Kinetics of Chemical Reactions PDF

KINETICS THE RATES OF CHEMICAL REACTIONS The rate of a reaction measures how fast a reactant is consumed or how fast a product is formed. The rate is expressed as a ratio of the change in concentration to elapse time....

KINETICS THE RATES OF CHEMICAL REACTIONS The rate of a reaction measures how fast a reactant is consumed or how fast a product is formed. The rate is expressed as a ratio of the change in concentration to elapse time. Rate Law/Equation Experimental measurements of the rate leads to the rate law for the reaction, which expresses the rate in terms of the rate constant and the concentration of the reactants. the dependence of rate on concentration gives the orders of a reaction. A reaction will be.spontaneous if ∆𝐺 for the reaction is negative. The term spontaneous does not means that the reaction will occur suddenly. Rather, it means that the reaction is thermodynamically favourable, ie the reaction favours formation of products. Spontaneity has nothing to do with the speed of the reaction. For example, the conversion of diamond into graphite is a spontaneous process at standard pressure and temperature. But even though this process is spontaneous, it is nevertheless very slow, it can take millions of years, but ultimately all diamond will eventually turn in to graphite (Diamond-> Graphite , ∆𝐺 = negative) (Some spontaneous processes are fast like explosions, while others are slow, like diamond turning into graphite. The rate of any reaction is described by a rate equation, which has the following general form; Rate= k(reactants) Rate const. Concentration. Of starting materials A+B=Products −𝑑[𝐴] The differential rate low= = k[A] [B] (1) 𝑑𝑡 The general equation above (1) indicates the rate of a reaction is dependent on the rate constant (k) and on the concentration of the reaction k is a value that is specific for each reaction and is dependent on a number of factors. C Slope ∝ rate o n Product c. Reactant Time Figure 1: Plot of concentration against time  EMPERICAL OBSERVATIONS: Measurement of Reaction Rates One of the most fundamental empirical observations that a chemist can make is how the concentration of a reactant and product vary with time. The 1st substantial qualitative study of the rate of a reaction was performed by L. Wilhelm, who in 1850 studied the inversion of sucrose in an acidic solution with a Polarimeter. There are many methods for making such observation. One might monitor the concentration spectrophotometrically, through absorption, florescence or light scattering, or electrochemically, for example potentiometric determination of the pH. Whatever the method, the overall result is usually something like, that illustrated in Fig 1. In general, as it is true in the figure (fig 1), the reactant concentration will decrease as time goes on, while the product concentrations will increase. There may also be intermediate in the reaction, species whose concentration first grow and then decay with time. From fig 1, the slope varies with time and generally approaches zero as the reaction approaches equilibrium. Consider the general reaction. aA+ bB -> cC + dD, the rate of change of [C] is rate= [1/c] d[c]/dt. The rate varies with time and is equal to some functins of the concentrations. [1/c] d[c]/dt = f[A] [B] [C] [D]. of course the time rates of change for the concentrations of the other species in the reaction are related to that of the first species by the stoichiometry of the reaction. 1 𝑑[𝐶] 1 𝑑[𝐷] 1 𝑑[𝐴] 1 𝑑[𝐵] = = − =− 𝑐 𝑑𝑡 𝑑 𝑑𝑡 𝑎 𝑑𝑡 𝑏 𝑑𝑡 By conversion, the rate would be positive if the reaction proceeds from left to right, 1 𝑑[𝐶] hence positive derivatives for the equation = f[A] [B] [C] [D]= rate law while 𝑐 𝑑𝑡 f[A] [B] [C] [D] = function of concentration, f can be expressed as a simple product of the a rate constant k and concentration each raised to some power 𝑑[𝐶] 1/c = 𝑘[A]m[B]n[c]o[D]p 𝑑𝑡 Overall order= sum of the power i.e q= m+ n+ o+ p order of reaction with respect to a particular species can be defined as the power to which its concentration is raised in the rate law  Determination of order of reaction through experimental method Data for the Reaction between F2 & ClO2 F2(g) + 2 ClO2(g) -> 2FClO2(g) Experiment [F2]M [ClO2]M Initial rate M/s 1 0.10 0.010 1.2X10-3 2 0.10 0.040 4.8X10-3 3 0.20 0.010 2.4X10-3 Rate= K[F2]x [ClO2]y 𝐾(0.10)𝑥 (0.04)𝑦 4.8𝑋 10−3 Rate 2/1 = 𝐾(0.01)𝑥 (0.01)𝑦 = 1.2𝑋10−3 4y= 4 42y= 22 2y= 2 Y = 1 𝐾(0.20)𝑥 (0.01)𝑦 2.4𝑋 10−3 R3/R1= = 𝐾(0.1)2 (0.01)𝑦 1.2𝑋10−3 2x = 2 X=1 Consider the following reaction CH3Cl + OH- → CH3OH + Cl- The rate of the reaction was found to be dependent on the concentration of both reactants. The rate equation. Rate=k[CH3Cl] [OH] K=rate constant for any given temperature. The reaction is a 2nd order reaction 1st order with respect to CH3Cl , 1st Order with respect to OH These reactants collide with each other, and must do so with an orientation that allows bonding to take place Approach of hydroxide ion that leads to reactions with chloromethane. Attraction between negatively charged hydroxide ion Approach of hydroxide to chloromethane that and carbon atom with positive charge will not lead to chemical reaction. repulsion between negatively charged hydroxide ion & chlorine atom with partial negative charge Therefore not all encounters between potentially reactive species produce chemical reaction The reaction of chloromethane with hydroxide ion involves the breaking of a bond between carbon and chlorine and the forming of a new bond between oxygen and carbon. At some point during the reaction, the carbon atom partially bonded to both the hydroxide ion and the chlorine atom. This intermediate state lying between the reactants and the products is known as the transition state. The molecular complex that exists at the transition state in equilibrium with the reactants is called activated complex and it is represent in equations enclosed in square brackets. Fig 2: Reaction