Day1n2 - CE 561 Lecture Notes Fall 2009 Days 1 and 2...

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CE 561 Lecture Notes Fall 2009 p. 1 of 13 Days 1 and 2: Introduction and Overview Motivation for understanding chemical kinetics and reaction design: This is what makes us chemical engineers – the reactor is the central feature of most chemical processes. Even if separation costs dominate, the reactor often determines the separation costs. Chemical reactions are ubiquitous in nature and industry. In this course, we will construct mathematical descriptions of chemical reactions and chemical reactors. These allow us to predict and understand the behavior of these reactions and reactors. Definitions of, and Notation for, Reaction Rates: Reaction rate: In a perfectly mixed, closed, constant volume system (or in some region of space over which conditions are uniform) with the generic reaction a A + b B c C + d D The reaction rate is defined as 1 111 C AB D dC dC dC dC r a dt b dt c dt d dt = = = In these expressions, - a , - b , c , and d are the stoichiometric coefficients of the chemical species A, B, C, and D, respectively. C A , C B , C C , and C D are the concentrations (number of molecules or moles per unit volume) of the chemical species. For a more general system of reactions, written as 1 0, 1, N ij j j A iM α = = = ( α ij < 0 for reactants, > 0 for products) where N is the number of species, M is the number of reactions, and ij is the stoichiometric coefficient of species j in reaction i , the rate of reaction i is defined such that the rate of change of concentration of species j is given by 1 j M A ij i i dC r dt = = Note that for multiple reactions, this may not uniquely define the rates of reaction. There is some minimum set of reactions required to describe the rates of change of species concentrations. Any linear combination of those reactions could equally well be used to describe the overall changes in composition.
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CE 561 Lecture Notes Fall 2009 p. 2 of 13 For a homogeneous reaction (occurring in the gas, liquid, or solid phase) the rate has units of concentration per time or moles per volume per time. For a heterogeneous reaction (occurring at a surface or interface) the rate has units of moles per area per time or surface concentration per time. As presented here, the rate is an intensive quantity, which means that it is independent of the size of the system, and is defined for a homogenous system. Sometimes, it is more appropriate to describe systems in terms of the extensive rate, which is simply the intensive rate multiplied by the total system volume. In general, the reaction rate is a function of temperature, pressure, and composition. At fixed temperature and pressure, the reaction rate is usually expressed as a function of the species concentrations. That is 12 ( , ,..., ) N i AA A r fC C C = The most commonly used functional dependence of the rate on the concentrations is to set the rate proportional to a product of algebraic powers of the species concentrations: 1 ij j N iA j rC ν = or 1 ij j N ii A j rk C = = The constant of proportionality ( k i ) is often referred to as the rate constant . Perhaps a better term is rate coefficient – since it is only constant with respect to the species concentrations.
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Day1n2 - CE 561 Lecture Notes Fall 2009 Days 1 and 2...

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