Determination of the Arrhenius Activation Energy Using a Temperature-Programmed Flow Reactor Kit-ha C. Chan and R. S. Tse University of Hong Kong, Pokfulam Road, Hong Kong The Arrhenius activation energy is commonly determined by measuring either rate constants or initial rates at se\,eral
isothermal temperatures. Such measurements are timtl-cim suming due to the need to change the temperature of a wellinsulated, isothermal reactor. This activation energy can be obtained more quickly and directly by using a temperature-programmed flow reactor connected to a concentration detector, such as a thermal conductivity detector (TCD) which is widely used in gas chromatographs. Under a constant flow condition, the detector output is proportional to the rate of reaction, and, if onlv the verv first detectable chanae genuine - is recorded,. . initial rates can be obtained.' Consider for e x a m ~ l ethe unimolecular decomposition of cyclopentene (CP)=
change in concentration in CP a t To, the same quantity a t another temperature T becomes
ideal gas conditions being assumed. The residence time, At = ulf, where u is the volume of the reaction zone and f , the volumetric flowrate in the reaction zone. If fo is the flowrate a t To, then the flowrate at another temperature T becomes fo X (TITo); again ideal gas conditions are assumed. Thus
Therefore the left-hand side of eqn. (1) becomes
Thus the whole of eqn. (1) becomes
Moreover, A[CP]T, is in practice proportional to the TCD signal over several orders of magnitude. Thus
assuming ideal gas conditions and rearranging -T--= d[CP1 dt
A[CP]oToe-EJRT
-A[CPIT,
=K
x (detectorsignal)
Under initial rate conditions, this becomes - T -A[CP1 = At
A(CP]OTO~-~J~~
TEMP
where k is the rate constant; A, the Arrhenius pre-exponential factor; E., the Arrhenius activation energy; R, the gas constant:~,T., the absolute tem~erature: . .ICPlo. the initial CP concentration a t a reference temperature To, say room temoerature: and At the residence time which the reaction stream spends in the reaction zone. Both the numerator and the denominator of the left-hand side of eqn. (1)are temperature dependent. If A[CP]T, is the ~
PROGRAMMER
(1)
FURNACE
~~~~
VENT OR GSU
TCO POWER SUPPLY & BRIDGE C O N T R O L
' If the reactant stream consists of a reactant at its saturated vapor pressdre at room temperatLre of -300 ton 1e.g.. cyclopentene) in a stream of nitrogen at a total pressure of 1 atm, the concentration of me mollml. If me relative molecular mass reactant amounts to -1.6 X glml.~hedeis 68 (forcyclopentene), this becomes -1.1 X lectability and sensitivity of TCD's are frequently quoted respectively glml and 7 X lo3 mV-mllmg for butane in helium. As a as 3 X result of differences in thermal conductivity for cyclopentene in nitrogen. the delectability is expected to be higher, and the sensitivity lower, by a factor of -15. In any case, genuine initial rates are measured. This reaction has been selected as an undergraduate classical gas kinetics experiment in Shoemaker,D. P., Garland, C. W., Steinfeld.J. I.. and Nibler, J. W., "Experiments in Physical Chemistry." 4th ed., McGraw-Hill. New York. 1981, p. 298.
4u
bAj
X-Y R E C O R D E R
Figure 1.Thelemperatue-programmdtlaw reactor wimaUwrmal conduCIlvity detector. I, 2. 3, 4 are pwous glass bubblers containing cyclopentene, cyclohexene, cycloheptene, and cyclooctene, respectively. M needlevalve: R: Rotameter flowmeter;T W : m l conductivity detector,Oow-Mac madel 10-952; TC:thermocouole: B10: a 10/19 cone andsocket joint, but no grease is used; ST:Swagelok T union: GSV:gas sampling valve of a gas chroiatograph.The temperature programmer is a combination of EuroIherm modules 127-03276-25-03-19-00,017-001-03-025-01-19-00. and 031-080-06.All stopcocks are greaseless.
Volume 61 Number 5 May 1984
547
where K is a proportionality constant specific for the particular TCD. the carrier and sample . eases used. and the TCD operating conditions.3 Thus eqn. (2) hecomes A u T X detector signal = - - [ C P ] O T O ~ - ~ J ~ ~
Kfo
When logarithms are taken, this becomes E. RT
A u
In (T X detector signal) = - -+ in ~ - [ C P ] O T ~ (3) fa
Thus E, can he ohtained from the slope of the plot between In (TX detector signal) and 1IT. If the reaction under investigation is a himolecular one, in (T2 X detector signal) should he plotted. The apparatus shown in Figure 1has been constructed for an undergraduate physical chemistry experiment, and typical data ohtained are shown in Figure 2. The corresponding Arrhenius plot is shown in Figure 3. The reaction takes place in a small reaction zone in a 12.9-mm-0.d. quartz tube. The furnace is made of 20 turns of SWG20 nichrome wire wound on the outside of the quartz tube and is -3 cm long. A thermoeouple in a thin, fused-silica sheath is placed concentrically in the reactor, fed to the temperature programmer, and also used for temperature meaurement. The short tubing between the furnace and the TCD is wrapped with heating tape. The TCD itself is also wrapped with heating tape and placed in an insulated box. Nitrogen as a carrier gas is hubhled through a reservoir of the liquid reactant. The reactant stream should presumably contain a saturated vapor pressure of the reactant at room temperature in a stream of nitrogen carrier. This reactant McNair, H. M., and Bonelli. E. J.. "Basic 9 s Chromatography." Varian. 1969, p. 96.
stream passes through the reference arm of the TCD, and then to the reactor. The exit stream from the reactor is ~ a s s e dto the sample side of the TCD. Thus any change in co&position in the stream after passing through the reaction zone will cause a signal from the previously balanced TCD hridge. Reactant or product analysis, if desired, can be done by connecting the exit stream from the TCD to the gas sampling valve of a gas chromatograph. Such analysis should he able to provid' the value of K in eqn. (3). -Subsequently, the Arrhenius A can he ohtained from the intercept of the plot, after estimating the value of u. Temperature profiles in the reactor have been measured. Radiallv there is a madient of about 5'C hetween the wall and the cenier of the rektor at an overall temperature of-600°C. 1.oneitudinallv the temperature is uniform within f1 rm fore andaft of thetip of the thermocouple. The reaction zone is thus -2 cm lona. The estimated maximum probable error in our results is -f 8%. Possibly, the tempera
