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Title: ODE & Excel CSTR Modeling with Heat Exchange

Authors: Jason Bourgeois, Michael Kravchenko, Nicholas Parsons, Andrew Wang

Date Presented: 10/3/06 Date Revised: 10/19/06



CSTR with Heat Exchange

A CSTR (Continuous Stirred-Tank Reactor) is a chemical reaction vessel in which an impeller continuously stirs the contents ensuring proper mixing of the reagents to achieve a specific output. Useful in most all chemical processes, it is a cornerstone to the Chemical Engineering toolkit. Proper knowledge of how to manipulate the equations for control of the CSTR are tantamount to the successful operation and production of desired products.


The purpose of the wiki is to model dynamic conditions within a CSTR for different process conditions. Simplicity within the model is used as the focus is to understand the dynamic control process.



For the purposes of this Wiki, we have made the following assumptions to explain CSTR with heat exchange modeling.

Perfect mixing

  • The agitator within the CSTR will create an environment of perfect mixing within the vessel. Exit stream will have same concentration and temperature as reactor fluid.

Single, 1st order reaction

  • To avoid confusion, complex kinetics are not considered in the following modeling.

Parameters specified

  • We assume that the necessary parameters to solve the problem have been specified.

Volume specified

  • In a control environment, the size of the vessel is usually already specified.

Constant Properties

  • For this model, we have made the assumption that the properties of the species we are trying to model will remain constant over the temperature range at which we will be looking at. It is important to make this assumption, as otherwise we will be dealing with a much more complex problem that has a varying heat capacity, heat of reaction, etc.

ODE Modeling in Excel

To setup the model, the mass and energy balances need to be considered across the reactor. From these energy balances, we will be able to develop relationships for the temperature of the reactor and the concentration of the limiting reactant inside of it.


Variable Definitions

The following table gives a summary of all of the variables that we used in our mathematical formulas.







Volume of Reactor


Density of Stream


Mass Flow Rate


Original Concentration


Current Concentration


Original Temperature


Current Temperature


Coolant Temperature


Heat of Reaction


Overall change in Heat Capacity


Rate Law Constant


Activation Energy


Ideal Gas Constant


Overall Heat Transfer Coefficient

Symbol Explanations


Mass Balance

From our energy and material balances coursework, we know that the general equation for a mass balance in any system is as follows:





In the case of a CSTR, we know that the rate of accumulation will be equal to

. This comes from the fact that the overall number of moles in the CSTR is

, so the accumulation of moles will just be the differential of this. Since

is a constant, this can be pulled out of the differential, and we are left with our earlier result. We also know that the flow of moles in versus the flow of moles out is equal to

, which is the mass flow rate, divided by the density of the flow, and then multiplied by the difference in the concentration of moles in the feed stream and the product stream. Finally, we can determine what the rate of generation of moles in the system is by using the Arrhenius Equation. This will give us the rate of generation equal to

. Combining all of these equations and then solving for

, we get that:

Energy Balance

From our thermodynamics coursework, we know that the general equation for an energy balance in any system is as follows:






In the case of a CSTR, we know that the rate of energy accumulation within the reactor will be equal to

. This equation is basically the total number of moles (mass actually) in the reactor multiplied by the heat capacity and the change in temperature. We also know that the heat generated by this reaction is

, which is the rate of mass generation ( Vra) times the specific heat of reaction (ΔHrxn). The overall rate of heat transfer into and out of the system is given by

. This equation is the flow rate multiplied by the heat capacity and the temperature difference, which gives us the total amount of heat flow for the system. Finally, the amount of heat transferred into the system is given by

. Combining all of these equations and solving the energy balance for

, we get that:

In a realistic situation in which many chemical processed deal with multiple reactions and heat effects slight changes to the modeled equation must be done. The diagram below evaluates the heat exchanger under heat effects in which there is an inlet and outlet temperature that is accounted for in the enthalpy term in the newly modeled equation.

