Chemical Reactions • The following table summarizes the common Driving forces that tend to make reactions go in the direction of the arrow: Reactants Products Formation of a solid Formation of water Formation of gas Transfer of electrons • When two or more chemicals are brought together, if any of the above can occur, a chemical reaction is likely to take place! CHEMISTRY - science of properties and transformations of matter CHEMICAL REACTIONS - central to CHEMSITRY CLASSIFICATION of REACTIONS Precipitation Oxidation-reduction Acid-base Gas forming Precipitation Reactions Solubility Rules • There are simple guidelines that allow one to predict whether or not a reaction will produce an insoluble compound: these are called the Solubility Rules Ionic Equations: Net Ionic • The ions that appear on both sides of the equation in identical forms. These ions are not involved directly in the reaction and are called spectator ions. Pb2+(aq) + 2NO3-(aq) + 2K+(aq) + 2I-(aq) PbI2 (s) + 2K+(aq) + 2NO3-(aq) spectator ions • In the net ionic equation, the spectator ions are omitted leaving only the ions directly involved in the reaction. Pb2+(aq) + 2I-(aq) PbI2 (s) Ionic Equations: Summary • Summary of the 3 different chemical equations: – Molecular equation Pb(NO3)2(aq) + 2KI(aq) PbI2 (s) +2KNO3(aq) – Complete ionic equation Pb2+(aq) + 2NO3-(aq) + 2K+(aq) + 2I-(aq) PbI2 (s) + 2K+(aq) + 2NO3-(aq) – Net ionic equation Pb2+(aq) + 2I-(aq) PbI2 (s) Acid-Base Reactions: Neutralization • Consider the reaction between Mg(OH)2 [milk of magnesia] and HCl (stomach acid) 2HCl(aq) Mg(OH )2 (aq) MgCl2 (aq) 2H 2O(l ) • The net reaction is: H (aq) OH (aq) H 2O(l ) The acid has been neutralized یونهای دارای عدد اکسایش و کاهش متفاوت Half-Reaction Method Of Balancing Redox Equations • • • • • • • • • • • • • Assign oxidation numbers to each atom and identify the species undergoing oxidation and reduction. Write two skeleton halfreactions. oxidation # increase => oxidation; oxidation # decrease => reduction (1) Balance the numbers of atoms in each half-reaction. (a) Balance all atoms except O and H. (b) Balance O atoms by adding H2O molecules. (c) Balance H atoms by adding H+ ions. (2) Balance electric charge by adding electrons to more positive side. (3) Combine two half-reactions to obtain balanced equation. (a) Multiply each half-reaction by factors that make the number of electrons in two half-reactions equal. (b) Combine the adjusted half-equations into an overall equation. Simplify the balanced equation if necessary. Verify that the equation is balanced. • • • • Balance the following redox equation in acidic solution: Fe2+ (aq) + Cr2O72- (aq) Fe3+ (aq) + Cr3+ (aq) Fe2+ (aq) Fe3+ (aq)+e Cr2O72- (aq) +e Cr3+ (aq) تعریف سینتیک شیمیایی • ترمودینامیک شیمیایی علمی است که پیرامون خود بخود بودن یا خود بخود نبودن یک تغییر فیزیکی یا شیمیایی از نظر انرژی مطالعه می نماید • سینتیک شیمیایی مطالعه سرعت یا تندی واکنش های شیمیایی است .عوامل کمی در تعیین سرعت یک واکنش دخالت دارند .مطالعه این عوامل به ما کمک می کند تا سر نخهایی پیرامون نحوه تبدیل مواد واکنش دهنده به فراورده ها در واکنش شیمیایی بدست آوریم .