Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

406 TREATMENT OF EXPERIMENTAL DATAestimated standarderror of theactivationenergy. To afirst approximation, the standarderror of the slope of a straight line is proportional to the standard error of a pointof unit weight and inversely proportional to the product of the range of the quantityx and the square root of the number of observations defining the line. In thedetermination of the activation energy of a reaction, it is usually only possible tocover a small range of values of 1/T since the normal experimental techniquesemployed are unable to follow much more than a 100-fold change in rate. Consequentlythe precision with which E can be measured is limited; it is for this reasonthat the temperature dependence of the activation energy cannot normally bemeasured. Incidently, the previous comment regarding the precision of the slopeindicates that, as far as this quantity is concerned, it is more profitable to doublethe range of 1/T than to double the number of points within a particular temperatureinterval.4.2 INFLUENCE OF THE CONCENTRATION OF CATALYSTIn general, the rate coefficient is related to the concentration of catalyst by thesimple expressionk = k'[catalystIcwhere c is usually integral or half-integral and k' is a rate coefficient. To determinethese quantities, we simply have to find c from the slope of the straight line of Inkagainst In [catalyst] in the usual way and then calculate k'. Occasionally, the relationshipbetween k and [catalyst] is of the formk = k'[catalystIc+ k"Since there are but a limited number of values of c, namely 0.5, 1.0, 1.5, and 2.0,the four plots generalized in the above equation can be constructed; the values ofc, k' and k" can be found from that plot which gives the best straight line.4.3 INFLUENCE OF IONIC STRENGTHFor reactions involving ions, the rate coefficient is a functionof the ionic strength,p, of the reaction system. If .the two reactants A and B are ions and if the totalionic strength is small, the rate coefficient is exponentially related to the squareroot of the ionic strength, thus :k = ko exp ( 22,~~ Cp3)