CHEM 1212 1nd Edition Lecture 11 Outline of Last Lecture In class practice problems Outline of Current Lecture Linear formats Half Life Collision Theory Current Lecture First order integrated rate equation ln A t akt ln A 0 in a linear format y logA at some time y intercept logA0 x time Slope ak The square of the correlation coefficient will help you determine the best fit The half life of a reaction is the time it takes for half of the reactants to be consumed The half life is constant Half life for a first order reaction is t1 2 ln2 0 693 ak ak You can have a fraction of a half life Radioactive decay is a first order process Vanadium 48 has a half life of 15 97 days How long would it take for a sample of vanadium 48 to decompose to the point that less than 10 remains K 693 t1 2 a o K 0433 days 1 A 0 1 A t 0 1 A 0 1 ln 1 ln 1 t 53 07 days 0 0433 days 1 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute We usually only speak of half lives as first order properties because other order s half lives are not constant Collision Theory For a reaction to occur reactants must come together with enough energy and the proper orientation to react Not all collisions meet these requirements Concentration and reactant rate o A reaction can only occur if reactants collide o In a gas phase reaction the number of collisions is dependent on the number of gas particles in the system o Increasing the amount of reactants increase the total number of collisions Temperature and Reaction Rate o When a collision occurs the reactants must have enough energy to overcome the activation energy Molecular orientation and reaction rate o When the reactants collide they must have the proper orientation to each other for a reaction to occur The Arrhenius Equation o K Ae x Ea RT o Relates the rate constant temperature and activation energy o The A parameter is reaction specific and takes care of the fraction of collisions that have the proper orientation o Also ln k2 k1 Ea R x 1 T2 1 T1 Use values of k determined at two different temperatures to calculate the value of E a in kJ mol for the decomposition of HI Temperature 650K 700K Rate constant 2 15x10 8 2 39x10 7 Ea 182 kJ mol Reaction Mechanisms A reaction mechanism is the sequence of bond making and bond breaking steps that occurs during the conversion of reactants to products Oxygen atom transfers from NO2 to CO produces nitrogen monoxide and carbon dioxide o NO2 g CO g NO g CO2 g o The rate equation for this reaction at temperatures less than 500K is rate k NO2 2 o Could this reaction occur in one bimolecular step False o Could this mechanism explain the rate equation False NO2 NO O Slow O CO CO2 Fast Slow step determines rate o Could this mechanism explain the rate equation 2NO2 NO3 NO Slow NO3 CO NO2 CO2 Fast