مسیر تبدیل مواد اولیه به محصول مکانیسم واکنش نام دارد. تعریف سرعت واکنش Reaction rate: changes in a concentration of a product or a reactant per unit time. [ ] Reaction rate = —— t [] concentration change [ ] t Define reaction rate and explain Average reaction rate Instantaneous reaction rate (2 tangents shown) Initial reaction rate t سرعت نسبی واکنش For a chemical reaction, there are many ways to express the reaction rate. The relationships among expressions depend on the equation. Note the expression and reasons for their relations for the reaction 2 NO + O2 (g) = 2 NO2 (g) [O2] 1 [NO] 1 [NO2] Reaction rate = – ——— = – — ———— = — ——— t a t b t Make sure you can write expressions for any reaction and figure out the relationships. For example, give the reaction rate expressions for 2 N2O5 = 4 NO2 + O2 How can the rate expression be unique and universal? Calculating reaction rate The concentrations of N2O5 are 1.24e-2 and 0.93e-2 M at 600 and 1200 s after the reactants are mixed at the appropriate temperature. Evaluate the reaction rates for 2 N2O5 = 4 NO2 + O2 Solution: (0.93 – 1.24)e-2 – 0.31e-2 M Decomposition rate of N2O5 = – ———————— = – —————— 1200 – 600 600 s = 5.2e-6 M s-1. Note however, rate of formation of NO2 = 1.02e-5 M s-1. rate of formation of O2 = 2.6e-6 M s-1. Be able to do this type problems The reaction rates are expressed in 3 forms سرعت کلی واکنش یا قانون سرعت Dependence of reaction rate on the concentrations of reactants is called the rate law, which is unique for each reaction. For a general reaction, a A + b B + c C products the rate law has the general form order wrt A, B, and C, determined experimentally reaction rate = k [A]X [B]Y [C]Z the rate constant For example, the rate law is rate = k [Br-] [BrO3-] [H+] for 5 Br- + BrO3- + 6 H+ 3Br2 + 3 H2O Use differentials to express rates The reaction is 1st order wrt all three reactants, total order 3. مرتبه واکنش -1مجموع توانهای عبارتهای غلظت در معادله قانون سرعت مرتبه واکنش نامیده می شود -2مرتبه واکنش به دو صورت مرتبه کلی یا مرتبه گردد می بیان جزئی -3مرتبه کلی یا جزئی یک واکنش را تنها از طریق آزمایش می توان بدست آورد نمودار تغییرات سرعت برای واکنش با مرتبه های مختلف 2nd order, rate = k [A]2 rate First order, rate = k [A] k = rate, 0th order [A] = ___? [A] The variation of reaction rates as functions of concentration for various order is interesting. Mathematical analysis is an important scientific tool, worth noticing. مثال در واکنش زیر مرتبه واکنش نسبت به تک تک واکنشگرها را بدست آورده سپس مقدار ثابت سرعت واکنش را محاسبه نمایید .در صورتی که غلظت تمام واکنشگرها یک موالر باشد سرعت واکنش چقدر است؟ H2O2 + 3 I- + 2 H+ I3- + 2 H2O Initial rate M s-1 1.15e-6 R = k [H2O2]x [I-]y [H+]z 2.30e-6 R = k [H2O2]1 [I-]y [H+]z 2.30e-6 R = k [H2O2]1 [I-]1 [H+]z 1.15e-6 R = k [H2O2]1 [I-]1 [H+]0 ][H+ 0.0050 0.0050 0.0050 0.0100 ][I- 0.010 0.010 0.020 0.010 ][H2O2 0.010 0.020 0.010 0.010 Exprmt 1 2 3 4 )R = 1.15e-6 = k (0.010)(0.010 k =0.0115 M-1 s-1 R = k [H2O2] [I-]=0.0115(1)(1)=0.0115 Solution next Differential Rate Law determination - continue From the following reaction rates observed in 4 experiments, derive the rate law for the reaction A + B + C products where reaction rates are measured as soon as the reactants are mixed. Expt [A]o [B]o [C]o rate 1 0.100 0.100 0.100 0.100 2 0.200 0.100 0.100 0.800 3 0.200 0.300 0.100 7.200 4 0.100 0.100 0.400 0.400 This example illustrates the strategy to determine, and a reliable method to solve rate-law experimentally. Solution next Differential Rate Law determination - continue From the following reaction rates, derive the rate law for the reaction A + B + C products where reaction rates are measured