 Langmuir Hinshelwood model
 Rate of reaction and temperature
Relationship between rate equation and temperature: Equilibrium constant K decreases with increase in temperature and is independent of pressure
 Equilibrium constant and pressure
For an ideal gas mixture undergoing a reversible gaseous phase chemical reaction the equilibrium constant increases of decreases with pressure depending upon stoichiometric coefficient of the reaction.
 Equations for PFR, CSTR and batch reactor
 Equation for PFR
 Equation for CSTR
 Constant volume first order reaction in PFR/batch reactor
 Varying volume reaction
In case of varying volume (presence of inerts) constant pressure gas phase reaction A –> B
 Rate Constant K for first order irreversible system for any ϵ_{A}
 Rate constant K for Zero order irreversible system for any ϵ_{A}
 Varying volume batch reactor
Rate equation for varying volume batch reactor
Rate equation for varying volume batch reactor first order reaction system
Rate equation for Varying volume batch reactor zero order reaction system
 Conversion for constant volume second order irreversible reaction
Conversion for second order irreversible reaction (constant volume) A –> B in batch reactor/plug flow reactor
 Final rate equation for a constant volume reaction of order n is
For A constant volume reaction A to B with order n and rate constant k, final rate equation is
 Zero order reaction
Rate equation for zero order reaction is defined such that
 Arrhenius law
Relationship between different rate constants
 Thiele Modulus
 Thiele modulus for n^{th} order irreversible reaction
 Thiele modulus for solid catalyzed reaction
 Thiele modulus for spherical pellet
 Relation between rates r_{A1} and r_{A2} with thiele modulus M_{T1} and M_{T2}
In case of strong pore diffusion resistance relation between rates r_{A1} and r_{A2} with thiele modulus M_{T1} and M_{T2}
 Effective order of reaction
In case of strong pore diffusion for n^{th} order reaction effective order becomes (n+1)/2 order reaction as evident by below equation:
 Reactors in series
 PFR and CSTR in First order reaction
For N CSTR in series each of same volume V in first order reaction
For N plug flow reactors in series of same volume in first order reaction
 Space time and holding time
 Holding time in batch reactor
 Space time in plug flow reactor
 Exit age distribution
The distribution of residence times is represented by an exit age distribution, E(t). The function E(t) has the units of time^{1} and is defined such that
The fraction of the fluid that spends a given duration, t inside the reactor is given by the value of E(t)dt.
The fraction of the fluid that leaves the reactor with an age less t_{1} is
The fraction of the fluid that leaves the reactor with an age greater than t_{1}
E is defined as
 Exit age distribution for CSTR
Exit age distribution E(t) for CSTR is defined as
 Exit age distribution for PFR
Exit age distribution E(t) for PFR is defined as
The E curve for plug flow reactor is called Diracdelta function.
 Controlling activation energy
Controlling activation energy when one of the actual activation energy and diffusion activation energy controls the reaction
 Interfacial area per unit volume of dispersion in gasliquid contactor
 Peclet number
Peclet number for ideal CSTR and ideal PFR
 Conversion
 Conversion in adiabatic reactor
 Finding conversion given heat of reaction
 Effectiveness factor of catalyst
Effectiveness factor of catalyst is defined as ratio of reaction rate with diffusion resistance to reaction rate without diffusion resistance
 Effective rate constant
Effective rate constant in case of first order gaseous phase reaction catalyzed by nonporous solid
 Concentration after temperature and pressure correction
C_{A}, concentration of A inside reactor with temperature and pressure correction
 Semibatch reactor
Rate equation for semi batch reactor
 Packed bed reactor
Rate equations for packed bed reactor
 Equlibrium constant and gibbs energy
Calculating equilibrium constant for reaction given gibbs energy for the reaction
 Reaction in series
Calculating time for concentration of B to be maximum
 Reversible reaction
For a reversible reaction
 Instantaneous fractional yield
Instantaneous fractional yield in case of pore diffusion

