dynamic behavior of continuous stirred tank
The aim of the experiment was to determine the dynamic behavior of continuous stirred tank behaviors. Sodium hydroxide solution of concentration 0.1M was prepared and put into one of the batch vessels. The other vessel was filled with water and the two solutions were reacted by pumping both solutions into a reactor vessel.
After the solution have reacted for sometime the solution is collected in a cuvvett and sent to a spectrophotomet5er to determine the concentration. The collections of the reacted samples were done at a time interval and then the values recorded against the time.
A graph of concentration against time is then plotted.
Reactors can take wide variety of forms depending on the chemical process involved. A type of reactor used very commonly in industrial processing is continuous – stirred tank reactor (CSTR). The CSTR is normally run at steady state and is usually operated so as to be well mixed.
In a CSTR, one or more fluid reagents are introduced into a tank reactor equipped with an impeller while the reactor effluent is removed. The impeller stirs the reagents to ensure proper mixing. Simply dividing the volume of the tank by the average volumetric flow rate through the tank gives the residence time, or the average amount of time a discrete quantity of reagent spends inside the tank. Using chemical kinetics, the reaction’s expected percent completion can be calculated.
At steady-state, the flow rate must be equal to the mass flow rate out, otherwise the tank will overflow or go empty (transient state). While the reactor is in a transient state the model equation must be derived from the differential mass and energy balances.
The reaction proceeds at the reaction rate associated with the final (output) concentration.
Often, it is economically beneficial to operate several CSTRs in series. This allows, for example, the first CSTR to operate at a higher reagent concentration and therefore a higher reaction rate. In these cases, the sizes of the reactors may be varied in order to minimize the total capital investment required to implement the process.
It can be seen that an infinite number of infinitely small CSTRs operating in series would be equivalent to a PFR. The experiment was done under room condition.
During the experiment 16.16g of dry NaOH was weighed using an electric balance, the sample was put into a 4l gallon. The sample was diluted with distilled water until the 4l liter mark was reached. The prepared solution was 0.1M NaOH which was poured into feed vessel one of the CSTR. The pump one connected to the NaOH was switched on ands after the reactor have overflow it was reduced to the required flow rate. The water feed pump was also switched on and then dilution begins.
Samples were then collected to the spectrophotometer with a curvet for conductivity reading to be recorded.
The conductivity of the reactor tank should reduce with time and at a certain time the concentration of the reaction tank should be equal to that of the feed solutions
5.0liters of a solution of 0.1M sodium hydroxide was prepared and then filled into one of the feed vessel to approximately 50.0mm fro the tip of the vessel. The other feed vessel was filled with demineralised water.
At a time interval of 1minute the samples were taken to the spectrophotometer for conductivity reading to be taken. But before this the spectrophotometer was prepare before using it o take the readings.
The reaction rate or rate of reaction for a reactant or product in a particular reaction is intuitively defined as how fast a reaction takes place. For example, the oxidation of iron under the atmosphere is a slow reaction which can take many years, but the combustion of butane in a fire is a reaction that takes place in fractions of a second.
Chemical kinetics is the part of physical chemistry that studies reaction rates. The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering, enzymology and environmental engineering
Formal definition of reaction rate
Considering a typical chemical reaction
aA + bB ? pP + qQ
The lowercase letters (a, b, p, and q) represent stoichiometric coefficients while the capital letters represent the reactants (A and B) and the product (P and Q).
According to Jerrica IUPAC’s Gold Book definition the reaction rate v (also r or R) for a chemical reaction occurring in a closed system under constant-volume conditions, without a build-up of reaction intermediates is defined as:
The IUPAC recommends that the unit of time should always be the second. In such a case the rate of reaction differs from the rate of increase of concentration of a product P by a constant factor (the reciprocal of its stoichiometric number) and for a reactant A by minus the reciprocal of the stoichiometric number. Reaction rate usually has the units of mol dm-3 s-1. It is important to bear in mind that the previous definition is only valid for a single reaction, in a closed system of constant volume. This most usually implicit assumption must be stated explicitly, otherwise the definition is incorrect: If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
For any system in general the full mass balance must be taken into account:
IN – OUT + GENERATION = ACCUMULATION
When applied to the simple case stated previously this equation reduces to:
For a single reaction in a closed system of varying volume the so called rate of conversion can be used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time.
is the stoichiometric coefficient for substance i , is the volume of reaction and is the concentration of substance i.
When side products or reaction intermediates are formed, the IUPAC recommends the use of the terms rate of appearance and rate of disappearance for products and reactants, respectively.
