Chemical Reaction Engineering is a fascinating field that deals with the study of the chemical reactions that take place in industrial settings. This branch of engineering explores the way in which chemicals interact with one another and how they can be used in various applications. Chemical Reaction Engineers have a unique skill set, combining knowledge of chemistry, mathematics, and engineering to design and optimize chemical processes. In this blog post, we will explore the basics of Chemical Reaction Engineering and discuss some of the exciting developments in this field.
Table of Contents
Introduction to Chemical Reaction Engineering
Chemical reaction engineering is a branch of chemical engineering that deals with the design, optimization, and analysis of chemical reactions and their reactors. Chemical reactions are at the heart of many industrial processes, from the production of food, pharmaceuticals, and chemicals to the generation of energy. The main goal of chemical reaction engineering is to understand and manipulate the chemical reactions that occur in these processes to increase efficiency, yield, and product quality.
Fundamentals of Chemical Reaction Engineering
In chemical reaction engineering, understanding the fundamentals of chemical reactions is key to designing efficient and effective reactors. Chemical reactions involve the conversion of reactants into products and can be described by a chemical equation that specifies the stoichiometry of the reaction. The stoichiometry of a chemical reaction is the relationship between the amounts of reactants and products that are involved in the reaction.
The rate of a chemical reaction is the change in concentration of a reactant or product per unit time. The rate of a chemical reaction can be affected by many factors such as temperature, pressure, concentration, and the presence of a catalyst. The study of how these factors affect the rate of a chemical reaction is known as reaction kinetics.
Overview of Chemical Reactions
A chemical reaction is a process in which one or more reactants are converted into one or more products through the rearrangement of atoms. Chemical reactions can be represented by balanced chemical equations, which describe the stoichiometry of the reaction, i.e., the number of moles of each reactant and product that participate in the reaction. For example, the balanced chemical equation for the reaction between hydrogen gas and oxygen gas to form water is:
2 H2 + O2 -> 2H2O
where H2 and O2 are the reactants, and H2O is the product.
Types of Chemical Reactions
Chemical reactions can be classified into several types based on the nature of the reactants and products, the mechanism of the reaction, and the energy changes that occur during the reaction. Some of the common types of chemical reactions are:
Combination reactions: A combination reaction is a type of reaction in which two or more substances combine to form a single new substance. The general equation for a combination reaction is:
A + B → AB
Example: Formation of water from hydrogen and oxygen gas:
2H2(g) + O2(g) → 2H2O(l)
Decomposition reactions: A decomposition reaction is a type of reaction in which a single compound breaks down into two or more simpler substances. The general equation for a decomposition reaction is:
AB → A + B
Example: Thermal decomposition of calcium carbonate to form calcium oxide and carbon dioxide gas:
CaCO3(s) → CaO(s) + CO2(g)
Single displacement reactions: A single displacement reaction is a type of reaction in which an element or ion in a compound is replaced by another element or ion. The general equation for a single displacement reaction is:
A + BC → AC + B
Example: Zinc metal displacing copper ion in copper sulfate solution to form zinc sulfate and copper metal:
Zn(s) + CuSO4(aq) → ZnSO4(aq) + Cu(s)
Double displacement reactions: A double displacement reaction is a type of reaction in which two compounds exchange ions or elements to form two new compounds. The general equation for a double displacement reaction is:
AB + CD → AD + CB
Example: Precipitation reaction between lead nitrate and potassium iodide to form lead iodide and potassium nitrate:
Pb(NO3)2(aq) + 2KI(aq) → PbI2(s) + 2KNO3(aq)
Acid-base reactions: An acid-base reaction is a type of reaction in which an acid and a base react to form a salt and water. The general equation for an acid-base reaction is:
acid + base → salt + water
Example: Reaction between hydrochloric acid and sodium hydroxide to form sodium chloride and water:
HCl (aq) + NaOH (aq) → NaCl (aq) + H2O (l)
Redox reactions: A redox reaction is a type of reaction in which electrons are transferred between reactants. The general equation for a redox reaction is:
oxidation + reduction → redox reaction
Example: Combustion of methane with oxygen to form carbon dioxide and water:
CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (l)
These are just a few examples of the different types of chemical reactions that occur in nature and are used in various industrial processes.