To model a heat exchanger that accounts for multiple reactions simply take the deltaHrxn and deltaCp term and add the greek letter sigma for summation in front of the terms. When considering a case with multiple reactions and heat effects, the enthalpy and heat capacity of each reaction must be implemented in the energy balance, hence i and j represents the individual reaction species. The equation now looks something like this:

Euler's Method

In order to model an ODE in Excel, we will be using Euler's Method. The reason why we chose Euler's Method over other methods (such as Runge-Kutta) was due to the simplicity associated with Euler's. Trying to model with methods such as Runge-Kutta are much more difficult in Excel, while Euler's method is quite simple. We also checked the accuracy of our results using Euler's Method by comparing our answers with that of Polymath, a highly accurate ODE modeling program. We found that our answers were the same as that of Polymath, so we are quite comfortable using Euler's Method for our model. Here are the full details on Euler's Method. For this model, we will primarily be interested in the change in concentration of a reactant and the temperature of the reactor. These are the two differential equations that we were able to obtain from the mass and energy balances in the previous section. The following is an application of Euler's method for the CSTR on the change in concentration:

This same application can be made to the change in temperature with respect to time:

Assuming that all values in the ODE's remain constant except for


, the new value is then found by taking the pervious value and adding the differential change multiplied by the time step.

List of Equations

The following are a summary list of all of the equations to be used when modeling CSTR with a heat exchange.






Combining Using Excel

To model the CSTR using Excel you use Euler's Method, Energy Balance and Mass Balance together to solve for the concentration at time t.

Screenshot of Excel Model for CSTR with Heat Exchange


How to Use Our Model

In order to help facilitate understanding of this process, we have developed an Excel spreadsheet specifically for looking at the changes in concentration and temperature given some change in the input to the CSTR system. An example of a change to the system could be that the temperature of the feed stream has dropped by a given number of degrees, or that the rate at which the feed stream is being delivered has changed by some amount. By using our spreadsheet, you will be able to easily plug in your given parameters, and look at the trend of the concentration and temperature over a wide time interval.

The way in which this spreadsheet works is quite simple. Boxes are provided for you to input all of the given information for your CSTR problem. Various columns containing values for the temperature, concentration, etc., with respect to time have also been provided. There are then more columns that contain the values for the various differential equations from above. With the time derivative in hand, we are then able to predict the value of the temperature or concentration at the next given time interval.

Our easy-to-use Excel model is given here: CSTR Modeling Template. In our model, you will find a column of unknowns that must be specified in order to solve for the optimal conversion temperature and optimal concentration of A. There are then two cells that will display the optimal temperature and concentration. Graphs are also provided to look at the change in temperature and concentration over time. Most of the variables in the model are self-explanatory. One important feature of our model is the option to have a change in the temperature of the feed stream or the concentration of A after a given time t. You do not need to input a value for these cells if there is no change in the feed; it just provides a convenient way to look at the change of temperature and concentration of A. You are also provided with a cell for the time step,

. Depending on what size time step you choose, you may need to choose a larger value if your graphs do not reach steady state. If this is the case, the output cells will tell you to increase the time step.

Applications to Process Control

The model created can account for many different situations. However, in process control, it is very important for the following to be considered.

Exothermic reaction - In industry, the exothermic reaction is typically of more importance to controls as there is a safety factor involved. (i.e. explosive reactor conditions)

Volume constant - For CSTRs, liquids are mostly used.

The model developed can assist in controlling an actual process in many ways including the following, but not limited to:

  • Maintaining product concentration despite changes operating conditions
  • Predicting and preventing explosive reactor conditions
  • Flow rate optimization
  • Input concentration optimization
  • Operating temperature optimization
  • Coolant temperature optimization

This model is very useful for many simple reactor situations and will aid in the understanding of a process and how dynamic situations will affect operation.

In real-life applications, the reaction may not be first order or irreversible or involve multiple reactions. In all these cases, we modify the Energy and Mass Balance with additional rate law considerations.

Worked out Example 1

You are contracted by WOW Chemical to control the operation of their 3000 L jacketed CSTR. They desire to create chemical B from chemical A at an optimal conversion. What is the temperature at which the optimal conversion is achieved?

A B is a first order, irreversible reaction.

Some information about the process:

Feed stream temperature = 400 K

Coolant temperature = 350 K

Heat of reaction = -200 J/mol

Inlet concentration of A = 9 mol/L

Inlet flow rate = 4 kg/s

Density of A = 1000 g/L

UA of the heat exchanger = 7 kcal/s

Rate constant = 1.97x1020 s-1

Activation energy = 166 kJ/mol

Overall change in Heat capacity = 1 kcal/kg-K.

