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Chapter 25 The Rates of chemical reactions

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## Chapter 25 The Rates of chemical reactions

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**Contents**Empirical chemical kinetics • 25.1 Experimental techniques • 25.2 The rates of reactions • 25.3 Integrated rate laws • 25.4 Reaction approaching equilibrium • 25.5 The temperature dependence of reaction rates Accounting for the rate laws • 25.6 Elementary reactions • 25.7 Consecutive elementary reactions • 25.8 Unimolecular reactions**Assignment for chapter 25**• 25.4(b),25.6(a),25.10(b),25.15(a) • 25.2,25.5,25.11,25.23**Empirical chemical kinetics**St. John’s wort is an herb that is thought to create a sense of tranquility. Herbs and other medicines have been used through the ages to cure disease and to relieve pain. In many cases, the medicine is effective because it controls the rates of reactions within the body. In this chapter, we examine the rates of chemical reactions and the mechanisms by which they take place.**Monitoring the progress of a reaction**2N2O5(g) 4NO2(g)+O2(g) Initial pressure of n moles of N2O5 is p0. Progress of the reaction: N2O5NO2 O2 Total Initial n 0 0 n At time t n(1-a) 2an 0.5an n(1+1.5a) Progress of the reaction: N2O5NO2 O2 Total Initial p0 0 0 p0 At time t n(1-a) p0 2an p0 0.5an p0 n(1+1.5a) p0**Classroom exercise**2NOBr(g) 2NO(g)+Br2(g) Initial pressure of n moles of N2O5 is p0. Progress of the reaction: NOBr NO Br2 Total Initial n 0 0 n At time t n(1-a) an 0.5an n(1+0.5a) Progress of the reaction: N2O5NO2 O2 Total Initial p0 0 0 p0 At time t n(1-a) p0 an p0 0.5an p0 n(1+0.5a) p0**Other properties to be monitored in the progress of chemical**reactions • Absorption of radiation (spectrophotometry) • Ions in solution (Electrical conductivity) • Emission of radiation (emission spectroscopy) • Mass of ions (mass spectrometry) • Adsorption of molecules (gas chromatography) • Absorption of radiofrequency radiation (NMR spectroscopy) • Absorption of microwave radiation (ESR spectroscopy) • Etc.**Cl**Cl Cl Cl Experimental techniques:flash photolysis**Cl**Cl Cl Cl Experimental techniques:flash photolysis**Experimental techniques:quenching methods**• Chemical quench flow method: quench by chemical reactants such as acids • Freeze quench method: quench by rapid cooling**Definition**kAmC+nD Rate=change in concentration of reactant / time interval 2HI(g) H2(g)+I2(g)**The activity of penicillin declines over several weeks when**it is stored at room temperature in the absence of stabilizers. The shape of this graph of concentration of penicillin as a function of time is typical of the behavior of chemical reactions, although the time span may vary from fractions of a second to years.**This graph shows two examples of how the rate of consumption**of penicillin can be monitored while it is being stored. The red line shows the average rate calculated from measurements at 0 and 10 weeks, and the blue line shows the average rate calculated from measurements at 2.5 and 7.5 weeks. The instantaneous rate at 5 weeks is the tangent to the curve at that time (not shown).**To calculate the instantaneous reaction rate, we draw the**tangent to the curve at the time of interest and then calculate the slope of this tangent. To calculate the slope, we identify any two points, A and B, on the straight line and identify the molar concentrations and times to which they correspond. The slope is then worked out by dividing the difference in concentrations by the difference in times. Notice that this graph shows the concentration of a product.**Instantaneous Rate of Reaction**A+2B3C+D v is the same for all species in a reaction.**The initial rate of reaction for the decomposition of N2O5**in five experiments. The initial rate of disappearance of a reactant is determined by drawing a tangent to the curve at the start of the reaction. 2N2O5(g)4NO2(g)+O2(g)**Instantaneous Rate of Reaction**For a homogeneous reaction, For a heterogeneous reaction, The surface density of species J**The plot of the initial rate of decomposition of N2O5 as a**function of initial concentration for the five samples in previous figure is a straight line. The linear plot shows that the rate is proportional to the concentration. The graph also illustrates how we calculate the rate constant, k , from the slope of the straight line. Initial rate=k x initial concentration**(a) The instantaneous reaction rates for the decomposition**of N2O5 at five different times during a single experiment are obtained from the slopes of the tangents to the line at each of the five points. (b) When these rates (the slopes) are plotted as a function of the concentration of N2O5 remaining, the result is a straight line with a slope equal to the rate constant. In (b), we have indicated the rates by redrawing the tangents. rate=k x concentration**Illustration**• In the reaction 2NOBr(g)2NO(g)+Br2(g), the rate of formation of NO is 0.16 mmol/L/s. Calculate the rate of consumption of NOBr.**Classroom exercise**• In the reaction 2CH3(g)CH3CH3(g), the rate of consumption of CH3 is -1.2 mol/L/s. Calculate the rate of the reaction and the rate of formation of CH3CH3.**Order of a Reaction**• a: order of reaction, determined by experiment. • k: rate constant, determined by experiment.**(a) The concentration of the reactant in a zero-order**reaction falls at a constant rate until the reactant is exhausted. (b) The rate of a zero-order reaction is independent of the concentration of the reactant and remains constant until all the reactant has been consumed, when it falls abruptly to 0. v=constant**More Complicated Rate Laws**nAA+nBB+nCC+…nPP+nQQ+nRR+… Order=a+b+…-p-q…**More Complicated Rate Laws**nAA+nBB+nCC+…nPP+nQQ+nRR+… Order=a for A b for B,-p for P, -q for Q…**(a) When sulfur dioxide and oxygen are passed over hot**platinum foil, they combine to form sulfur trioxide. (b) The sulfur trioxide forms dense white fumes of sulfuric acid when it comes into contact with moisture in the atmosphere. The rate law for the formation of sulfur trioxide shows that its rate of formation decreases as its concentration increases, so the sulfur trioxide must be removed as it is formed if the reaction is to proceed rapidly. 2SO2(g)+O2(g)2SO3(g) SO3(g)+H2O(g)H2SO4(l)**The determination of rate law**• Method of initial rates: Only one reactant is left limited, all the rest are in large excess. True rate law: By making B in large excess, [B]=[B]0 The rate law with respect to A can be determined.**The determination of rate law**• Isolation method: Only one reactant is left limited, all the rest are in large excess. True rate law: By making B in large excess, [B]=[B]0 The rate law with respect to A can be determined.**Using the method of initial rates**• The initial rates of the reaction of 2I(g)+Ar(g)I2(g)+Ar(g) were measured as follows: Determine the orders of reaction with respect to I and Ar and the rate constant.**Logv0=8.94,8.88,8.75**Log[I]0=0**Integrated Rate Law**• Find the concentration of a reactant at time t from reaction order and initial concentration. • First order reaction:**The characteristic shape of the graph showing the time**dependence of the concentration of a reactant in a first-order reaction is an exponential decay, as shown here. The larger the rate constant, the faster the decay from the same initial concentration.**Half-Lives of First Order Reactions**Time constant:**The half-life of a reactant is short if the first-order rate**constant is large, because the exponential decay of the concentration of the reactant is then faster.**Second Order Integrated Rate Laws**Prove above equation (classroom exercise).**The characteristic shapes (orange and green lines) of the**time dependence of the concentration of a reactant during two second-order reactions. The gray lines are the curves for first-order reactions with the same initial rates. Note how the concentrations for second-order reactions fall away much less rapidly than those for first-order reactions do.**Second Order Integrated Rate Laws**For A+BP