Errors in Determining the Rate Constant of a First-order Gaseous Reaction by the Flow Method

1963 ◽  
Vol 16 (4) ◽  
pp. 527 ◽  
Author(s):  
MFR Mulcahy ◽  
MR Pethard
Keyword(s):  
Rate Constant ◽  
Thermal Equilibrium ◽  
Contact Time ◽  
Experimental Conditions ◽  
Gaseous Reaction ◽  
Flow Method ◽  
First Order ◽  
Upper Limit ◽  
Piston Flow ◽  
Organic Vapour

The rate constant of a gaseous reaction calculated from data obtained by the conventional flow method is subject to errors arising from departures from piston flow and thermal equilibrium in the reaction tube. An approximate theoretical analysis of the errors is given for the first-order pyrolysis or isomerization of an organic vapour. In the case of a reaction occurring near 1000�K in a tube 2 cm in diameter, it is shown that for the measured value of the rate constant to be accurate within about 10% the experimental conditions should be such that z > tc/p > 0.5, where p cmHg is the total pressure and tc sec the average contact time. The upper limit (z) of tc/p increases from 3 under conditions of 50% conversion to 10 at 25% and ∞ at 0%. The analysis is applied to measurements of the rate of pyrolysis of toluene. Lack of thermal equilibrium could be at least partly responsible for the observed effect of contact time on the rate constant but does not account for the effect of pressure. The error incurred by assuming piston flow in an isothermal reactor when in fact viscous flow is occurring is discussed in the Appendix.

A Stirred-Flow Reactor for Investigating the Kinetics of Gaseous Reactions: Application to the Decomposition of Di-t-butyl Peroxide

1961 ◽  
Vol 14 (4) ◽  
pp. 534 ◽  
Author(s):  
MFR Mulcahy ◽  
DJ Williams
Keyword(s):  
Excellent Agreement ◽  
Rate Constant ◽  
Flow Reactor ◽  
Reaction Times ◽  
Static Method ◽  
Flow Conditions ◽  
Gaseous Reaction ◽  
Flow Method ◽  
Butyl Peroxide ◽  
Kinetics Of

The uncertainty regarding temperature and flow conditions which attaches to the conventional flow method of determining the rate of a gaseous reaction can be substantially reduced by using a stirred-flow reactor. The reagents, products, and carrier-gas (if any) are mixed sufficiently vigorously for the composition of the gas in the reactor to be virtually uniform. A reactor designed to achieve the required degree of mixing at pressures of about 1 cmHg and reaction times of the order of 1 sec to 1 min is described. The rate constant of the decomposition of di-t-butyl peroxide was determined over the temperature range 430-550 �K. The values derived on the assumption of complete mixing in the reactor were independent of the degree of conversion and in excellent agreement with those obtained by previous authors using the static method.

THE PYROLYSIS OF TOLUENE

1962 ◽  
Vol 40 (7) ◽  
pp. 1310-1317 ◽  
Author(s):  
S. J. Price
Keyword(s):  
Activation Energy ◽  
Rate Constant ◽  
Rate Constants ◽  
Contact Time ◽  
Flow System ◽  
Kcal Mole ◽  
Homogeneous Process ◽  
First Order ◽  
Order Rate ◽  
Toluene Concentration

The pyrolysis of toluene has been studied in a flow system from 913 to 1143 °K. First-order rate constants are independent of the toluene concentration but decrease approximately 9% when the contact time is reduced from 1.0 to 0.41 second. Increasing the contact time from 1.0 second to 2.07 seconds does not affect the rate constant. The overall rate has been resolved into homogeneous and heterogeneous components. It is suggested that the activation energy of the homogeneous process, 85 kcal/mole, may be associated with D(C6H5CH2—H).

scholarly journals Kinetic study on the removal of mercury by fly ash

2014 ◽  
Vol 16 (2) ◽  
pp. 385-392 ◽  
Keyword(s):  
Experimental Data ◽  
Fly Ash ◽  
Rate Constant ◽  
Contact Time ◽  
Order Rate Constant ◽  
First Order ◽  
Pseudo Second Order ◽  
Pseudo First Order ◽  
Percent Removal ◽  
Adsorbent Dose

<div> <p>The removal of mercury by adsorption process using fly ash was investigated in this study. Mercury removal capacity of fly ash was performed by batch mode adsorption experiment with the effect of various parameters i.e., contact time (0.5-3.5) h, pH of 2-10, concentration of adsorbate (1, 5 and 10)<br /> mg l<sup>-1</sup>, adsorbent dose (100-1000) mg per 100 ml solution and temperature (303, 313 and 323) K. Mercury concentration (10 mg l<sup>-1</sup>) was chosen for all parameters except adsorbent dose. The experimental data were showed that the adsorbent dose of 200, 400 and 600 mg per 100 ml were sufficient to maximum removal of mercury (98 percent) from aqueous solution of mercury (1, 5 and 10) mg.L<sup>-1</sup> at equilibrium and 89 percent mercury was removed when concentration was 10 mg l<sup>-1</sup> at 303K temperature. Adsorbent dose of 100 mg per 100 ml solution showed 74 percent removal of mercury for 2 hours contact time and 90 percent removal at pH 10. The experimental data were fitted with pseudo first order and pseudo second order kinetics which was proposed by Lagergreen. The value of pseudo first order rate constant, k<sub>1</sub> is 0.697 h<sup>-1</sup> and pseudo second order rate constant k<sub>2</sub> is 0.135 l mg<sup>-1</sup> h<sup>-1</sup>.</p> </div> <p>&nbsp;</p>