Answer to Example Problem #1

From using our handy-dandy worksheet, we see that the optimal conversion occurs at 368.4 K. This comes from inputting all of the given information from the problem statement into the Excel sheet, and then reading off the value for the optimal temperature. Also, make sure you are converting to proper units, such as from kJ to J, for use of our model (just to see if you were paying attention to units).

Example 1 Solution


Worked out Example 2

1. In the previous example, the plant was operating in the daytime. At night, there is a drop of 5 K in feed stream temperature. In order to maintain the same concentration do we need to...

A. Decrease the temperature of the cooling water in the heat exchanger.

B. Increase the temperature of the cooling water in the heat exchanger.

C. Maintain the same temperature of the cooling water in the heat exchanger.


2. At night, the inlet flow rate of the system also decreases due to the plant not operating at full capacity. What happens to the temperature of the reaction if concentration of A in the feed stream stays the same?

A. Decrease

B. Increase

C. Stay the same


3. Finally, if the rate constant doubled, what effect will this have on the overall concentration if temperature is held constant?

A. Increase

B. Decrease

C. Stay the same


Answers to Example Problem #2

1: B. Since the temperature of the feed stream has decreased, we will need to increase the temperature of the cooling stream in order to maintain the same temperature at which the CSTR was operating at before. Using the Excel spreadsheet from Example 1 and lowering the feed stream temperature by 5 K, we can first see that the temperature of the CSTR has fallen to 366.5 K.

We can then adjust the temperature of the feed stream and see that it must be raised by 3 K in order to return to the original operating temperature of 368.4 K.


2: A. Since there is less feed coming into the CSTR, the optimal temperature of the reactor will decrease as well. This can again be seen by using our Excel model from Example 1. We know that originally the temperature of the reactor was at 368.4 K. By decreasing the flow rate to 3 kg/s, we can see that the temperature of the reactor decreases by over 3 K down to 365.1 K.


3: B. We see in the equations for the differential equations that the rate constant has a negative effect on the conctration of A. By doubling its value, we will then be decreasing CA as well. This can also be seen in the Excel model from Example 1. We see that the original concentration of A is 6.3 mol/L. We can then double the value of the rate constant, and we see that the concentration of A drops down to 4.8 mol/L, which is what we had predicted would happen.




출처: <https://controls.engin.umich.edu/wiki/index.php/CSTRHeatExchangeModel>

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Plug flow reactor model

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Schematic diagram of a plug flow reactor

The plug flow reactor model (PFR, sometimes called continuous tubular reactor, CTR, or piston flow reactors) is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict the behavior of chemical reactors of such design, so that key reactor variables, such as the dimensions of the reactor, can be estimated.

Fluid going through a PFR may be modeled as flowing through the reactor as a series of infinitely thin coherent "plugs", each with a uniform composition, traveling in the axial direction of the reactor, with each plug having a different composition from the ones before and after it. The key assumption is that as a plug flows through a PFR, the fluid is perfectly mixed in the radial direction but not in the axial direction (forwards or backwards). Each plug of differential volume is considered as a separate entity, effectively an infinitesimally small continuous stirred tank reactor, limiting to zero volume. As it flows down the tubular PFR, the residence time (

) of the plug is a function of its position in the reactor. In the ideal PFR, the residence time distribution is therefore a Dirac delta function with a value equal to




PFR modeling[edit]

The PFR is governed by ordinary differential equations, the solution for which can be calculated providing that appropriate boundary conditions are known.

The PFR model works well for many fluids: liquids, gases, and slurries. Although turbulent flow and axial diffusion cause a degree of mixing in the axial direction in real reactors, the PFR model is appropriate when these effects are sufficiently small that they can be ignored.

In the simplest case of a PFR model, several key assumptions must be made in order to simplify the problem, some of which are outlined below. Note that not all of these assumptions are necessary, however the removal of these assumptions does increase the complexity of the problem. The PFR model can be used to model multiple reactions as well as reactions involving changing temperatures, pressures and densities of the flow. Although these complications are ignored in what follows, they are often relevant to industrial processes.