Reaction kinetics is the study of the rate at which a chemical reaction occurs and the factors that affect the rate. It is an important aspect of chemical reaction engineering as it helps in optimizing the reaction conditions and designing reactors for industrial processes.
The rate of a chemical reaction can be expressed as the change in concentration of a reactant or product per unit of time. It can be determined experimentally by monitoring the concentration of reactants or products at different time intervals.
The rate of a chemical reaction depends on several factors such as the nature of the reactants, temperature, pressure, catalysts, and the concentration of reactants. The rate law equation expresses the relationship between the rate of reaction and the concentration of reactants:
Rate = k[A]m[B]n
Where k is the rate constant, [A] and [B] are the concentrations of reactants, and m and n are the orders of reaction with respect to reactants A and B, respectively.
Example: An example of a chemical reaction and its rate law equation is the reaction between hydrogen and iodine to form hydrogen iodide:
H2 (g) + I2 (g) → 2HI (g)
The rate law equation for this reaction can be determined experimentally and is found to be:
Rate = k[H2]1[I2]1
The rate of this reaction is directly proportional to the concentrations of hydrogen and iodine, both of which have an order of reaction of 1. The rate constant, k, depends on the temperature and other reaction conditions.
Reaction kinetics plays a crucial role in chemical reaction engineering, as it helps in predicting and optimizing reaction rates and designing efficient reactors for industrial processes.
Types of Chemical Reactors
Chemical reactors are vessels in which chemical reactions take place. There are many types of chemical reactors, each with its own advantages and disadvantages. The choice of reactor depends on the reaction conditions, the reaction kinetics, and the desired product properties. Different types of chemical reactors are shown in below figure:
Batch Reactor: The batch reactor is the simplest type of reactor and is typically used for small-scale processes. In a batch reactor, all reactants are added to the reactor vessel at the beginning of the process, and the reaction is allowed to proceed until completion. Once the reaction is complete, the product is removed from the reactor. The main advantage of a batch reactor is its simplicity, but it is not suitable for large-scale production due to the long cycle times and high labor costs.
Example: Examples of chemical reactions that can occur in a batch reactor include polymerization reactions, such as the reaction between ethylene and propylene to form polyethylene and polypropylene.
Continuous Stirred-Tank Reactors (CSTR): The CSTR is a common type of reactor used in the chemical industry. In a CSTR, reactants are continuously added to the reactor vessel, and products are continuously removed. The reactor operates at a steady state, with the reaction proceeding until equilibrium is reached. The CSTR is widely used due to its simplicity and ease of operation, but it is not suitable for processes that require high selectivity or tight control of reaction conditions.
Example: One example of a chemical reaction that can occur in a CSTR is the oxidation of sulfur dioxide to sulfur trioxide using a vanadium oxide catalyst:
SO2 + 1/2 O2 → SO3
Plug Flow Reactor (PFR): The PFR is a tubular reactor in which the reactants are continuously fed into one end of the reactor and the products are continuously removed from the other end. The reactor is designed to ensure that there is no mixing of reactants and products, resulting in a narrow residence time distribution. The PFR is ideal for reactions with a high selectivity or for processes that require tight control of reaction conditions.
Example: The most common example of a chemical reaction that can occur in a PFR is the production of ammonia by the Haber-Bosch process:
N2 + 3H2 → 2NH3
Packed Bed Reactor: The packed bed reactor consists of a cylindrical vessel filled with a solid catalyst. The reactants are passed through the packed bed, where they react with the catalyst. The main advantage of the packed bed reactor is its high surface area, which allows for a high rate of reaction. However, it is difficult to control the temperature and concentration gradients within the reactor.
Example: One example of a chemical reaction that can occur in a fixed-bed reactor is the production of gasoline from crude oil:
C10H22 → C5H12 + C5H10
Fluidized Bed Reactor: The fluidized bed reactor consists of a bed of solid particles that are suspended in a fluid. The reactants are introduced into the fluid, and the solid particles act as a catalyst for the reaction. The fluidized bed reactor offers excellent heat transfer and mass transfer properties, making it ideal for high-temperature reactions or processes that require good mixing.
Example: One example of a chemical reaction that can occur in a fluidized bed reactor is the production of ethylene oxide from ethylene and oxygen:
C2H4 + 1/2 O2 → C2H4O
These are just a few examples of the types of chemical reactors and the corresponding chemical reactions that can occur in each type.