 For reaction
 Concentration inside and outside catalyst surface
For catalytic reaction, relationship between concentration inside catalyst surface and concentration at catalyst surface
 Fractional yield
For a reaction, fractional yield is defined as ratio of moles of desired product formed to moles of desired product that would have been formed if there were no side reactions and limiting reactant would have reacted completely
 Series parallel reaction
In case of series plus parallel reaction, try to solve by mass balance
 Selectivity of a reaction
Selectivity of a reaction is defined as ratio of moles of desired product formed to moles of undesired product formed
 Fractional conversion of reactant
Fractional conversion of reactant is defined as ratio of moles of reactant reacted to form desired product to total reactant in the feed
 Half life of a reactant
Half life of a reactant in a first order system is defined as follows
 Dispersion of PFR and CSTR
Zero dispersion implies reactor is plug flow reactor (PFR) and infinite dispersion implies reactor is CSTR
 Rate of reaction of species j
For homogenous system rate of reaction for species j is defined as
 First moment of RTD function
First moment of RTD function is mean residence time
 Mean residence time
In a pulse tracer experiment mean residence time is given by
 Recycle ratio
Recycle ratio is defined as ratio of volume of liquid returned to entrance of the reactor to volume of liquid leaving the reactor
 Ratio of volume of reactors
In CSTR ratio of volumes V_{1} and V_{2} for different conversion x_{1} and x_{2}
 Catalytic reaction rate
Rate of reaction for a catalytic reaction = KC_{A}a; where a = activity coefficient.
 Second order batch reactor/PFR
For second order batch/Plug flow constant volume reactor, rate equation is defined such that
 Time required for conversion F
Time required in a reaction for conversion F (conversion F is the fraction of reactants converted to products)
 Plug flow reactors in parallel
If two plug flow reactors PFR_{1} and PFR_{2} are in parallel then
 Vapour phase catalytic reaction
Vapour phase catalytic reaction with equimolar reactants and surface reaction is rate controlling then rate equation becomes
 Least square regression method
 Second order unimolecular reaction rate
 Rate constant dependency on temperature
Rate constant dependency on temperature according to transition state theory, collision theory and Arrhenius law
 Second order nonideal liquid phase reaction
The mean conversion in the exit stream for a second order liquid phase reaction in a nonideal flow reactor is given by
 Chemical Reaction Engineering
 Rate variation with temperature


 Transition state theory approaches the problem of calculating reaction rates by concentrating on idea of intermediates and intermediates immediately breaking to products.

 Space time and holding time


 For same conversion in a constant volume reaction, holding time required in batch reactor is equal to space time in plug flow reactor.
 For constant density system, space time and holding time are equal. For changing density, they are unequal.

 Rate and rate equation


 If the reactor volume is changed, rate will also change as degree of conversion will change.
 Energy balance equation over a tubular reactor under transient conditions is a linear partial differential equation.
 When an exothermic reaction is conducted adiabatically, rate of reaction passes through maximum (K increases first).
 Rate of reaction doesn’t depend on how we write the stoichiometric equation. It is an experimentally determined expression.

 Reaction in presence of catalyst


 A reaction A –> B. If the concentration of A at the center of the pellet is much less than at the external surface, the process is limited by diffusion within the pellet. This is a case of large Thiele modulus which means that the surface reaction is rapid and the reactant is consumed to a major extent close to external surface of the catalyst pellet. Very little of the reactant gets opportunity to penetrate inside the catalyst particle. Therefore, the reaction is limited by diffusion within the catalyst particle.
 If for a heterogeneous catalytic reactions A + B –> C, with equimolar A and B, the initial rate –r_{Ao} is invariant with total pressure, it means that rate controlling step is desorption of C.
 Examples of trickle bed reactor – hydrogenation, hydrodesulphurization and hydronitrogenation in refineries (three phase hydro treator); oxidation of harmful chemical compounds in waste water streams; in cumene process.
 At steady state, reactant transport (diffusion) rate = reaction rate.
 When due to decrease in particle size, conversion increases, the reaction is controlled by pore diffusion in the catalyst.

 NonIdeal reactions


 The E curve for an nonideal reactor defines the fraction of fluid having age between t and t+dt at the outlet and is given by Edt.

 Extent of a rection


 Extent of a reaction is same for all reactant and products. It has dimension of mole or mole/sec and it is independent of stoichiometric coefficients.
 In exothermic first order reaction, maximum heat generated will be at the beginning of the reaction when C_{A} = C_{Ao}.

 Reactors

 If an endothermic aqueous phase first order reaction is carried out in a plug flow reactor then rate of reaction is maximum at inlet of reactor.
 For a packed bed reactor, the presence of long tail in the residence time distribution curve is an indication of dead zone.
 Consider a reversible exothermic reaction in a plug flow reactor. T_{max} = maximum permissible temperature. T_{min} = minimum permissible temperature. To achieve desired conversion, temp profile that will require shortest residence time is initially a straight line at T_{max} and then a downward parabola which would asymptote the x – axis.