ChE 402: Chemical Reaction Engineering Rate Laws, Stoichiometry-Chapter 3 Reaction order, reaction rate constant and rate law Reversible and irreversible reactions Elementary and non-elementary reactions Batch and continuous flow reactors Stoichiometry in batch and flow systems Industrial reactors

Reactor Sizing Summary (Design Equation) Differential Algebraic Integral BATCH CSTR PFR PBR

Isothermal Reactor Design Algorithm

Specific Rate of Reaction or Rate Constant Until now we could calculate reactor volumes necessary to achieve a specified conversion for flow systems (CSTR, PFR, PBR) and time to achieve a given conversion in a batch system---- Provided the reaction rate is available as a function of conversion, -rA = f (x). The limiting reactant is usually choose as the basis of reaction For many reaction the rate of disappearance -rA can be written as the function of a reaction rate constant, kA Unfortunately, -rA = f (x) is seldom available. Therefore, we have to obtain the rate of reaction as a function of conversion.

Rate Laws and Stochiometry The relationship between reaction rate and conversion can be obtained in two steps: Step 1- first define the rate law, which relates the rate of reaction to the concentration of the reacting species and to temperature Step 2- define the concentration s as a function of conversion Two steps to get: Step 1- Rate Law: Step 2- Stoichiometry: Combine step 1 and step 2 to get:

Relative Rate of Reaction The relative rates of reaction of the various species involved in a reaction can be obtained from the ratio of Stoichiometric coefficients. we see that for every mole of A that is consumed, c/a moles of C appear. In other words, Rate of formation of C = ( (Rate of disappearance of A) Similarly, the relationship between the sates of formation of C and D is Reaction stoichiometry

Relative Rate of Reaction If NO2 is being formed at a rate of 4 mol/m3/s the rate of disappearance of NO is the rate of disappearance of oxygen, O2, is

Power Law Model The exponents of the concentrations lead to the concept of reaction order The order of a reaction refers to the powers to which the concentrations are raised in the kinetic rate law the reaction is α order with respect to reactant A. and β order with respect to ractant B. The overall order of the reaction, n, is

Power Law Model

Rate Laws Elementary reactions Non elementary reactions

Elementary Reactions Such reactions in which the rate equation corresponds to a stoichiometric equation are called elementary reactions. A reaction fulfilling the following criteria can be defined as elementary: The reaction occurs in a single step The reaction shows an exact correspondence of at least one of the overall stochiometric equation with the observed rate The observed rate equation is consistent with the events at molecular scale

Non-elementary Reactions A large number of both homogeneous and heterogeneous reactions do not follow simple rate laws. Examples of reactions that don't follow simple elementary rate laws are discussed below. When there is no direct correspondence between stoichiometry and rate, then we have nonelementary reactions.

Non-elementary Reactions Homogeneous Reactions Heterogeneous Reactions

Non-elementary Reactions Homogeneous Reactions The overall order of a reaction does not have to be an integer. nor does the order have to be an integer with respect to any individual component. As an example. consider the gas-phase synthesis of phosgene, kinetic rate law is Sometimes reactions have complex rate expressions that cannot be separated into solely temperature-dependent and concentration-dependent portions. In the decomposition of nitrous oxide,

Non-elementary Reactions Heterogeneous Reactions In many gas-solid catalyzed reactions. it historically has been the practice to write the rate law in terms of partial pressures rather than concentrations. An example of a heterogeneous reaction and corresponding rate law is the hydrodcmethylation of toluene (T) to form benzene (Bj and methane (MI carried out over a solid catalyst.

Reversible Reactions A11 rate laws for reversible reactions must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium. At equilibrium, the rate of reaction is identically zero for all species (i-e., ). the concentrations at equilibrium are related by the thermodynamic relationship for the equilibrium constant Kc

Reversible Reactions how to write rate laws for reversible reactions? Elementary and reversible symbolically, The forward and reverse specific reaction rate constants, kB, and k-B, must be defined with respect to (a particular species) benzene. the rate of disappearance of benzene is For the reverse reaction between diphenyl (D) and hydrogen (H2 ). the rate of formation of benzene is given as

Reversible Reactions Where, Similarly with respect to D Using the relationship

Reversible Reactions Finally, we need to check to see if the rate law is thermodynamicaIly consistent at equilibrium At equilibrium,

Reaction Order Molecularity Elementary reaction: Rate law: Reaction order: 2 with respect to CO, 1 with respect to O2 and overall order of this reaction is 3 Molecularity = 2 + 1 = 3 Molecularity of an elementary reaction is defined as the number of molecules involved in the controlling step of the reaction. Typical molecularity of reaction has been found to be 1, 2 and up to 3.

Reaction Order Molecularity Non-elementary reaction: Rate law, The rate of formation of HBr is considered to be first order with respect to H2 and a number (not necessarily and integer).

The Reaction Rate Constant k Specific rate constant or Reaction rate constant is truly constant It is merely depend on concentrations It is strongly dependent on temperature Arrhenius law: specific reaction rate at a temperature at T0 specific reaction rate at a temperature at T

Activation energy The molecules need energy to distort or stretch their bonds so that the break them and thus form new bonds.