  • plug flow
  • steady state
  • constant density (reasonable for some liquids but a 20% error for polymerizations; valid for gases only if there is no pressure drop, no net change in the number of moles, nor any large temperature change)
  • single reaction occurring in the bulk of the fluid (homogeneously).

A material balance on the differential volume of a fluid element, or plug, on species i of axial length dx between x and x + dx gives:

[accumulation] = [in] - [out] + [generation] - [consumption]

Accumulation is 0 under steady state; therefore, the above mass balance can be re-written as follows:




  • x is the reactor tube axial position, m
  • dx the differential thickness of fluid plug
  • the index i refers to the species i
  • Fi(x) is the molar flow rate of species i at the position x, mol/s
  • D is the tube diameter, m
  • At is the tube transverse cross sectional area, m2
  • ν is the stoichiometric coefficient, dimensionless
  • r is the volumetric source/sink term (the reaction rate), mol/m3s.

The flow linear velocity, u (m/s) and the concentration of species i, Ci (mol/m3) can be introduced as:


On application of the above to Equation 1, the mass balance on i becomes:



When like terms are cancelled and the limit dx 0 is applied to Equation 2 the mass balance on species i becomes



The temperature dependence of the reaction rate, r, can be estimated using the Arrhenius equation. Generally, as the temperature increases so does the rate at which the reaction occurs. Residence time,

, is the average amount of time a discrete quantity of reagent spends inside the tank.


After integration of Equation 3 using the above assumptions, solving for CA(x) we get an explicit equation for the concentration of species A as a function of position:



where CA0 is the concentration of species A at the inlet to the reactor, appearing from the integration boundary condition.

Operation and uses[edit]

PFRs are used to model the chemical transformation of compounds as they are transported in systems resembling "pipes". The "pipe" can represent a variety of engineered or natural conduits through which liquids or gases flow. (e.g. rivers, pipelines, regions between two mountains, etc.)

An ideal plug flow reactor has a fixed residence time: Any fluid (plug) that enters the reactor at time

will exit the reactor at time

, where

is the residence time of the reactor. The residence time distribution function is therefore a dirac delta function at

. A real plug flow reactor has a residence time distribution that is a narrow pulse around the mean residence time distribution.

A typical plug flow reactor could be a tube packed with some solid material (frequently a catalyst). Typically these types of reactors are called packed bed reactors or PBR's. Sometimes the tube will be a tube in a shell and tube heat exchanger.

Advantages and disadvantages[edit]

This article contains a pro and con list, which is sometimes inappropriate. Please help improve it by integrating both sides into a more neutral presentation, or remove this template if you feel that such a list is appropriate for this article. (November 2012)

CSTRs (Continuous Stirred Tank Reactor) and PFRs have fundamentally different equations, so the kinetics of the reaction being undertaken will to some extent determine which system should be used. However there are a few general comments that can be made with regards to PFRs compared to other reactor types.

Plug flow reactors have a high volumetric unit conversion, run for long periods of time without maintenance, and the heat transfer rate can be optimized by using more, thinner tubes or fewer, thicker tubes in parallel. Disadvantages of plug flow reactors are that temperatures are hard to control and can result in undesirable temperature gradients. PFR maintenance is also more expensive than CSTR maintenance.[2]

Through a recycle loop a PFR is able to approximate a CSTR in operation. This occurs due to a decrease in the concentration change due to the smaller fraction of the flow determined by the feed; in the limiting case of total recycling, infinite recycle ratio, the PFR perfectly mimics a CSTR.


Plug flow reactors are used for some of the following applications:

  • Large-scale production
  • slow reactions
  • Homogeneous or heterogeneous reactions
  • Continuous production
  • High-temperature reactions


출처: <https://en.wikipedia.org/wiki/Plug_flow_reactor_model>

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Continuous stirred-tank reactor

From Wikipedia, the free encyclopedia

Jump to: navigation, search

CSTR symbol

The continuous flow stirred-tank reactor (CSTR), also known as vat- or backmix reactor, is a common ideal reactor type in chemical engineering. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous[†] agitated-tank reactor to reach a specified output. (See Chemical reactors.) The mathematical model works for all fluids: liquids, gases, and slurries.

