Abstract
Starting from the experimental concentration-time ( cA,t diagram this work gives the construction of the rate of reaction-time (rA,t diagram using the pure graphic method. The diagram was constructed based on the constructed tangents in arbitrary points of the starting diagram by drawing lines parallel to them in the predetermined pole. The evidence of the construction was derived using differential geometry, i.e. the main theorem of differential calculus. Differential properties between the observed values were used in the method. Starting from the analytic relations rA = rA(t) and cA = cA(t), which can be very complex (polynomes of the n-th order), and, eliminating time t in order to give a full description of the process, we obtain the analytical relation rA = rA(cA), which is then graphically represented. Hoewever, this elimination of time can also be done graphically, in a relatively simple way. After that, through the use of the integral calculus, it was shown that concentration increase in a time interval is proportional to the (rA,t) diagram surface area. Using a similar procedure, further in the paper, it was shown that the time increase is proportional to the (1/rA, cA) diagram surface area. In order for the method to be applicable in practice, we have derived relations for appropriate coefficients of proportionality. Verification of the method is illustrated by the two characteristic examples from chemical kinetics at different monotonies of the starting experimental functions.
Highlights
STRUČNI RADU hemijskom inženjerstvu, čest je slučaj određivanja brzine hemijske reakcije na bazi eksperimentalnog dijagrama koncentracija–vreme (cA,t) [1,2,3,4]
Verification of the method is illustrated by the two characteristic examples from chemical kinetics
Summary
U hemijskom inženjerstvu, čest je slučaj određivanja brzine hemijske reakcije na bazi eksperimentalnog dijagrama koncentracija–vreme (cA,t) [1,2,3,4]. Pri ovome brzina reakcije u proizvoljnoj tački, dobija se kao: dcA dt. Tangenta τ povučena u tački C dijagrama (cA,t), gradi sa x-osom ugao α, pa je prema definiciji prvog izvoda [9,10]: tgα = dy = dy (6). Pri ovome uzeto je u obzir da je brzina reakcije po definiciji [1,2,3,4]:. Iz iste relacije sledi da je brzina reakcije srazmerna nagibnom uglu tangente povučene na dijagram (cA,t) i jednaka je: ucA ut tgα =ktgα (9). O, i na rastojanju Hr od nje označimo sa P pol, tako da je PO' = Hr. Kao što je pokazano, tangenta τ u tački C gradi sa t-osom ugao koji je srazmeran brzini reakcije.
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