as soon as the reactants are mixed. Expt [A]o [B]o [C]o rate 1 0.100 0.100 0.100 0.100 2 0.200 0.100 0.100 0.800 3 0.200 0.300 0.100 7.200 4 0.100 0.100 0.400 0.400 order 3 from expt 1 & 2 2 expt 1, 2 & 3 1 expt 1 & 4 Assume rate = k [A]x[B]y[C]z Therefore 8 = 2x log 8 = x log 2 x = log 8 / log 2 =3 0.800 k 0.2x 0.1y 0.1z ----- = ---------------------0.100 k 0.1x 0.1y 0.1z نمایش مشتقی و انتگرالی قانون سرعت نمایش مشتقی نمایش انتگرالی R= – d[A] / dt = k [A] = [A]o – k t d[A] R= – —— = k [A] dt [A] = [A]o e – k t or ln [A] = ln [A]o – k t d[A] R= – —— = k [A]2 dt 1 1 —— – —— = k t [A] [A]o Describe, derive and apply the integrated rate laws Learn the strategy to determine rate-law [A] conc at t [A]o conc at t = 0 نمودار تغییرات غلظت در سرعت مرتبه اول Describe the features of plot of [A] vs. t and ln[A] vs. t for 1st order reactions. Apply the technique to evaluate k or [A] at various times. [A] ln[A] ln [A] = ln [A]o – k t [A] = [A]o e – k t t½ t t نمودار تغییرات غلظت در سرعت مرتبه دوم t= [B] 1 5 10 15 30 35 [B] = 1.67 1.0 0.67 0.50 0.29 0.25 1 — [B] [B]o 1 1 [B] = —————— ——= k t + —— [B]o k t + 1 [B] [B]o t What kind of plot is linear for 1st and 2nd reactions? t نیمه عمر The time required for half of A to decompose is called half life t1/2. Since [A] = [A]o e – k t or When t = t1/2, [A] = ½ [A]o Thus ln ½ [A]o = ln [A]o – k t1/2 ln [A] = ln [A]o – k t – ln 2 = – k t1/2 k t1/2 = ln 2 = 0.693 relationship between k and t1/2 Radioactive decay usually follow 1st order kinetics, and half life of an isotope is used to indicate its stability. Evaluate t½ from k or k from t½ 1st order reaction calculation N2O5 decomposes according to 1st order kinetics, and 10% of it decomposed in 30 s. Estimate k, t½ and percent decomposed in 500 s. If the rate-law is known, what are the key parameters? Solution next 1st order reaction calculation N2O5 decomposes according to 1st order kinetics, and 10% of it decomposed in 30 s. Estimate k, t½ and percent decomposed in 500 s. Solution: Assume [A]o = [N2O5]o = 1.0, then [A] = 0.9 at t = 30 s or 0.9 = 1.0 e – k t apply [A]o = [A] e– k t ln 0.9 = ln 1.0 – k 30 s – 0.1054 = 0 – k * 30 k = 0.00351 s – 1 t½ = 0.693 / k = 197 s apply k t ½ = ln 2 [A] = 1.0 e – 0.00351*500 = 0.173 Percent decomposed: 1.0 – 0.173 = 0.827 or 82.7 % After 2 t½ (2*197=394 s), [A] = (½)2 =¼, 75% decomposed. After 3 t½ (3*197=591 s), [A] = (½)3 =1/8, 87.5% decomposed. Apply integrated rate law to solve problems Typical Problem wrt Reaction st 1 Order The decomposition of A is first order, and [A] is monitored. The following data are recorded: t / min 0 [A]/[M] 0.100 2 0.0905 4 0.0819 8 0.0670 Calculate k (What is the rate constant? k = 0.0499) Calculate the half life (What is the half life? Half life = 13.89) Calculate [A] when t = 5 min. (What is the concentration when t = 5 min?) Calculate t when [A] = 0.0100. (Estimate the time required for 90% of A to decompose.) Work out all the answers مقایسه واکنش با مرتبه های مختلف مرتبه دو مرتبه یک مرتبه صفر قانون سرعت واحد ثابت سرعت معادله خط راست شیب و عرض از مبدا نیمه عمر The Arrhenius Equation The temperature dependence of the rate constant k is best described by the Arrhenius equation: or k = A e – Ea / R T ln k = ln A – Ea / R T If k1 and k2 are the rate constants at T1 and T2 respectively, then k1 Ea 1 1 ln —— = – — — – — k2 R T1 T2 1903 Nobel Prize citation” …in recognition of