THE MONO-OXALATO COMPLEXES OF IRON(III): PART II. KINETICS OF FORMATION

1965 ◽  
Vol 43 (10) ◽  
pp. 2763-2771 ◽  
Author(s):  
R. F. Bauer ◽  
W. MacF. Smith
Keyword(s):  
Rate Constant ◽  
Order Rate Constant ◽  
Hydrogen Ion ◽  
Ion Concentration ◽  
Experimental Conditions ◽  
Hydrogen Ion Concentration ◽  
First Order ◽  
Independent Path ◽  
Kinetics Of ◽  
Oxalato Complexes

The kinetics of the formation of the mono-oxalato complexes of iron (III) have been examined spectrophotometrically over the range of temperatures 5 to 25 °C in an aqueous medium of ionic strength 0.50 and the range of hydrogen ion concentrations 0.03 to 0.45 M. The kinetic-ally significant paths under the conditions studied involve reactions first order in iron (III) and in bioxalate but there appears to be some decrease in the second order rate constant with increase in hydrogen ion concentration at the highest acidities and at the highest temperatures. Although there is no significant contribution to the rate by an acid-independent path first order in free oxalate under the experimental conditions, the possibility of the rate constant for such a path being greater than that first order in bioxalate is not precluded.

Antithrombin-mediated Inhibition of Factor Vlla-Tissue Factor Complex by the Synthetic Pentasaccharide Representing the Heparin Binding Site to Antithrombin

1996 ◽  
Vol 76 (01) ◽  
pp. 005-008 ◽  
Author(s):  
Jean Claude Lormeau ◽  
Jean Pascal Herault ◽  
Jean Marc Herbert
Keyword(s):  
Binding Site ◽  
Tissue Factor ◽  
Residual Activity ◽  
Coagulation Factors ◽  
Heparin Binding ◽  
Experimental Conditions ◽  
First Order ◽  
Heparin Binding Site ◽  
Coagulant Activity

SummaryWe examined the effect of the synthetic pentasaccharide representing the minimal binding site of heparin to antithrombin on the antithrombin-mediated inactivation of factor Vila bound to tissue factor. This effect was compared to the effect of unfractionated heparin. Using purified recombinant human coagulation factors and either a clotting or an amidolytic assay for the determination of the residual activity of factor Vila, we showed that the pentasaccharide was an efficient antithrombin-dependent inhibitor of the coagulant activity of tissue factor-factor Vila complex. In our experimental conditions, assuming a mean MW of 14,000 for heparin, the molar pseudo-first order rate constants for ATIII-mediated FVIIa inhibition by ATIII-binding heparin and by the synthetic pentasaccharide were found to be similar with respective values of 104,000 ± 10,500 min-1 and 112,000 ± 12,000 min-1 (mean ± s.e.m., n = 3)

Development of Sustained Release Multi-Component Microparticulate System of Diclofenac Sodium and Tizanidine Hydrochloride

1970 ◽  
Vol 1 (1) ◽  
pp. 97-105
Author(s):  
Kamlesh Dashora ◽  
Shailendra Saraf ◽  
Swarnalata Saraf
Keyword(s):  
Particle Size ◽  
Sustained Release ◽  
Cellulose Acetate ◽  
Rate Constant ◽  
Diclofenac Sodium ◽  
Order Rate Constant ◽  
Anomalous Transport ◽  
First Order ◽  
Sem Study ◽  
Transport Type

Sustained released tablets of diclofenac sodium (DIC) and tizanidine hydrochloride (TIZ) were prepared by using different proportions of cellulose acetate (CA) as the retardant material. Nine formulations of tablets having different proportion of microparticles developed by varied proportions of polymer: drug ratio ‘’i.e.’’; 1:9 -1:3 for DIC and 1:1 – 3:1 for TIZ. Each tablet contained equivalent to 100 mg of DIC and 6mg of TIZ. The prepared microparticles were white, free flowing and spherical in shape (SEM study), with  the particle size varying from 78.8±1.94 to 103.33±1.28 µm and 175.92± 9.82 to 194.94±14.28µm for DIC  and TIZ, respectively.  The first order rate constant K1 of formulations were found to be in the range of  K1 = 0.117-0.272 and 0.083- 0.189 %hr-1for DIC and TIZ, respectively. The value of exponent coefficient (n) was found to be in the range of 0.6328-0.9412  and 0.8589-1.1954 for DIC and TIZ respectively indicates anomalous  to  non anomalous transport type of diffusions among different formulations

scholarly journals Determination of exothermic batch reactor specific model parameters

