CHEM 1120 1st Edition Lecture 7 Outline of last lecture 1 Finish up last lectures 14 3 2 Change of concentration with time 3 First order reactions 4 Second order reactions 5 Zeroth order reactions Outline of Current Lecture 1 Half lives 2 Collision model theory 3 The Arrhenius Equation Current Lecture Half Life t1 2 o Half life t1 2 time required for the concentration of a reactant to decrease to one half of its initial value o Oth 1st and 2nd order reactions o o o Subsequent half lives get shorter for zeroth order do not change for first order and get longer for second order The values you need to find k can be read off of the graph Half life provides a third method for determining reaction order Zero order First order Second order Rate law Rate k Rate k A Rate k A Units for k mol L s 1 s L mol s Integrated rate law in straight line form A kt A t ln A k t ln A t 0 1 A k t 1 A t 0 Plot for straight line A vs t t ln A vs t t 1 A vs t t Slope y intercept k A k ln A k 1 A Half life A 2k 0 0 ln 2 k 0 1 k A 0 0 Determining empirical rate law we can now use these empirical methods o Initial rates Systematically vary concentrations and observe the effect on rate o Integrated rates Solve the calculus differential to give a concentration versus time equation often uses line plots o Half lives Use integrated rate laws solved for time specifically at the point where concentration in one half the original amount o The experimental results determine rate law Rate law is the mathematical expression that describes how the reaction depends on some key factors Rate k A m B n 14 5 Temperature and rate Generally as temp increases rate increases The rate constant is temp dependent it increases as temp increases Rate constant will double with every 10 degrees C rise The collision model collision theory o Reaction rate depend on collisions which in t will likely depend on at least 3 factors Collision frequency Number of collisions per second per liter Collision energy Fraction of collisions that are sufficiently forcefuk Collision orientation Fraction of the collisions with correctly oriented molecules Consider the Reaction A BC AB C o o Collision Frequency higher concentrations more frequent collisions higher temperatures more frequent collisions Collision Energy powerful collision reaction gentle collision no reaction o o Collision Orientation correct alignment reaction i incorrect alignment no reaction Activation energy Ea Minimum collision energy required for molecules to react o o Distribution of energy Usually only a fraction of the molecules f in a sample possess sufficient energy to react The higher the temp higher this fraction f e Ea RT The Arrhenius Equation o If reaction rate varies with temp so must rate constant k o Man named Arrhenius proposed this relationship k Ae Ea RT k rate constant A frequency factor or pre exponential factor is related to collision frequency and collision orientation Ea activation energy R gas constant 8 314 J mol K T temp in kelvins Higher T larger k increased rate o Non linear example o Linear example