the extraordinary services he has rendered to the advancement of chemistry by his electrolytic theory of dissociation” How does temperature affect reaction rates? Derive and apply these relationship to solve problems, and recall the Clausius-Clapeyron equation. Energy in chemical reactions Potential energy R +A H exothermic RA-PD activated complex Ea Ea for reverse reaction P+D Endothermic rxn Progress of reaction Explain the various terms and energy changes in a chemical reaction نظریه های موجود برای تفسیر پدیده های سینتیکی -1نظریه برخورد Collision theory -2نظریه حالت گذار Transition state theory A---B---C The height of the barrier is called the activation energy, Ea. The configuration of atoms at the Ea maximum in the P.E. profile is called Potential Energy the transition state. A + BC Reactants AB + C Products Reaction Progress A2(g) + B2(g) 2AB(g) برخورد موثر فرضیه تشکیل کمپلکس فعال انواع واکنشها از نظر مکانیسمی -1واکنشهای بنیادی واکنشهایی هستند که تنها از یک مرحله تشکیل شده اند و در آنها مرتبه واکنش برابر مجموع ضرایب استوکیومتری واکنش است. ]O3 O2 + O rate = k [O3 rate = k [NO2]2 NO2 + NO2 NO3 + NO -2واکنشهای غیر بنیادی واکنشهایی که در آنها مراحل مختلفی برای تبدیل مواد اولیه به محصول و جود دارد را گویند در این گونه واکنشها مرتبه واکنش با ضرایب استوکیومتری برابر نمی باشد تقریبا همه واکنشها از این نوع می باشند. واکنشهای بنیادی در یک واکنش واقعی ،فرضی بوده و به کمک مکانیسم ،تشخیص حد واسطها و قانون سرعت واکنش می توان به صحت آنها پی برد NO2 + CO NO + CO2 )(an elementary reaction Step 1 NO2 + NO2 NO3 + NO مولکوالریته مرتبه کل واکنش در یک واکنش بنیادی را مولکوالریته گویند واکنشهایی بنیادی که که در آن مرتبه واکنش یک باشد را تک مولکولی واکنشهایی بنیادی که که در آن مرتبه واکنش دو باشد را دو مولکولی و واکنشهایی بنیادی که که در آن مرتبه واکنش سه باشد را سه مولکولی گویند Molecularity of elementary reactions Example Some elementary reactions for the reaction between CH4 and Cl2 are Cl2 2 Cl 2 Cl Cl2 2Cl + CH4 Cl2 + CH4* Cl + CH4 HCl + CH3 CH3 + Cl CH3Cl CH3 + CH3 CH3-CH3 CH3Cl + Cl HCl + CH2Cl CH2Cl + Cl CH2Cl2 * * * (more) Write down the rate laws and describe them as uni- bi- or ter-molecular steps yourself, please. Rate Laws and Mechanisms A mechanism is a collection of elementary steps devise to explain the the reaction in view of the observed rate law. You need the skill to derive a rate law from a mechanism, but proposing a mechanism is task after you have learned more chemistry For the reaction, 2 NO2 (g) + F2 (g) 2 NO2F (g), the rate law is, rate = k [NO2] [F2] . Can the elementary reaction be the same as the overall reaction? If they were the same the rate law would have been rate = k [NO2]2 [F2], Therefore, they the overall reaction is not an elementary reaction. Its mechanism is proposed next. Rate-determining Step in a Mechanism The rate determining step is the slowest elementary step in a mechanism, and the rate law for this step is the rate law for the overall reaction. The (determined) rate law is, rate = k [NO2] [F2], for the reaction, 2 NO2 (g) + F2 (g) 2 NO2F (g), and a two-step mechanism is proposed: i NO2 (g) + F2 (g) NO2F (g) + F (g) ii NO2 (g) + F (g) NO2F (g) Which is the rate determining step? Answer: The rate for step i is rate = k [NO2] [F2], which is the rate law, this suggests that step i is the rate-determining or the s-l-o-w step. Explain rate determining step in a mechanism and use it to derive the rate law. 