Final answer:
The order of an ordinary differential equation is determined by the highest derivative in the equation. Integrated rate laws help to determine the reaction order from experimental data by plotting concentration against time. To determine the reaction order, known values should be listed, the appropriate equation used, and the solution checked for unit consistency and overall reasonability.
Step-by-step explanation:
The order of an ordinary differential equation is determined by the highest derivative (or highest order differential) present in the equation. For example, if the highest derivative is the first derivative with respect to time, such as dI/dt, it is a first-order differential equation; if the highest derivative is the second derivative, such as d²y/dx², it is a second-order differential equation. When analyzing the reaction order from experimental data, it is important to consider differential and integrated rate laws, and understand how the reaction rates change with the concentration of reactants (referred to as reaction kinetics).
Integrated rate laws describe how reactant concentrations change over time and can be used to determine the reaction order by plotting concentration data against time and studying the resultant curve. Reaction order can often be zero, first, or second, which corresponds to the exponents in the rate law. Zero order means the rate is constant and does not depend on the concentration of reactants, first order means the rate is directly proportional to the concentration of one reactant, and second order means the rate depends on either the square of the concentration of one reactant or the product of the concentrations of two reactants.
To determine the reaction order, list all known values, use the appropriate equation, and verify the units and reasonability of the solution. In the process of determining the reaction order, understanding how to solve the equation and interpret its results is essential.