The behavior of a CSTR is often approximated or modeled by that of a Continuous Ideally Stirred-Tank Reactor (CISTR). All calculations performed with CISTRs assume perfect mixing. In a perfectly mixed reactor, the output composition is identical to composition of the material inside the reactor, which is a function of residence time and rate of reaction. If the residence time is 5-10 times the mixing time, this approximation is valid for engineering purposes. The CISTR model is often used to simplify engineering calculations and can be used to describe research reactors. In practice it can only be approached, in particular in industrial size reactors.


  • perfect or ideal mixing, as stated above

Integral mass balance on number of moles Ni of species i in a reactor of volume V.



Cross-sectional diagram of Continuous flow stirred-tank reactor

where Fio is the molar flow rate inlet of species i, Fi the molar flow rate outlet, and

stoichiometric coefficient. The reaction rate, r, is generally dependent on the reactant concentration and the rate constant (k). The rate constant can be determined by using a known empirical reaction rates that is adjusted for temperature using the Arrhenius temperature dependence. Generally, as the temperature increases so does the rate at which the reaction occurs. Residence time,

, is the average amount of time a discrete quantity of reagent spends inside the tank.


  • constant density (valid for most liquids; valid for gases only if there is no net change in the number of moles or drastic temperature change)
  • isothermal conditions, or constant temperature (k is constant)
  • steady state
  • single, irreversible reactionA = -1)
  • first-order reaction (r = kCA)

A products

NA = CA V (where CA is the concentration of species A, V is the volume of the reactor, NA is the number of moles of species A)



The values of the variables, outlet concentration and residence time, in Equation 2 are major design criteria.

To model systems that do not obey the assumptions of constant temperature and a single reaction, additional dependent variables must be considered. If the system is considered to be in unsteady-state, a differential equation or a system of coupled differential equations must be solved.

CSTR's are known to be one of the systems which exhibit complex behavior such as steady-state multiplicity, limit cycles and chaos.



  1. ^ Jump up to: a b Schmidt, Lanny D. (1998). The Engineering of Chemical Reactions. New York: Oxford University Press. ISBN 0-19-510588-5.


Chemical reactors often have significant heat effects, so it is important to be able to add or remove heat from them. In a CSTR (continuous stirred tank reactor) the heat is added or removed by virtue of the temperature difference between a jacket fluid and the reactor fluid. Often, the heat transfer fluid is pumped through agitation nozzle that circulates the fluid through the jacket at a high velocity. The reactant conversion in a chemical reactor is a function of a residence time or its inverse, the space velocity. For a CSTR, the product concentration can be controlled by manipulating the feed flow rate, which changes the residence time for a constant chemical reactor. Occasionally the term "continuous" is misinterpreted as a modifier for "stirred", as in 'continuously stirred'. This misinterpretation is especially prevalent in the civil engineering literature. As explained in the article,"continuous" means 'continuous-flow' — and hence these devices are sometimes called, in full, continuous-flow stirred-tank reactors (CFSTR's).


출처: <https://en.wikipedia.org/wiki/Continuous_stirred-tank_reactor>

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Redox Reactions

Process2016.06.27 10:40

Oxidation/Reduction (Redox)  Reactions

Acid/base reactions, which involve proton transfer, represent one kind of charge transfer reactions.   Now we will discuss another kind of charge transfer, electron  transfer or oxidation/reduction  reactions. In oxidation/reduction reactions, there is a transfer of charge - an electron - from one species to another. Oxidation is the loss of electrons and reduction is a gain in electrons. (Remember Leo Ger - Lose of electrons oxidation; Gain of electrons reduction or Oil Rig - Oxidation involves loss, Reduction involves gain - of electrons.) These reactions always occur in pair. That is, an oxidation is always coupled to a reduction. When something gets oxidized, another agent gains those electrons, acting as the oxidizing agent, and gets reduced in the process. When a substance gets reduced, it gains electrons from something that gave them up, the reducing agent, which in the process gets oxidized.

Reactions in which a pure metal reacts with a substance to form a salts are clearly oxidation reactions. Consider for example the reaction of sodium and chlorine gas.