2 مثال The decomposition of H2O2 in the presence of I– follow this mechanism, i ii H2O2 + I– k1 H2O + IO– H2O2 + IO– k2 H2O + O2 + I– What is the rate law? slow fast Energy Eai Eaii reaction Solve the problem The decomposition of H2O2 in the presence of I– follow this mechanism, i ii H2O2 + I– k1 H2O + IO– slow H2O2 + IO– k2 H2O + O2 + I– fast What is the rate law? Solution The slow step determines the rate, and the rate law is: rate = k1 [H2O2] [I –] Since both [H2O2] and [I –] are measurable in the system, this is the rate law. مثال ( 3تمرین 24پایان فصل) در واکنش زیر معادله سرعت به صورت N2O5+NO 3NO2 ]k1k3[ N 2O5 ][NO ]k2 [ NO2 ] k3[ NO RN 2O5 است مکانیسم پیشنهادی به صورت زیر است k1 N 2O5 NO2 NO3 k2 NO2 NO3 N 2O5 k3 NO NO3 2NO2 مرحله سوم مرحله کند واکنش بوده و با توجه به تقریب حالت پایا نشان دهید که مکانیسم فوق همان معادله سرعت را تایید می کند در صورتی که k2<<k3باشد معادله سرعت چه تغییری مینماید راه حل -1نوشتن معادله سرعت واکنش چون در مسئله مشخص نشده که کدام مرحله مرحله کند واکنش است بنابر این مرحله آخر به عنوان مرحله تعیین کننده سرعت در نظر گرفته می شود سرعت واکنش = ]k3[NO][NO3 -2تقریب حالت پایا :در این تقریب فرض می شود که غلظت حد واسط ثابت است و سرعت تولید شدن آن و سرعت مصرف شدنش برابر باشد پس سرعت تولید ]=[NO3سرعت مصرف ][NO3 سرعت تولید ]K1[N2O5]=[NO3 سرعت مصرف ]K2[NO2][NO3]+k3[[NO][NO3]=[NO3 -3با برابر قرار دادن سرعت تولید و مصرف حد واسط خواهیم داشت ] k1[ N 2O5 [ NO3 ] ]k2 [ NO2 ] k3[ NO باجانشین کردن غلظت حد واسط در رابطه سرعت خواهیم داشت ]k1k3[ N 2O5 ][NO ]k2 [ NO2 ] k3[ NO RN 2O5 درصورتی که k2<<k1خواهیم داشت k1k3 ] [ N 2O5 ] k[ N 2O5 k3 RN 2O5 Deriving rate laws from mechanisms – steadystate approximation The steady-state approximation is a general method for deriving rate laws when the relative speed cannot be identified. It is based on the assumption that the concentration of the intermediate is constant. [Intermediate] Rate of producing the intermediate, Rprod, is the same as its rate of consumption, Rcons. Rprod > Rcons Be able to apply the steadystate approximation to derive rate laws Rprod = Rcons Rprod < Rcons time Steady-state Let’s assume the mechanism for the reaction. H2 + I2 2 HI approximatio as follows. n-2 Step (1) I2 —k1 2 I Step (1) 2 I —k-1 I2 Step (2) H2 + 2 I —k2 2 HI Derive the rate law. Derivation: rate = k2 [H2] [I] 2 (‘cause this step gives products) but I is an intermediate, this is not a rate law yet. Since k1 [I2] (= rate of producing I) Steady state = k-1 [I]2 + k2 [H2] [I]2 (= rate of consuming I) Thus, k1 [I2] [I]2 = —————— k-1 + k2 [H2] rate = k1 k2 [H2] [I2] / {k-1 + k2 [H2] } Steady-state approximation - 3 From the previous result: k1 k2 [H2] [I2] rate = ——————— {k-1 + k2 [H2] } Discussion: (i) If k-1 << k2 [H2] then {k-1 + k2 [H2]} = k2 [H2] , then rate = k1 k2 [H2] [I2] / {k2 [H2] } = k1 [I2] (pseudo 1st order wrt I2) using large concentration of H2 or step 2 is fast (will meet this condition). (ii) If step (2) is slow, then k2 << k1, and if [H2] is not large, we have {k-1 + k2 [H2]} = k-1 and rate = k1 k2 [H2] [I2] / k1 = k2 [H2] [I2] Steady-state approximation - 4 In an alkaline solution, peroxydisulfate oxidizes sulfite to yield sulfate, S2O82- + SO32- + 2 OH- 3 SO42- + H2O. The following mechanism has been proposed: i S2O82- + SO32- —k1 S2O72- + SO42ii S2O72- + H2O —k2 2 SO42- + 2 H+ iii H+ + OH- —k3 H2O (fast equilibrium to be discussed) Steady-state approximation follows these