Graphic constructions of characteristic diagrams in chemical engineering and the application of differential geometry

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.

Keywords

• experimental time diagrams
• concentration of a compound
• rate of a chemical reaction
• chemical engineering
• differential and integral calculus
• differential function
• graphic methods
• coefficient of proportionality
• qualitative analysis