CHEM 1120 1st Edition Lecture 7Outline of last lecture1. Finish up last lectures 14.3 2. Change of concentration with time3. First order reactions4. Second order reactions5. Zeroth order reactionsOutline of Current Lecture 1. Half lives2. Collision model theory3. The Arrhenius EquationCurrent 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 Subsequent half lives get shorter for zeroth order, do not change for first order, and get longer for second ordero The values you need to find k can be read off of the grapho Half life provides a third method for determining reaction orderZero order First order Second orderRate law Rate=k Rate=k[A] Rate=k[A]Units for k mol/L*s 1/s L/mol*sIntegrated rate law in straight-line formA]t =-kt + [A] ln[A]t =-k t + ln[A]0 1/[A]t =k t + 1/[A]0 Plot for straight line[A]t vs. t ln[A]t vs. t 1/[A]t vs. t Slope, y-intercept-k, [A]0 k, ln[A]0 k, 1/[A]0 Half-life[A]0/2k ln 2/k 1/k [A]0- Determining empirical rate law we can now use these empirical methodso Initial rates: Systematically vary concentrations and observe the effect on rateo 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 amounto The experimental results determine rate law Rate law is the mathematical expression that describes how the reactiondepends on some key factorsRate = k[A]m[B]n14.5 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 theoryo 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 moleculesConsider the Reaction: A + BC AB + C o Collision Frequency higher concentrations more frequent collisions higher temperatures more frequent collisions o Collision Energy powerful collision reaction gentle collision no reactiono Collision Orientation correct alignment reaction i incorrect alignment no reaction o Activation energy (Ea) Minimum collision energy required for molecules to reactoo Distribution of energy Usually only a fraction of the molecules (f) in a sample possess sufficientenergy to react, The higher the temp, higher this fraction f=e^-Ea/RT- The Arrhenius Equationo If reaction rate varies with temp, so must rate constant ko 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 Tlarger kincreased rateo Non-linear example:o Linear
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