From the slope of the line given in Figure

ChE 402: Chemical Reaction Engineering Rate Laws, Stoichiometry-Chapter 3 Reaction order, reaction rate constant and rate law Reversible and irreversible reactions Elementary and non-elementary reactions Batch and continuous flow reactors Stoichiometry in batch and flow systems Industrial reactors

Reactor Sizing and Design

Reactor Sizing Summary (Design Equation) Differential Algebraic Integral BATCH CSTR PFR PBR

Reactor Sizing and Design The relationship between reaction rate and conversion can be obtained in two steps: Step 1- first define the rate law, which relates the rate of reaction to the concentration of the reacting species and to temperature Step 2- define the concentration s as a function of conversion Two steps to get: Step 1- Rate Law: Step 2- Stoichiometry: Combine step 1 and step 2 to get:

STOICHIOMETRY The relative rates of reaction of the various species involved in a reaction can be obtained from the ratio of Stoichiometric coefficients. we see that for every mole of A that is consumed, c/a moles of C appear. In other words, Rate of formation of C = ( (Rate of disappearance of A) Similarly, the relationship between the sates of formation of C and D is Reaction stoichiometry

Stoichiometric Table Batch System Species A is our basis of calculation, NAo is the number of moles of A initially present in the reactor. NAo X moles of A are consumed in the system as a result of the chemical reaction the number of moles of A remaining in the system. To calculate the number of moles of species B remaining at time t, the number of moles of B remaining in the system.

Stoichiometric Table Components of the stoichiornettic table : Column 1: the particular species Column 2: the number of moles of each species initially present Column 3: the change in the number of moles brought about by reaction Column 4: the number of moles remaining in the system at time t

Stoichiometric Table Batch Concentration System The stoichiometric coefficients in parentheses (d/a + c/a – b/a - 1) represent the increase in the total number of moles per mole of A reacted. Batch Concentration System

Stoichiometric Table We further simplify these equations by defining the parameter

Stoichiometric Table Concentration as a function of conversion when no volume change occurs with reactron if

Stoichiometric Table

ChE 402: Chemical Reaction Engineering Rate Laws, Stoichiometry-Chapter 3 Reaction order, reaction rate constant and rate law Reversible and irreversible reactions Elementary and non-elementary reactions Batch and continuous flow reactors Stoichiometry in batch and flow systems Industrial reactors

Reactor Sizing and Design

Reactor Sizing Summary (Design Equation) Differential Algebraic Integral BATCH CSTR PFR PBR

Reactor Sizing and Design The relationship between reaction rate and conversion can be obtained in two steps: Step 1- first define the rate law, which relates the rate of reaction to the concentration of the reacting species and to temperature Step 2- define the concentration s as a function of conversion Two steps to get: Step 1- Rate Law: Step 2- Stoichiometry: Combine step 1 and step 2 to get:

STOICHIOMETRY The relative rates of reaction of the various species involved in a reaction can be obtained from the ratio of Stoichiometric coefficients. we see that for every mole of A that is consumed, c/a moles of C appear. In other words, Rate of formation of C = ( (Rate of disappearance of A) Similarly, the relationship between the sates of formation of C and D is Reaction stoichiometry

Stoichiometric Table Batch System Species A is our basis of calculation, NAo is the number of moles of A initially present in the reactor. NAo X moles of A are consumed in the system as a result of the chemical reaction the number of moles of A remaining in the system. To calculate the number of moles of species B remaining at time t, the number of moles of B remaining in the system.

Stoichiometric Table Components of the stoichiornettic table : Column 1: the particular species Column 2: the number of moles of each species initially present Column 3: the change in the number of moles brought about by reaction Column 4: the number of moles remaining in the system at time t

Stoichiometric Table Batch Concentration System The stoichiometric coefficients in parentheses (d/a + c/a – b/a - 1) represent the increase in the total number of moles per mole of A reacted. Batch Concentration System

Stoichiometric Table We further simplify these equations by defining the parameter

Stoichiometric Table Concentration as a function of conversion when no volume change occurs with reactron if

Stoichiometric Table

Flow Concentration System

For liquids, volume change with reaction is negligible

Variable Volume System (Batch Reactor) At time t = o

the total number of mole where where yAo is the mole fraction of A initially present,

In the gas-phase systems that we shall be studying, the temperatures and pressures are such that the compressibility factor will not change significantly

Variable Volume System (Flow Reactor) At the entrance to the reactor:

The molar flow rate of species j is

ChE 402: Chemical Reaction Engineering Rate Laws, Stoichiometry-Chapter 3 Reaction order, reaction rate constant and rate law Reversible and irreversible reactions Elementary and non-elementary reactions Batch and continuous flow reactors Stoichiometry in batch and flow systems Industrial reactors

Flow Concentration System

For liquids, volume change with reaction is negligible

Variable Volume System (Batch Reactor) At time t = o

the total number of mole where where yAo is the mole fraction of A initially present,

In the gas-phase systems that we shall be studying, the temperatures and pressures are such that the compressibility factor will not change significantly

Variable Volume System (Flow Reactor) At the entrance to the reactor:

The molar flow rate of species j is

ChE 402: Chemical Reaction Engineering Rate Laws, Stoichiometry-Chapter 3 Reaction order, reaction rate constant and rate law Reversible and irreversible reactions Elementary and non-elementary reactions Batch and continuous flow reactors Stoichiometry in batch and flow systems Industrial reactors