2Na(s) + Cl2 -----> 2NaCl(s)

Na is a pure metal. Although we discussed that it really exists as copper ions and ions surrounded by a sea of electrons, consider it for our purposes elemental Na, which has a formal charge of 0. Likewise, Cl2 is a pure element. To determine the charge on each Cl atoms, we divide the two bonded electrons equally between the two Cl atoms, hence assigning 7 electrons to each Cl. Hence the formal charge on each Cl is 0. In a similar fashion we can determine the oxidation number of an atom bonded to another atom. We can assign electrons to a bonded atoms, compare that number to the number in the outer shell of the unbonded atoms, and see if there is an excess or lack. The other substance must be getting reduced. In these cases, the same number of electrons get assigned to each atoms as when we are calculating formal charge. Hence the oxidation numbers are equal to the formal charge in these examples. Clearly, Na went from an oxidation number and formal charge of 0 to 1+ and Cl from 0 to 1-. Therefore, Na was oxidized by the oxidizing agent Cl2, and Cl2 was reduced by the oxidizing agent Na.

Lets consider other similar redox reactions:

2Mg(s) + O2(g) ----> 2MgO(s)

Fe(s) + O2(g) ---> Fe oxides (s)

C(s) + O2(g) ----> CO2(g)

In the first two reactions, a pure metal (with formal chargess and oxidation numbers of 0) lose electrons to form metal oxides, with positive metal ions. The oxygen goes form a formal charge and oxidation number of 0 to 2- and hence is reduced.

What about the last case? Each atom in both reactants and products has a formal charge of 0. This reaction, a combustion reactions with molecular oxygen, is also a redox reaction. Where are the electrons that are lost or gained? This can be determined by assigning the electrons in the different molecules in a way slightly different than we did with formal charge. For shared (bonded) electrons, we give both electrons in the bond to the atom in the shared pair that has a higher electronegativity. Next we calculate the apparent charge on the atom by comparing the number of assigned electrons to the usual number of outer shell electrons in an atom (i.e. the group number). This apparent charge is called the oxidation number. When we use this method for the reaction of C to CO2, the C in carbon dioxide has an oxidation number of 4+ while the two oxygens have an oxidation number of 2- . Clearly, the C has "lost electrons" and has become oxidized by interacting with the oxidizing agent O2. as it went from C to CO2. If the atoms connected by a bond are identical, we split the electrons and assign one to each atom. In water, the O has an oxidation number of 2- while each H atom has an oxidation number of 1+. Notice that the sum of the oxidation numbers of the atoms in a species is equal to the net charge on that species.

What we have done is devise another way to count the electrons around an atom and the resulting charges on the atoms. See the animation below to review electron counting, and the 3 "types of charges" - partial charges, formal charges, and now oxidation numbers.

ANIMATION: Counting electrons and determining "charge" on an atom.

Consider an O-X bond, where X is any element other than F or O. Since O is the second most electronegative atom, the two electrons in the O-X bond will be assigned to O. In fact all the electrons around O (8) will be assigned to O, giving it always an oxidation number of 2-. This will be true for every molecule we will study this year except O2 and H2O2 (hydrogen peroxide). Now consider a C-H bond. Since C is nearer to F, O, and N than is H, we could expect C (en 2.5) to be more electronegative than H (en 2.1). Therefore, both electrons in the C-H bond are assigned to C, and H has an oxidation number of 1+. This will always be true for the molecules we study, except H-H. A quick summary of oxidation numbers shows that for the molecules we will study:

  • O always has an oxidation # of 2- (except when it is bonded to itself or F)
  • H always has an oxidation # of 1+ (except when it is bonded to itself)
  • The sum of the oxidation numbers on a compound must equal the charge on the compound (just like the case of formal charges)

Notice in each of the reactions above, oxygen is an oxidizing agent. Also notice that in each of these reactions, a pure element is chemically changed into a compound with other elements. All pure, uncharged elements have formal charges and oxidation numbers of 0. When they appear as compounds in the products, they must have a different oxidation number. The disappearance or appearance of a pure element in a chemical reaction makes that reaction a redox reaction.

Now lets consider a more complicated case - the reaction of methane and oxygen to produce carbon dioxide and water:

CH4 + O2 -----> H2O + CO2.

