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Scruggs Chapter 14b

# Scruggs Chapter 14b - Half-life q Half Life(t1/2 the time...

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Unformatted text preview: Half-life q Half Life (t1/2) - the time to consume half of the current reactant ; reduce its concentration to 1/2 Half-Life: Zero Order q Zero Order Half Life q Integrated Rate Law: [A] = [A]o - kt [A] - [A]o = -kt [A]o - [A] = kt q At first t1/2, [A] = 1/2[A]o [A]o - 1/2[A]o = k t1/2 1/2[A]o = k t1/2 t = [A] /2k Half-Life: First Order q Integrated Rate Law: ln[A] = ln[A]o - kt ln[A] - ln[A]o = -kt ln[A]o - ln[A] = kt ln ([A]o / [A]) = kt q At t1/2, [A] = 1/2[A]0 ln ([A]o / 1/2[A]o) = k t1/2 ln2 = k t1/2 t = ln 2/k = 0.693/k q Half Life: 2N2O5 4NO2 + O2 1st order Approximate the k Value Half-Life: Second Order q Integrated Rate Law: 1/[A] = 1/[A]o + kt q Rearrange and substitute [A] = 1/2[A]0 at t1/2 1/[A]o = kt1/2 n = 2, t q = 1/k[A] Summary of Half-Life Equations q n = 0, t1/2 = [A]o/2k t1/2 decreases as the reaction proceeds q n = 1, t1/2 = ln 2/k = 0.693/k t1/2 is constant throughout the reaction q n = 2, t1/2 = 1/k[A]o t1/2 increases as the reaction proceeds q Use these equations to calculate k or t1/2 from one another. q Often used for radioactivity - Chapter 21 If k=0.00462s-1 for a first order reaction, how long will it take for 75% of the reactant to be consumed? 20% 20% 20% 20% 20% t1/2=ln 2/k 1. 2. 3. 4. 5. 9.2 x 10-3 s 150s 300s 75s 225s 1 2 3 4 5 14.5 Temperature and Rate Examples q N2 and O2 coexist in air, but combine at high temperatures (in auto engines) to form NOx q Rates generally increase with increasing T q 2Cr3+ + 6Mn3+ + 7H2O CrO42- + 6Mn2+ + 14H+ cold hot Rates and Temperature q k increases with temperature, causing the increase in rate Rate = k[NO2]2 q 2NO2 2NO + O2 q Often k increases ~ x 2 for 10oC T increase Rates and Temperature q What must the reactants do in order for a reaction to occur? q Consider the following reaction as an example: 2O3(g) 3O2(g) 1 Collision Theory explains why k increases with T q Collision Theory: For reaction to occur, 1. molecules must collide; more collisions higher rate 2. colliding molecules must be oriented properly to react 3. properly oriented colliding molecules must have sufficient energy (which explains the T dependence) (The average kinetic energy of molecules 1 Collision Theory q Not all collisions lead to products. 1 Which collision is most likely to be effective? 33% 33% 33% 1. 2. 3. 1 2 3 1 Activation Energy Why don't all properly-oriented collisions lead to products? q There must be sufficient energy to break reactant bonds. The activation energy, E , is the minimum q a 1 Average Kinetic Energy q The number of molecules with sufficient kinetic energy to react increases as the temperature increases. Not all molecules have the same kinetic energy. 1 Energy Barrier 1 Energy-Reaction Coordinate 1 Activation Energy CH3NC CH3CN 1 Activation Energy q The energy barrier is called the activation energy, Ea. This is the difference between the transition state energy and the average reactant energy. 1 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 250 q 3 2 2 200 150 E 100 50 0 Reaction Coordinate 2 Activation Energy q Exothermic reaction 2 Activation Energy q Endothermic reaction 2 Arrhenius Equation q Relates k to T and Ea and is used to calculate Ea q k = A e-Ea/RT A is frequency factor, T in Kelvins, R = 8.314 J/mol K q Measured experimentally by measuring k at different temperatures ln k = ln A - E /RT q 2 14.6 Reaction Mechanisms q Mechanism is a detailed pathway for a reaction q Proposed mechanism must be consistent with the rate law and other experimental evidence 3 Mechanisms q Usually have several mechanisms consistent with a given rate law q Mechanism identifies the elementary reactions (one-step reactions) that combine to make up the overall reaction. q Elementary steps must add up to give the balanced chemical equation. q Molecularity: number of reactant molecules in an elementary reaction unimolecular, bimolecular, termolecular (more is rare) 3 Mechanisms q Overall reaction may be elementary: q CH3NC CH3CN qorders = coefficients Rate = k[CH3NC] q For an elementary reaction q O3 + NO O2 + NO2 Rate = k[O3][NO] q This reaction may be elementary. 3 Multistep Mechanisms q Many rate laws are more complex, so the overall reaction cannot be an elementary reaction. These have multistep mechanisms. q One step in multistep mechanism is slower than the others called the rate-determining step. 3 Multistep Mechanisms q Tl3+ + 2Fe2+ Tl+ + 2Fe3+ q Rate = k[Tl3+][Fe2+]2/[Fe3+] Tl3+ + Fe2+ Tl + Fe3+ q fast Tl + Fe2+ Tl+ + Fe3+ 2+ slow (rate 3 Multistep Mechanisms q S2O82- + I- 2SO42- + I+ slow I+ + I- I2 fast Which step is rate determining? What is the intermediate? When the first step is slow, the rate law for the reaction = rate law for the first step Rate=k[S2O82-][I-] 3 Multistep Mechanisms q Overall reaction: S2O82- + I- 2SO42- + I q slow I + I I2 - + fast 3 In the equations below, identify any intermediates O3(g) + Cl(g) ClO(g) + O2(g) ClO(g) + O3(g) Cl(g) + 2O2(g) 2% 5 2% 5 2% 5 2 % 5 1. O2 2. 3. 4. Cl ClO O3 1 2 3 4 3 What is the overall reaction for the steps given? O3(g) + Cl(g) ClO(g) + O2(g) ClO(g) + O3(g) Cl(g) + 2O2(g) 1. 2Cl + 2ClO 2. 2O3 3O2 ClO + O2 2O2 + Cl 3. O3 + Cl 4. ClO + O3 2Cl2 + O2 2% 5 2% 5 2% 5 2% 5 1 2 3 4 3 14.7 Catalysis q Catalyst: substance that changes the rate of reaction but is not permanently changed itself q Metals catalyze many reactions of gases; called heterogeneous catalysis q Mechanism: adsorption, reaction, desorption 3 Heterogeneous Catalysis C2H4 + H2 C2H6 4 Catalysis q Catalyst changes the reaction mechanism and lowers the activation energy 4 Homogeneous Catalysis q In homogeneous catalysis, everything is in solution (or in gas phase) q Identify the intermediate(s) and catalyst(s) in the following mechanism q NO + O2 NO3 NO3 + NO 2NO2 NO2 + SO2 NO + SO3 NO2 + SO2 NO + SO3 ------------------------------------ 4 Homogeneous Catalysis q In homogeneous catalysis, everything is in solution (or in gas phase) q Identify the intermediate(s) and catalyst(s) in the following mechanism NO + O2 NO q NO + NO 2NO 3 4 Enzymes as Catalysts q Enzymes have cavities that just fit the reacting molecules and act to bring the reactants together in the proper orientation. 4 ...
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