Reaction rates may also be defined on a basis that is not the volume of the reactor. When a catalyst is used the reaction rate may be stated on a catalyst weight (mol g-1 s-1) or surface area (mol m-2 s-1) basis. If the basis is a specific catalyst site that may be rigorously counted by a specified method, the rate is given in units of s-1 and is called a turnover frequency.
Concentration: Reaction rate increases with concentration, as described by the rate law and explained by collision theory. As reactant concentration increases, the frequency of collision increases.
The nature of the reaction: Some reactions are naturally faster than others. The number of reacting species, their physical state (the particles that form solids move much more slowly than those of gases or those in solution), the complexity of the reaction and other factors can influence greatly the rate of a reaction.
Temperature: Usually conducting a reaction at a higher temperature delivers more energy into the system and increases the reaction rate by causing more collisions between particles, as explained by collision theory. However, the main reason why it increases the rate of reaction is that more of the colliding particles will have the necessary activation energy resulting in more successful collisions (when bonds are formed between reactants). The influence of temperature is described by the Arrhenius equation. As a rule of thumb, reaction rates for many reactions double or triple for every 10 degrees Celsius increase in temperature, though the effect of temperature may be very much larger or smaller than this (to the extent that reaction rates can be independent of temperature or decrease with increasing temperature.)
For example, coal burns in a fireplace in the presence of oxygen but it doesn’t when it is stored at room temperature. The reaction is spontaneous at low and high temperatures but at room temperature its rate is so slow that it is negligible. The increase in temperature, as created by a match, allows the reaction to start and then it heats itself, because it is exothermic. That is valid for many other fuels, such as methane, butane, hydrogen…
Solvent: Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength as well has an effect on reaction rate.
Pressure: The rate of gaseous reactions increases with pressure, which is, in fact, equivalent to an increase in concentration of the gas. For condensed-phase reactions, the pressure dependence is weak.
Electromagnetic Radiation: Electromagnetic radiation is a form of energy so it may speed up the rate or even make a reaction spontaneous, as it provides the particles of the reactants with more energy. This energy is in one way or another stored in the reacting particles (it may break bonds, promote molecules to electronically or vibrantly excited states…) creating intermediate species that react easily.
For example when methane reacts with chlorine in the dark, the reaction rate is very slow. It can be sped up when the mixture is put under diffused light. In bright sunlight, the reaction is explosive.
A catalyst: The presence of a catalyst increases the reaction rate (in both the forward and reverse reactions) by providing an alternative pathway with lower activation energy.
For example, platinum catalyzes the combustion of hydrogen with oxygen at room temperature..
Surface Area: In reactions on surfaces, which take place for example during heterogeneous catalysis, the rate of reaction increases as the surface area does. That is due to the fact that more particles of the solid are exposed and can be hit by reactant molecules.
Order: The order of the reaction controls how the reactant concentration affects reaction rate.
Stirring: Stirring can have a strong effect on the rate of reaction for heterogeneous reactions.
Intensity of light: The reactants involved in a photochemical reaction absorb energy from light and other EM radiation. As the intensity of light increases, the particles absorb more energy. Thus their kinetic energy increases, and there are more productive collisions. Hence the rate of reaction increases. The converse is also true as light intensity decreases.
All the factors that affect a reaction rate are taken into account in the rate equation of the reaction.
For a chemical reaction n A + m B ? C + D, the rate equation or rate law is a mathematical expression used in chemical kinetics to link the rate of a reaction to the concentration of each reactant. It is of the kind:
In this equation k(T) is the reaction rate coefficient or rate constant, although it is not really a constant, because it includes all the parameters that affect reaction rate, except for concentration, which is explicitly taken into account. Of all the parameters described before, temperature is normally the most important one.
The exponents n’ and m’ are called reaction orders and depend on the reaction mechanism.
Stoichiometric, molecularity (the actual number of molecules colliding) and reaction order only coincide necessarily in elementary reactions, that is, those reactions that take place in just one step. The reaction equation for elementary reactions coincides with the process taking place at the atomic level, i.e. n molecules of type A are colliding with m molecules of type B
For gases the rate law can also be expressed in pressure units using e.g. the ideal gas law.
By combining the rate law with a mass balance for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived. For a closed system with constant volume such an expression can look like
Each reaction rate coefficient k has a temperature dependency, which is usually given by the Arrhenius equation:
Ea is the activation energy and R is the gas constant. Since at temperature T the molecules have energies given by a Boltzmann distribution, one can expect the number of collisions with energy greater than Ea to be proportional to . A is the pre-exponential factor or frequency factor.
