Lab 6 CHEMICAL KINETICS TO DYE FOR Laboratory Goals In this week s lab you will Determine concentrations via spectroscopy using Beer s Law Determine the rate law for the reaction between bleach and two dyes Determine the rate constant for the same reaction Introduction In this lab you will be determining how quickly household bleach reacts with a couple of different dyes In order to be able to understand this we have to first visit the world of kinetics Kinetics Chemical Kinetics is the branch of chemistry which is concerned with the study of the rate of chemical reactions The rate of a reaction is a measure of how quickly reactants are turned into products This area of study directly complements the study of thermodynamics which focuses exclusively upon the energetic favorability of reactions Consider the hypothetical reaction A 2B 2C D The rate of formation of C is Rate c C f C i t f ti 1 C t 2 where C f and C i are the concentrations of C at times tf and ti respectively The symbol stands for change The rate of formation of C is the change in the concentration of C over the time interval t tf ti Similarly the rate of formation of D is Rate D D t 3 The rates of consumption of A and B are A t B Rate B t Rate E 4 5 The negative signs in equations 4 and 5 arise from the fact that although the rates are positive numbers the concentrations of the reactants decrease with time so their changes are negative From the stoichiometry of reaction 1 we see that the consumption of 1 mole of A results in the consumption of 2 moles of B and the formation of 2 moles of C and 1 mole of D B is consumed twice as fast as A and C is produced twice as fast as D Thus the relationships between the rate expressions in equations 2 5 is D 1 C 1 B A 6 t 2 t t 2 t 30 The rate of the reaction RateRXN can be expressed either in terms of the rate of disappearance of reactants or the rate of appearance of products Rate RXN A D 1 C 1 B t t 2 t 2 t 7 In general the rate of a reaction depends on the concentration of the reactant as follows 8 RateRXN k A x B y Equation 8 is the rate law for the reaction In the generic rate law the concentration of each of the reactants raised to a power to give the overall rate law This makes intuitive sense because one would anticipate that as the reactant concentration was increased that the rate of the reaction would also increase due to a greater number of molecular collisions between the reactants In this case it shows that the rate is proportional to the product of the concentrations of the reactants raised to some power x or y The proportionality constant k is the rate constant and depends only on temperature The exponents x and y are the reaction order with respect to A and B respectively These exponents are usually the integers 0 1 2 or 3 but in some reactions are found to be fractions or even negative The sum of the exponents is the overall order of the reaction For example if x 1 and y 2 then the reaction is said to be first order in A second order in B and third order overall The values of the exponents in the rate law MUST be determined by experiment and CAN NOT be determined from the stoichiometry of the reaction Rate Laws involving only one reactant For the reaction E products the rate law is Rate RXN If x 1 then the reaction is first order and E k E x t E k E x t Using calculus and integrating this equation give equation 9 which is known as the integrated rate law yes this is creative naming here ln E kt ln E 0 31 9 In equation 9 E 0 is the initial concentration of E and E is it concentration at time t The integrate rate law gives the concentration of reactant as a function of time Integrated rate laws for zero second and third order reactions are given below Order Rate Law Integrated Rate Law E E E 0 kt k Zero 10 T E ln E kt ln E 0 k E 9 First T 1 1 E kt k E 2 11 Second E E 0 T Third E k E 3 T 1 1 2kt 2 E 02 E 12 The integrated rate laws can be used to determine the order of a reaction For example if a reaction is first order equation 9 predicts that a plot of ln E vs time is linear with a slope of k If the reaction is zero order then a plot of E vs time is linear with a slope of k If the reaction is 2nd or 3rd order then graphs of either 1 E or 1 E 2 vs time will be linear respectively and the slope will again relate to k Some examples are shown in Figure 1 Figure 1 Pseudo rate orders The above rate laws can not directly be used for reactions with more than one reactant and most reactions fit into this category since changes in both reactant concentrations are occurring simultaneously and potentially with different reaction order Any reaction that has more than one reactant usually falls into this category including the ones you will do In such situations chemists often will instead find the pseudo rate law for the reaction In this method one of the reactants is present in large excess relative to the other For example consider the reaction E B C D Suppose that the initial concentrations of E and B are 1 000 x 10 4 M and 0 2000 M respectively We see that B E If the reaction goes to completion all of E is consumed as it is the limiting reactant and the concentrations of both reactants will have decreased by 1 00 x 10 4 M The final concentration of B at the end of the reaction is 0 2000 1 000 x 10 4 M 0 1999 M a decrease of only 0 05 Therefore the concentration of B remains essentially constant during the reaction and equation 8 becomes 32 RateRXN kobs E x where kobs is the observed k and kobs k B y a constant 13 14 The only variable in equation 13 is the concentration of E and just like before the order with respect to E can be determined by plotting each of the quantities E ln E 1 E and 1 E 2 vs time to determine which plot is linear As indicated above kobs can be determined directly from the graphs The order with respect to B can be determined by using different excess concentrations and observing the effect this has on kobs For example if doubling B …