First Order Kinetics by Spectrophotometry INTRODUCTION The first order kinetics for the dissociation of a coloured complex is followed using a spectrophotometer to measure the absorbance of the complex at a particular wavelength. Rate constants are determined at a number of temperatures, from which the activation energy of the reaction can be calculated. BACKGROUND In a first order reaction, the rate at any time is proportional to the concentration, , of reacting substance at that time: - = The minus sign shows that the reactant is being consumed and ensures that the rate constant, is positive. Rearranging gives: - = and integrating: - ∫ 0 = ∫ 0 gives: ( 0 ) = or: - = ktA reaction is shown to be first order by plotting against , and obtaining a straight line. The rate constant is the negative value of the slope, i . e . , = - slope. Another useful method of recognizing first order reactions depends on determining the time taken, 2 , for half of the reactant to be used up . Under these circumstances = 2 and eqn ( 1 ) becomes 2 = 1 2 , and , 1 2 = 0 . 6 9 3 Because eqn ( 2 ) does not depend on concentration for a first order process, a determination of the half - life can begin at any time. The time taken for the concentration of reactant to halve will be the same at the beginning when the rate is relatively high, and the concentration is high, as near the end when the reaction is proceeding much more slowly, but the concentration is lower. 1 2 1 - 1 where is the order. ) Equation ( 2 ) is particularly useful as any number of determinations of 2 , and hence , can be made from a plot of against . For any reaction, the variation of the rate constant with temperature is reflected by the Arrhenius equation: = Aexp ( - ) From this expression a plot of Ink against the reciprocal