Industrial application of CRE
Chemical reaction engineering has a wide range of industrial applications, some of which are:
Petrochemical industry: Chemical reaction engineering plays a crucial role in the petrochemical industry. The production of fuels, lubricants, and other petrochemical products involves complex chemical reactions that must be carefully controlled to ensure optimal yield and quality.
Pharmaceutical industry: The pharmaceutical industry relies heavily on chemical reaction engineering to develop and manufacture drugs. The synthesis of active pharmaceutical ingredients (APIs) involves complex chemical reactions that must be carefully monitored and controlled to ensure purity and efficacy.
Polymer industry: Polymerization reactions are a critical part of the polymer industry. Chemical reaction engineering is used to optimize the production of polymers with specific properties, such as strength, flexibility, and heat resistance.
Food industry: The food industry uses chemical reaction engineering to optimize food processing and preservation. For example, enzymes and other catalysts can be used to speed up reactions that improve the texture, flavor, and nutritional value of food products.
Environmental engineering: Chemical reaction engineering is used in environmental engineering to develop technologies for treating wastewater, air pollution, and other environmental contaminants. Chemical reactions can be used to break down harmful pollutants into harmless byproducts.
Energy production: Chemical reaction engineering plays a crucial role in the production of energy from fossil fuels, such as coal and natural gas. Chemical reactions are used to convert the fuel into heat, which is then used to generate electricity.
Chemical manufacturing: Chemical reaction engineering is used in the manufacturing of a wide range of chemical products, including fertilizers, pesticides, and specialty chemicals. The optimization of chemical reactions is critical for maximizing product yield and quality while minimizing waste and energy consumption.
One example of an industrial application of chemical reaction engineering is the production of ammonia. The Haber-Bosch process is used to produce ammonia by combining nitrogen gas and hydrogen gas under high pressure and temperature in the presence of an iron catalyst. The chemical reaction is as follows:
N2(g) + 3H2(g) → 2NH3(g)
The reaction rate and equilibrium conversion of this reaction must be carefully controlled to maximize yield and minimize energy consumption. Chemical reaction engineering principles are used to optimize the process parameters, such as temperature, pressure, and catalyst concentration, to achieve the desired product yield and quality.
Formulas in chemical reaction engineering
Here are some important formulas used in chemical reaction engineering:
Rate of reaction (r): The rate of a chemical reaction is defined as the change in the concentration of reactants or products with respect to time. It can be calculated using the following formula:
r = (1/V)(dC/dt) or r = -(1/V)(dP/dt)
Where, V = Volume of reactor, C = Concentration of reactants, P = Concentration of products, t = Time
Example: For the reaction A + B → C, the rate of reaction can be calculated as
r = -(1/V)(d[A]/dt) = -(1/V)(d[B]/dt) = (1/V)(d[C]/dt)
It can also be expressed as the change in concentration per unit time and can be calculated using the following formula:
r = -dC/dt
where r is the rate of reaction, C is the concentration, and t is time.
Stoichiometry: Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It can be used to calculate the number of reactants or products required or produced in a reaction. The stoichiometric equation for a reaction can be written as:
aA + bB → cC + dD
Where, a, b, c and d are the stoichiometric coefficients.
Example: For the reaction 2H2 + O2 → 2H2O, the stoichiometric coefficients are a=2, b=1, c=2 and d=0.
Reaction rate constant (k): The reaction rate constant is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. It can be calculated using the Arrhenius equation:
k = A exp(-Ea/RT)
Where, A = pre-exponential factor or frequency factor
Ea = activation energy
R = gas constant
T = temperature
Example: For the reaction A → B, the reaction rate constant can be calculated using the Arrhenius equation as k = A exp(-Ea/RT).
Reaction order (n): The reaction order is the exponent to which the concentration of a reactant is raised in the rate equation. It can be determined experimentally by conducting experiments with different initial concentrations of reactants. The rate equation for a reaction with multiple reactants can be written as:
r = k [A]m [B]n
Where, [A] and [B] are the concentrations of reactants A and B, respectively, and m and n are the reaction orders with respect to A and B, respectively.
Example: For the reaction A + B → C, if the rate equation is given as r = k [A]2 [B]1, then the reaction order with respect to A is 2 and the reaction order with respect to B is 1.