Since H has an oxidation # of  1+, the oxidation # of C in CH4 is 4-, while in CO2 it is 4+. Clearly C has been oxidized by the oxidizing agent O2. O2 has been reduced to form both products.

Now consider a series of step-wise reactions of CH4 ultimately leading to CO2


You should be able to determine that the oxidation numbers for the central C in each molecule are 4-, 2-, 0, 2+, and 4+ as you proceed from left to right, and hence represent step-wise oxidations of the carbon. Stepwise oxidations of carbon by oxidizing agents different than O2 are the hallmark of biological oxidation reactions. Each step-wise step releases smaller amounts of energy, which can be handled by the body more readily that if it occurred in "one step", as indicated in the combustion of methane by O2 above.

You may have learned in a previous course that in oxidation reactions, there is an increase in the number of X-O bonds, where X is some atom. Alternatively, it also involves the decrease of X-H bonds. Reduction would be the opposite case - decreasing the number of X-O bonds and/or increasing the number of X-H bonds. This rule applies well to the above step-wise example. Consider, however, the following reaction:

In this example, the C in methane has an oxidation # of 4- while in the product it is 2-. Once again, the C has been oxidized, however, the number of bonds to O has not increased. This shows the importance of being able to calculate an oxidation number to determine if a redox reaction has occurred. Where is the loss of electrons? It comes about since C is now bonded to a more electronegative atom (N), which withdraws electron density form the C.

Redox reactions are common in nature. Some common redox reactions are reactions that occur in batteries, when metals rust, when metals are plated from solutions, and of course combustion of organic molecules such as hydrocarbons (like methane and gasoline) and carbohydrates (like wood). A simple redox reaction that leads to the plating or deposition of a pure metal from a solution of that metal is shown below.

Cu(s) + 2Ag+(aq) ---> Cu2+(aq) + 2Ag(s)

In this reaction, pure silver metal - Ag(s) is plated on the surface of Cu(s) In this reaction:

  • Cu is oxidized and is the reducing agent
  • Ag+ is reduced and is the oxidizing agent

If you look at the products, you could imagine they could also react in a reverse of the original reaction to produce the original reactants.

Cu2+(aq) + 2Ag(s) ---> Cu(s) + 2Ag+(aq)

In this reaction, pure copper metal - Cu(s) would be plated on the surface of the Ag(s). In this reaction:

  • Ag(s) is oxidized and is the reducing agent
  • Cu2+ is reduced and is the oxidizing agent

Why doesn't this reverse reaction also occur? It actually does to a small extent. You could actually envision the original reaction as reversible:

Cu(s)RA + 2Ag+(aq)OA <===> Cu2+(aq)OA + 2Ag(s)RA

where RA indicates which reactants/products are potential reducing agents in the forward and reverse reactions, and OA indicates potential oxidizing agents. Which way does this reaction go? We will discuss this in more detail next semester, but suffice it to say, the reaction goes in the direction from the strongest oxidizing and reducing agents to the weakest. In the above example, Cu(s) is the stronger RA and Ag+ is the stronger OA. You can't predict from looking at the possibilities, but next semester we will discuss how you can determine the relative strengths of OA's and RA's from tables.

Consider this reaction from Lab 3 when you added solid Zn to the blue copper sulfate solution to produce pure Cu(s):

Zn(s) + Cu2+(aq) ---> Zn2+(aq) + Cu(s)

This reaction can be thought of as 2 half-reactions which can be added together to get the top reaction:

Zn(s) + ---> Zn2+(aq) + 2e-

Cu2+(aq) + 2e- ---> Cu(s)

Image if you tried to separate the reactions into two beaker, one containing Zn(s) and the other Cu2+. Obviously the reactions could not occur. However, if we connected the two beakers with a wire (which would allow electrons to flow from Zn(s) to Cu2+(aq), then the reactions can occur. If we put a voltmeter or light bulb in between the two beakers, a voltage is recorded or the light bulb will light. We have made these redox reactions into a battery.

Redox Reactions - Voltage Cell and Battery


출처: <http://employees.csbsju.edu/hjakubowski/classes/ch112/organicchem/redoxreview.htm>

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