steps: What is or are the intermediates I? Use which step to give the rate law that may involve [I]? Express the rates of producing and consuming intermediate(s) Express [I] of intermediate(s) in terms of [Reactants] Derive the rate law in terms of [Reactants] Discuss See page 607 PHH Text Catalysis Energy A catalyst is a substance that changes the rate Uncatalyzed rxn of a reaction by lowing the activation energy, Ea. It participates a reaction in forming an intermediate, but is regenerated. Enzymes are marvelously selective catalysts. A catalyzed reaction, NO (catalyst) 2 SO2 (g) + O2 — 2 SO3 (g) via the mechanism i 2 NO + O2 2 NO2 (3rd order) ii NO2 + SO2 SO3 + NO Catalyzed rxn rxn Catalyzed decomposition of ozone R.J. Plunkett in DuPont discovered carbon fluorine chlorine compounds. The CFC decomposes in the atmosphere: CFCl3 CFCl2 + Cl CF2Cl3 CF2Cl + Cl. The Cl catalyzes the reaction via the mechanism: i O3 + h v O + O 2, ii ClO + O Cl + O2 iii O + O3 O2 + O2. The net result or reaction is 2 O3 3 O2 Scientists sound the alarm, and the CFC is banned now. Homogenous vs. heterogeneous catalysts A catalyst in the same phase (gases and solutions) as the reactants is a homogeneous catalyst. It effective, but recovery is difficult. When the catalyst is in a different phase than reactants (and products), the process involve heterogeneous catalysis. Chemisorption, absorption, and adsorption cause reactions to take place via different pathways. Platinum is often used to catalyze hydrogenation Catalytic converters reduce CO and NO emission. Heterogeneous catalysts Ceryx's vision is to design, produce, and commercialize advanced systems that balance Cost, Performance, Emissions Reduction, and Fuel Penalty to make the economics of pollution control viable. We explore new ways to look at the air quality challenges faced by industry and search for potential solutions by combining proven technologies with state-of-the-art science. Catalyzed reactions: CO + O2 CO2 2 NO N2 + O2 Enzymes – selective catalysts Enzymes are a long protein molecules that fold into balls. They often have a metal coordinated to the O and N sites. Molecules catalyzed by enzymes are called substrates. They are held by various sites (together called the active site) of the enzyme molecules and just before and during the reaction. After having reacted, the products P1 & P2 are released. Enzyme + Substrate ES (activated complex) ES P1 + P2 + E Enzymes are biological catalysts for biological systems. X-ray 3-D structure of fumarate reductase. It reduces fumerate, an important role in the metabolism of anaerobic bacteria, from Max Planck Inst. Chemical Kinetics - Summary Explain how the various factors affect reaction rates. Define reaction rates, average rates, initial rates and rate constants. Evaluate rate law from experiments Properly apply 1st and 2nd differential rate laws and integrated rate laws. Interpret elementary reactions and mechanisms. Derive rate laws from a given mechanism. Apply the steady-state method to derive the rate law of a given mechanism, and discuss the results. Explain the action of catalysts in terms of chemistry and in terms of energy of activation. Fig. 13.21 Fig. 13.23 Fig. 13.26 A) What is the Rate Law For This Reaction? B) What is the order in respect to each reactant? C) What is the overall reaction order? D) What is k, the rate constant?