2019 ◽  
Vol 292 ◽  
pp. 01063
Author(s):  
Lubomír Macků
Keyword(s):  
Rate Constant ◽  
Reaction Rate ◽  
Batch Reactor ◽  
Specific Model ◽  
Reaction Rate Constant ◽  
Order Reaction ◽  
First Order Reaction ◽  
Model Parameters ◽  
Reactor Model ◽  
First Order

An alternative method of determining exothermic reactor model parameters which include first order reaction rate constant is described in this paper. The method is based on known in reactor temperature development and is suitable for processes with changing quality of input substances. This method allows us to evaluate the reaction substances composition change and is also capable of the reaction rate constant (parameters of the Arrhenius equation) determination. Method can be used in exothermic batch or semi- batch reactors running processes based on the first order reaction. An example of such process is given here and the problem is shown on its mathematical model with the help of simulations.

The reaction of μ-oxo-bis(phthalocyaninato)iron(III) with hydrogen sulphide in the presence of pyridine: Evidence for axial coordination of dichloromethane

2005 ◽  
Vol 09 (03) ◽  
pp. 198-205 ◽  
Author(s):  
Fabrizio Monacelli ◽  
Elisa Viola
Keyword(s):  
Reaction Mechanism ◽  
Linear Function ◽  
Rate Constant ◽  
Hydrogen Sulphide ◽  
Stoichiometric Ratio ◽  
First Order ◽  
Axial Coordination ◽  
Elementary Sulphur ◽  
Increasing Function ◽  
Limiting Value

The oxo-bridged complex ( py ) FePc - O - FePc ( py ) ( py = pyridine , Pc = phthalocyaninato dianion) reacts in dichloromethane with hydrogen sulphide giving elementary sulphur and the reduced ( py )2( FePc ) complex in the stoichiometric ratio 1:1. Under excess py and H2S , the reaction is first-order and the rate constant at a given py concentration is an increasing function of the reducing agent concentration, with asymptotic tendency to a limiting value. This latter depends on the pyridine concentration being higher the lower is the base concentration. When the reaction is carried out in pure pyridine, the rate constant is, instead, a strictly linear function of [ H2S ], with zero intercept. A reaction mechanism is proposed where the dichloromethane is directly involved in the axial coordination about the iron centers and H2S competes efficiently with both pyridine and solvent.

scholarly journals Horse liver alcohol dehydrogenase. A study of the essential lysine residue

1975 ◽  
Vol 149 (3) ◽  
pp. 627-635 ◽  
Author(s):  
S S Chen ◽  
P C Engel
Keyword(s):  
Alcohol Dehydrogenase ◽  
Rate Constant ◽  
Lysine Residue ◽  
Horse Liver Alcohol Dehydrogenase ◽  
First Order ◽  
Liver Alcohol Dehydrogenase ◽  
Horse Liver ◽  
Lysine Residues ◽  
Modified Enzyme ◽  
Covalent Complex

1. The inactivation of horse liver alcohol dehydrogenase by pyridoxal 5'-phosphate in phosphate buffer, pH8, at 10°C was investigated. Activity declines to a minimum value determined by the pyridoxal 5'-phosphate concentration. The maximum inactivation in a single treatment is 75%. This limit appears to be set by the ratio of the first-order rate constants for interconversion of inactive covalently modified enzyme and a readily dissociable non-covalent enzyme-modifier complex. 2. Reactivation was virtually complete on 150-fold dilution: first-order analysis yielded an estimate of the rate constant (0.164min-1), which was then used in the kinetic analysis of the forward inactivation reaction. This provided estimates for the rate constant for conversion of non-covalent complex into inactive enzyme (0.465 min-1) and the dissociation constant of the non-covalent complex (2.8 mM). From the two first-order constants, the minimum attainable activity in a single cycle of treatment may be calculated as 24.5%, very close to the observed value. 3. Successive cycles of modification followed by reduction with NaBH4 each decreased activity by the same fraction, so that three cycles with 3.6 mM-pyridoxal 5'-phosphate decreased specific activity to about 1% of the original value. The absorption spectrum of the enzyme thus treated indicated incorporation of 2-3 mol of pyridoxal 5'-phosphate per mol of subunit, covalently bonded to lysine residues. 4. NAD+ and NADH protected the enzyme completely against inactivation by pyridoxal 5'-phosphate, but ethanol and acetaldehyde were without effect. 5. Pyridoxal 5'-phosphate used as an inhibitor in steady-state experiments, rather than as an inactivator, was non-competitive with respect to both NADH and acetaldehyde. 6. The partially modified enzyme (74% inactive) showed unaltered apparent Km values for NAD+ and ethanol, indicating that modified enzyme is completely inactive, and that the residual activity is due to enzyme that has not been covalently modified. 7. Activation by methylation with formaldehyde was confirmed, but this treatment does not prevent subsequent inactivation with pyridoxal 5'-phosphate. Presumably different lysine residues are involved. 8. It is likely that the essential lysine residue modified by pyridoxal 5'-phosphate is involved either in binding the coenzymes or in the catalytic step. 9. Less detailed studies of yeast alcohol dehydrogenase suggest that this enzyme also possesses an essential lysine residue.

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