt t; dt r. dr d J: The quantity ,6 is the molar density, expressed as kmolstma. Frequently, ,6 is called the molar concentration. The relationship between the mass density p and the molar density ,5 is p=aM <3) in which M is the molecular weight with units of kg/bnot. The minus signs in of the second and third terms of Eq. {2) are to be matched with the fact that the derivates 62;: and % are negative since the reaction is depleting both A and B. The reaction rate r is related to the reaction rate “constant” k by r : klﬁi )alﬁa )3 (4) The superscripts or and ,6 denote the orders of the reaction, i.e, ﬁrst order, second order, . For
certain reactions, {2' = o and f} = I). Otherwise, or and ,6 have to be determined experimentally or may be found in tables for speciﬁc reactions. In turn, the reaction rate constant k may be expressed as
k = sis—E‘ﬁr {5) The quantityA is called the pre—exponential constant, which is, in reality, not a constant. The
exponential factor is called the Arrhenius Factor. It is encountered in a great many rate—dependent processes. In the exponent, E ,1 is the activation energy, which is speciﬁc to the process, E is the universal gas constant, and Tis the absolute temperature inK. In order to make use of the foregoing equations, speciﬁc numerical information is needed for {x , ,6 , A, and E ,1 In later essays or in class, tables of these quantities will be distributed. ...
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 Spring '11
 Sparrow
 Combustion

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