The values for A and Ea are dependent on the reaction. There are also more complex equations possible, which describe temperature dependence of other rate constants which do not follow this pattern.
The rate of reaction is measured by the amount of reactants converted to products in a unit of time. In order for a reaction to occur, particles must come into contact and this contact must result in interaction. The rate of reaction depends on the collision frequency and collision efficiency of particles of the reacting substances. These factors are optimized by thorough mixing of the reactants using stirrers and baffles within the reactor. In efficient mixing will result in reduced reaction rate
Table 1.0 experimental data
Time (mins) Concentration (g/l) 1 -0.008 2 0.001 3 -0.001 4 -0.007 5 -0.008 6 0.0082 7 0.005 8 0.007 9 -0. 017 10 0.021 11 -0.016 12 0.023 13 -0.01 14 0.021 15 -0.09 16 0.018 17 -0.008 18 0.021 19 -0.016 20 0.018 21 -0.016 22 0.022 23 -0.013 24 0.022 25 -0.012 26 0.014 27 -0.009 28 0.015 29 -0.014 30 0.018 31 -0.007 32 0.022 33 -0.009 34 0.017 35 -0.008 36 0.022 37 -0.011 38 0.017 39 -0.004 40 0.008 41 -0.007 42 0.018 43 -0.009 44 0.011 45 -0.009 46 0.032 47 -0.005 48 0.027 49 -0.003 50 0.041 51 -0.001 52 0.019 53 0.002 54 0.028 55 0.003 56 -0.004 57 0.029 58 0.029 59 0.031 60 0.031
Calculating In where C0 is the concentration of NaOH at the start, C1 is the concentration at time t.Where Co=0.1, C8=0.078
Table 1.1 calculated and plotted values
Time (mins) Concentration =In 1 -0.693 2 -0.981 3 -0.693 4 -0.721 5 -0.693 6 -1.291 7 -1.141 8 -1.232 9 -0.470 10 -2.330 11 -0.492 12 -0.693 13 -2.485 14 -2.330 15 0.494 16 -1.974 17 -0.693 18 -2.33 19 -0.492 20 -1.974 21 -0.492 22 -2.485 23 -0.563 24 -2.485 25 -0.588 26 -1.638 27 -0.667 28 -1.712 29 -0.538 30 -1.974 31 -0.721 32 -2.485 33 -0.667 34 -1.878 35 -0.693 36 -2.485 37 -0.613 38 -1.878 39 -0.811 40 -1.218 41 -0.721 42 -1.974 43 -0.667 44 -0.443 45 -0.667 46 -2.890 47 -0.780 48 -4.277 49 -0.843 50 -1.712 51 -0.909 52 -2.079 53 -1.059 54 0 55 -1.058 56 0 57 -0.811 58 -4.277 59 -3.178 60 -3.178
Slope= [-8.43 -(-1.141 )]/ (49-7)
This was as a result of the of the spectrophotometer not properly prepared for the reading to readings to be taken for example the cuvettes that was used to collect the samples at the time intervals was not properly cleaned before used to take the readings. Dirt can affect the concentration value when using the spectrophotometer because they tend to block the part needed by the ultraviolet rays for the correct readings to be taken.
Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength as well has an effect on reaction rate. Since the water used to produce the 0.1M NaOH was not clean as a result reaction will take place in the in the solution before the dilution was done hence affecting the concentration of the final product.
The aim of the experiment was not achieved because the correct concentration was not achieved. The rate of reaction is measured by the amount of reactants converted to products in a unit of time. In order for a reaction to occur, particles must come into contact and this contact must result in interaction. The rate of reaction depends on the collision frequency and collision efficiency of particles of the reacting substances. These factors are optimized by thorough mixing of the reactants using stirrers and baffles within the reactor. In efficient mixing will result in reduced reaction rate. Usually conducting a reaction at a higher temperature delivers more energy into the system and increases the reaction rate by causing more collisions between particles.
1. Mark E. Davis and Robert J. Davis, Fundamentals of chemical reaction engineering, 1st edition, McGraw Hill Company,2003, page 70-71
2. J. F. Richardson and D.G. Peacock, chemical engineering,3rd editon,1994, Elsevier Science Inc. New York, page 43
3. Missen and Co., Introduction to Chemical engineering and Kinetics, 1st edition, 1999, John Wiley and Sons, New York City, pp 336-337.
4. (http://:en.wilkepidia.org/wilk 2/12/08)