## Document Type

Thesis

## Date of Award

6-30-1967

## Degree Name

Master of Science in Chemical Engineering - (M.S.)

## Department

Chemical Engineering

## First Advisor

Saul I. Kreps

## Second Advisor

Deran Hanesian

## Abstract

In reaction rate studies, experimental data is interpreted and correlated in terms of various mathematical models. The converse of the modeling of practical problems is the task- of experimental determination of reaction mechanisms. Generally, this approach is classified into integral and differential methods. Both involve trial and error techniques. The mathematical model which satisfies the test becomes the equation for mechanistic representation.

Both the integral and differential methods have been tried. Generally speaking, the differential method is more advantageous than the integral. For one thing, the parameters which are involved in the nodal can be determined directly by the differential method while the integral method calls for successive trials of the parameters. The differential method involves the first derivative of concentration with respect to time. The major difficulty encountered in approximating the derivative is the fact that experimental data are subject to errors. Numerical differentiation, using interpolation formulas cannot be applied. As a consequence, the data must be "smoothed" before performing numerical differentiation. For smoothing the data, the second or third degree polynomial is chosen as the mathematical representation of the given data and then the derivative is obtained by differentiating the resulting equation. The differential method requires the use of the method of least squares. The basic idea of the least square method involves the minimization of the sum of the sues of the residuals between the data points and the approximation function. The minimization of the percentage of residuals suggested in this paper offers a significant improvement in this technique.

In the integral method, the methods of computation examined here include: 1) Mean deviation method, 2) Iteration method, 3) Tabular method using time ratio and conversion ratio, 4) Nomographic method. Method (1) is based on the rate constant parameter. This is a function of temperature only, so that it remains constant in most of the actual data which are obtained under isothermal conditions. With the help of the statistical principle, this method gives quite satisfactory results. Method (2) is based on the fact that in simple reactions, the parameter can be easily cancelled from the equation and only the reaction order n is unknown in the iterations. It is found that the computation of n converges after only a few iterations. Method (3) is a "short cut" method to determine the order and reaction constant as well as the other variables. It is simple and convenient. Method (4) is also a short cut method. The idea underlying methods (3) and (4) is that only if the same pattern of mechanisms are involved, can the results be the same. These methods are implemented by cancelling the parameter of putting them into dimensionless groups by simple separation.

The purpose of the mathematics is to express the relationships in quantitative form, In this paper, we propose to show how to handle the existing models to get the desired analytical formulation.

## Recommended Citation

Lee, Hsu-Tung, "Approximation of reaction rate models" (1967). *Theses*. 2718.

https://digitalcommons.njit.edu/theses/2718