Residence time (t): The residence time is the average amount of time that a molecule spends inside a reactor. It can be calculated using the following formula:
t = V/Q
Where, V = Volume of reactor
Q = Flow rate of reactants
Residence time is an important parameter that determines the extent of the reaction in a reactor. A longer residence time generally means that the reaction will proceed to a greater extent, as the reactants will have more time to react. However, a longer residence time may also lead to higher operating costs, as it requires larger reactor volumes.
Example: For a reactor with a volume of 100 L and a flow rate of 10 L/min, the residence time can be calculated as t = 100/10 = 10 min.
Space-time (τ): Space-time is the time required to process one reactor volume of feed. It is denoted by the symbol “𝜏” (tau) and is defined as the reciprocal of the volumetric flow rate of the feed (F) entering the reactor. Mathematically, it can be expressed as:
𝜏 = V / F
Space-time is a useful parameter in comparing the performance of different reactors or reactor designs. A smaller space-time generally indicates better reactor performance, as it means that the reactor is able to process the feed more quickly. However, a smaller space-time may also lead to an incomplete reaction, as the reactants may not have enough time to react fully.
Conversion (X): Conversion is defined as the fraction of the reactant that has been converted to a product. It is given by the equation:
X = (n0 – n) / n0
where X is the conversion, n0 is the initial number of moles of reactant, and n is the number of moles of reactant remaining at a given time.
In terms of concentration, Conversion is the fraction of the reactant that has been consumed in a reaction. It can be calculated using the following formula:
X = (C0 – Ct)/C0
Where, C0 = Initial concentration of reactant, Ct = Concentration of reactant at time t
Example: For the reaction A → B, if the initial concentration of A is 1 M and the concentration of A after 5 min is 0.5 M, then the conversion of
Yield: Yield is defined as the mass of product produced per unit mass of reactant consumed. It is given by the equation:
Yield = (mass of product produced) / (mass of reactant consumed)
CSTR volume: The volume of a continuous stirred-tank reactor (CSTR) is given by the equation:
V = F0 / (-rA)
where V is the reactor volume, F0 is the feed flow rate, and -rA is the rate of disappearance of reactant A.
PFR volume: The volume of a plug-flow reactor (PFR) is given by the equation:
V = (-rA) / (FA0 X)
where V is the reactor volume, -rA is the rate of disappearance of reactant A, FA0 is the molar flow rate of reactant A at the inlet, and X is the conversion.
Selectivity: Selectivity is defined as the ratio of the mass of the desired product to the mass of all products produced. It is given by the equation:
Selectivity = (mass of desired product) / (total mass of products)
Molar flow rate (n): The amount of substance flowing per unit time, usually expressed in moles per second or mole per minute.
Reactor volume (V): The volume of the reactor vessel in which the chemical reaction takes place.
Arrhenius equation: The Arrhenius equation is a mathematical relationship that expresses the temperature dependence of the rate constant for a chemical reaction. It is given by the following equation:
k = A * exp(-Ea/RT)
k = rate constant
A = pre-exponential factor (or frequency factor), which is related to the frequency of collisions between reacting molecules
Ea = activation energy, which is the minimum energy required for a reaction to occur
R = gas constant
T = temperature in Kelvin
The Arrhenius equation helps to understand how temperature affects the rate of a chemical reaction. As temperature increases, the rate constant increases, and thus the rate of reaction increases. This equation is commonly used in chemical kinetics and chemical reaction engineering.
Important questions and answer from chemical reaction engineering
There are a few important questions and answer from chemical reaction engineering, which might be useful for competitive exams such as GATE and interviews.
Question 1: What is chemical reaction engineering?
Answer: Chemical reaction engineering is a branch of chemical engineering that deals with the design and optimization of chemical reactors to produce desired products through chemical reactions.
Question 3: What is a reaction rate?
Answer: The rate of reaction is the change in concentration of reactants or products per unit of time.
Question: What is a reaction order?
Answer: The order of a reaction is the exponent to which the concentration of a reactant is raised in the rate law equation.
Question: What is the difference between a homogeneous and heterogeneous reaction?
Answer: Homogeneous reactions involve reactants and products in a single phase, while heterogeneous reactions involve multiple phases.
Question: What is the difference between a batch and a continuous reactor?
A batch reactor operates in a closed system with a fixed amount of reactants, while a continuous reactor operates in a system where reactants are continuously fed into the reactor.