between Chloromethane and hydroxide ion The transition state is high energy state. Energy has been put into the molecule to partially break the carbon-chlorine bond, but the energy for the formation of the full carbon-oxygen bond has not been generated. Once the activated complex is formed, it is converted very rapidly to product, at some absolute rate, the number is of the same magnitude as the frequency of the vibrational motions of covalent bonds. FREE ENERGY OF ACTIVATION The energy relationship between the reactants, the transition state and the products for the reaction of chloromethane and hydroxide ion can be represented on an energy diagram. The y axis represents energy in this case, the free energy of the system. The x-axis is called the reaction coordinate and represents the change that must take place in bond lengths and bond angles within molecules as reactants are converted to products. Moving along these axis from left to right corresponds to the progress of the reaction from reactants to products. In going from reactants to the products, the system has to go over an energy barrier (the lump) the height of the energy barrier is the free energy of activation for the reaction (∆𝐺 th). Which is the energy that reactants attain in reaching the transition state. The energy barrier represents the minimum amount of energy required for a reaction to occur between two reactants that collide. If the collision between the reactants does not involve this much high energy, they will not react with each other to form products. The number of successful collisions is therefore dependent on the number of molecules that have certain threshold energy. Fig 3:: Relative energy levels for the reaction, transition state (Ts) and products for the reaction of chloromethane & hydroxide ion. Note: The rate of a reaction is different at different temperature. The rate constant for a reaction is related to the free energy of activation by the following equation 𝑘 = 𝑘𝑜 𝑒 −∆𝐺/𝑅𝑇 eis 2.718, the base of natural logarithms ko= absolute rate conflict As DG+ gets large, e-(DG//RT) must get smaller, therefore, the observed rate of the reaction decreases. And a smaller ∆𝐺# means an increased rate of reaction. TEMPERATURE DEPENDENCE OF RATE CONSTANTS The temperature dependence of the reaction, like the orders of reaction is another empirical measurement that provides a basis for understanding of reaction on a molecular level. Most rates for simple reactions increase with increasing temperature. A rule of thumb is that the rate will double for every10℃ increase in temperature. Arrhenius first proposed that the rate constant obeyed the rate 𝐸𝑎 𝑘 = 𝐴𝑒𝑥𝑝 − 𝑅𝑇 OR  𝑘 = 𝐴𝑒 −𝐸𝑎/𝑅𝑇 This relationship known as Arrhenius equation is similar in form to the relationship between the rate constant and constant and ∆𝐺# Fig 4: Distribution of energy (KE) among molecules at two different temperatures What physical model accounts for the dependence of rate on temperature. At any temperature, the molecules in a reaction mixture have a wide distribution of energies Raising the temperature of a reaction will cause the rate to increase because the molecules will have more kE- at higher temperature.. At higher temperature. a large number of molecules will have the KE (kinetic energy) sufficient to produce a reaction. NITROGLYCERINE AN EXPLOSIVE WITH MEDICAL PROPERTIES Explosives can be divided into two categories , primary(1o) explosive and secondary(20) explosive 1o explosive are very sensitive to stock or heat and they detonate very easily. i.e the energy of activation (𝐸𝑎 ) for the explosion is very small & easily overcome in contrast, 20 explosion have a larger 𝐸𝑎 ) and are therefore more stable.. 20 explosion are often detonated with a very small amount of 10 explosive Fig 5: Structure of nitroglycerin The first commercial 20 explosive was produced by Alfred Nobel in the mid-1800. At the time, there were no strong explosive safe enough to handle. Alfred focus his efforts on finding a way to stabilized Nitroglycerin. Nitroglycerin is very shock sensitive and unsafe to handle, in an effort to find a formulation of nitroglycerin that would have a large energy of activation, Nobel conducted many experiments. Many of those experiment caused explosions in the Nobel factory, one of which killed his younger brother, Emil, along with several coworkers. Ultimately, Nobel was successful in stabilizing nitroglycerin by mixing it with diatomaceous earth (a type of sedimentary rock that easily crumbles into a fine powders). The resulting mixture which he called dynamite became the 1st commercial 20 explosives and numerous factories across Europe were built in order to produce dynamite in large quantities. Alfred Nobel became fabulously wealthy from his invention. Overtime it was discovered that workers in the dynamite production factories experienced several physiological responses associated with prolonged exposure to nitroglycerin. Most importantly workers who suffered from heart problems found that their conditions greatly improved. For many decades, the reason for this response was not clear, but a clear pattern had been established. As a result doctors began to treat patients experiencing heart problems by giving them small amount of nitroglycerin to ingest. Ultimately Nobel himself suffered from heart problems and his doctor suggested that he eat nitroglycerin. Nobel refused to ingest what he considered to be explosive, and he died of heart complications. With the passing decades, it became clear that nitroglycerin serves as vasodilator (dilates blood vessels) and therefore reduces the chances of blockage that leads to heart attack. A scientist Louis Ignarro was interested in the pharmacological question and heavily investigated the action of nitroglycerin in the body, he discovered that metabolism of nitro glycerin produces nitric oxide (NO) and that the small compound is ultimately responsible for a large number of physiological processes.