Question: What is an isothermal reactor?
Answer: An isothermal reactor is a type of chemical reactor in which the temperature of the reactor is maintained constant throughout the reaction. This is achieved by using a cooling or heating jacket around the reactor vessel or by circulating a heat transfer fluid through a coil inside the reactor. In an isothermal reactor, the heat generated or consumed during the reaction is immediately removed or supplied to the reactor to maintain a constant temperature. Isothermal reactors are commonly used in industrial processes where maintaining a specific temperature is critical to achieving the desired product yield and selectivity.
Question: What is the overall order of a reaction?
The overall reaction order is the sum of the orders for each reactant.
Question: What is an adiabatic reactor?
Answer: A reactor in which there is little or no heat loss or gain from the reactor’s surroundings.
Question: What is a catalytic reactor?
Answer: A catalytic reactor is a type of chemical reactor in which a catalyst is used to speed up the rate of a chemical reaction. The catalyst helps to lower the activation energy required for the reaction to occur, thereby allowing the reaction to occur at a lower temperature and pressure than would otherwise be possible. Catalytic reactors are widely used in the chemical industry for the production of a variety of chemicals, including fertilizers, polymers, and fuels. They are also used in the petrochemical industry to convert hydrocarbons into more valuable products such as gasoline, diesel, and jet fuel.
Question: What is a heterogenous catalytic reactor?
Answer: When one reactant is a gas and the other is a liquid, and the catalyst is solid.
Question: What is a plug-flow reactor?
Answer: A plug-flow reactor is a type of reactor where reactants flow through the reactor as a plug, without mixing with the surrounding fluid.
Question: What is the difference between a CSTR and a PFR?
Answer: A CSTR is a continuous stirred-tank reactor where reactants are continuously mixed, while a PFR is a plug-flow reactor where reactants flow through the reactor as a plug without mixing.
Question: What is the difference between a batch and a semi-batch reactor?
Answer: A batch reactor operates in a closed system with a fixed number of reactants, while a semi-batch reactor is a reactor where some reactants are continuously fed into the reactor.
Question: What is a packed-bed reactor?
Answer: A packed-bed reactor is a type of reactor where the reactants flow through a bed of solid catalyst particles.
Question: What is a fluidized-bed reactor?
Answer: A fluidized-bed reactor is a type of reactor where the reactants flow through a bed of solid particles that are suspended and fluidized by a fluid.
Question: What is a reaction mechanism?
Answer: A reaction mechanism is the series of basic steps that occurs during a chemical reaction.
Question: What is the rate-determining step in a reaction mechanism?
Answer: The slowest step in a chemical reaction is the rate-determining step. The rate of a chemical reaction is determined by the slowest step.
Question: What is a catalyst?
Answer: A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process.
Question: What is the activation energy of a reaction?
Answer: The smallest amount of energy required to activate atoms or molecules to the point where they can undergo a chemical transformation or physical transport.
Question: What is the Arrhenius equation?
Answer: The minimum energy required for a reaction to occur, is often expressed in units of Joules per mole.
Question: What is the rate law of a reaction?
An equation that relates the rate of reaction to the concentration of reactants, often expressed in the form of a power-law relationship.
Question: What is a rate constant?
Answer: A proportionality constant that relates the rate of reaction to the concentration of reactants, as given by the rate law.
Question: What is a reactor yield?
Answer: The amount of product obtained per unit amount of reactant, expressed as a percentage or decimal.
Question: What is a yield equation?
Answer: Yield equation: This equation calculates the yield of a reaction, which is the ratio of the amount of product obtained to the amount of reactant used.
Question: What is selectivity?
Answer: Selectivity is defined as the ratio of the mass of the desired product to the mass of all products produced.
Question: What is a selectivity equation?
Answer: Selectivity equation: This equation calculates the selectivity of a reaction, which is the ratio of the amount of desired product to the amount of undesired product.
Question: What is the selectivity of a reaction?
Answer: The selectivity of a reaction is the ratio of the rate of formation of a desired product to the rate of formation of all products.
Question: What is a conversion?
Answer: The fraction of reactant that has been converted to product, expressed as a percentage or decimal.
Question: What is a conversion equation?
Answer: This equation calculates the extent to which a reactant has been converted to a product in a reaction.
Question: What is the difference between conversion and selectivity?
Answer: Conversion is the percentage of reactants that are converted to products, while selectivity is the percentage of reactants that are converted to a desired product.
Question: What is a stoichiometric coefficient?
Answer: In a chemical reaction, the stoichiometric coefficient is the number written in front of atoms, ions, and molecules to balance the number of each element on both the reactant and product sides of the equation.
Question: What is a stoichiometric equation?
Answer: A reaction’s stoichiometry describes the relative amounts of reactants and products in a balanced chemical equation.
Question: What is a stoichiometric table?
Answer: The Stoichiometry Table component is a self-calculating, fully chemically aware tool for performing stoichiometry calculations.
Question: What is a stream in chemical engineering?
Answer: The term “process stream” refers to all reasonably anticipated transfer, flow, or disposal of a chemical substance, regardless of physical state or concentration, through all intended processing operations, including equipment cleaning.
Question: What is a feed stream?
Answer: A feed stream refers to a stream of fluid or mixture that is introduced into a chemical process or unit operation. The feed stream is often a mixture of different chemical species and is typically used as a raw material to produce a desired product or to drive a particular chemical reaction.
Question: What is a product stream?
Answer: A product stream refers to the mixture of desired products and other components that exit a chemical reactor or separation unit.
Question: What is a recycle stream?
Answer: A recycle stream is one in which a portion of a process unit’s outlet is combined with fresh feed and returned to the same unit.
Question: What is a purge stream?
Answer: A purge stream is one that removes a portion of a recycle stream from the system to prevent the accumulation of unwanted material in a recycled system.
Question: What is a bypass stream?
Answer: A bypass stream is one that bypasses one or more stages of the process and proceeds directly to the next downstream stage.
Question: What is the difference between recycle and purge streams?
Answer: Recycle and purge streams are extensions of splitter streams in which one of the splitter’s product streams is routed back into a feed stream as a recycle stream and one is directed out of the process as a purge stream.
Question: What is residence time?
Answer: Discussed above
Question: What is space-time?
Answer: As discussed above
Question: What is the turnover frequency (TOF)?
Answer: The turnover frequency can be used to express the efficiency of an active catalytic site at the molecular level (TOF).
Question: What is a catalyst activity?
Answer: The catalyst has the ability to speed up the reaction. The ability of a catalyst is referred to as its activity.
Question: What is catalyst selectivity?
Answer: selectivity refers to a catalyst’s ability to promote favorable reaction pathways that maximize the yield of desired products while minimizing undesirable by-products.
Question: What is catalyst deactivation?
Answer: Loss of catalytic activity and/or selectivity over time,
Question: What is catalyst poisoning?
Answer: Catalyst poisoning is the partial or complete deactivation of a catalyst caused by a chemical compound.
Question: What is the difference between an isothermal and an adiabatic reactor?
Answer: An isothermal reactor operates at a constant temperature, while an adiabatic reactor does not exchange heat with its surroundings.
Question: What is an ideal reactor?
Answer: An ideal reactor is a hypothetical reactor that achieves maximum conversion of reactants to products.
Question: What is an autoclave?
Answer: An autoclave is a type of high-pressure reactor used in chemical reactions that require elevated temperatures and pressures.
Question: What is the Stoichiometry equation?
Answer: Stoichiometry equation: This equation shows the balanced chemical equation for a reaction, which is important for determining the stoichiometric coefficients.
Question: What is the purpose of a reactor design?
Answer: The purpose of reactor design is to maximize the efficiency of a chemical reaction in terms of conversion, selectivity, and yield.
Question: What is the role of a catalyst in a chemical reaction?
Answer: A catalyst increases the rate of a chemical reaction by lowering the activation energy required for the reaction to take place.
Question: Residence time distribution equation?
Answer: This equation is used to calculate the distribution of residence times for the reactants in a reactor.
Question: What is the Damkohler number equation?
Answer: This equation calculates the ratio of the characteristic time for a reaction to the characteristic time for transport.
Question: What is the Thiele modulus equation?
Answer: This equation is used to determine the effectiveness factor of a catalyst.
Question: What is the Langmuir-Hinshelwood rate equation?
Answer: This equation is used to describe the reaction rate for surface reactions on a catalyst.
Question: What is the Michaelis-Menten equation?
Answer: This equation is used to describe the rate of enzyme-catalyzed reactions.