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## Chapter 14: Chemical Kinetics

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**Chapter 14: Chemical Kinetics**Chemistry: The Molecular Nature of Matter, 6E Jespersen/Brady/Hyslop**Speeds at Which Reactions Occur**Kinetics: • Study of factors that govern • How rapidly reactions occur and • How reactants change into products Rate of Reaction: • Speed with which reaction occurs • How quickly reactants disappear and products form**Important Questions in Kinetics**Practical value • Chemical /pharmaceutical manufacturers • Is it practical to make drug? • Made on manageable time scale? • Can we adjust conditions to improve rate and yield? • Mechanism of Reaction • Series of individual steps leading to overall observed reaction • How do reactants change into products? • Detailed sequence of events**Factors that Affect Reaction Rates**1. Chemical nature of reactants • What elements, compounds, salts are involved? • What bonds must be formed, broken? • What are fundamental differences in chemical reactivity?**Factors that Affect Reaction Rates**• Ability of reactants to come in contact Reactants must meet in order to react • Gas or solution phase facilitates this • Reactants mix and collide with each other easily • Homogeneous reaction • All reactants in same phase • Occurs rapidly • Heterogeneous reaction • Reactants in different phases • Reactants meet only at interface between phases • Surface area determines reaction rate • Increase area, increase rate; decrease area, decrease rate**Factors that Affect Reaction Rates**3. Concentrations of reactants • Rates of both homogeneous and heterogeneous reactions affected by [X] • Collision rate between A and Bincrease if we increase [A] or increase [B]. • Often (but not always) reaction rate increases as [X] increases**Factors that Affect Reaction Rates**4. Temperature • Rates are often very sensitive to temperature • Raising temperature usually makes reaction faster for two reasons: a. Faster molecules collide more often and collisions have more energy • Most reactions, even exothermic reactions, require energy to occur • Rule of thumb: • Rate doubles if temperatureincreases by 10 °C (10 K)**Factors that Affect Reaction Rates**5. Presence of Catalysts • Catalysts • Substances that increase rates of chemical reactions without being used up • Rate-accelerating agents • Speed up rate dramatically • Rate enhancements of 106 not uncommon • Chemicals that participate in mechanism but are regenerated at the end • e.g. Enzymes and zeolites**Measuring Rate of Reaction**• Rate = ratio with time unit in denominator • e.g. Rate of pay = • Rate of Chemical Reaction • Change in concentration per unit time. • Always with respect to a given reactant or product • [reactants] decrease with time • [products] increase with time**Rate of Reaction with Respect to Given Species X**• Concentration in M units • Time in s units • Units on rate: • e.g. • [product] increases by 0.50 mol/L per second rate = 0.50 M/s • [reactant] decreases by 0.20 mol/L per second rate = 0.20 M/s**Rate of Reaction**• Always positive • Whether something is increasing or decreasing in [X] • Reactants • Reactant consumed • So [X] is negative • Need minus sign to make rate positive • Products • Produced as reaction goes along • So [X] is positive • Thus rate already positive**Rates and Coefficients**• Relative rates at which reactants are consumed and products are formed • Related by coefficients in balanced chemical equation • Know rate with respect to one product or reactant • Can use equation to determine rates with respect to all other products and reactants. C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(g) Rate of Reaction**Rates and Coefficients**• O2 reacts 5 times as fast as C3H8 • CO2 forms 3 times faster than C3H8 consumed • H2O forms 4/5 as fast as O2 consumed C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(g)**Rates and Coefficients**In general A + B C + D • Which one do I measure? • Doesn't matter • All interrelated • Often determined by which one is easily measured**Your Turn!**In the reaction 2CO(g) + O2(g) → 2CO2(g) the rate of the reaction of CO is measured to be 2.0 M/s. What would be the rate of the reaction of O2? • The same • Twice as great • Half as large • You cannot tell from the given information**Change of Reaction Rate with Time**• Generally reaction rate changes during reaction • i.e. Not constant • Often initially fast when lots of reactant present • Slower and slower as reactants are depleted Why? • Rate depends on the concentration of the reactants • Reactants being used up, so the concentration of the reactants are decreasing and therefore the rate decreases**Measuring Rates**• Measured in three ways: • Instantaneous rate • Average rate • Initial rate**Instantaneous Reaction Rates**• Instantaneous rate • Slope of tangent to curve at some specific time • Initial rate • Determined at time = 0**Average Rate of Reaction**• Slope of line connecting starting and ending coordinates for specified time frame**Concentration vs. Time Curve for HI Decomposition at 508**C • Rate at any time t = negativeslope (or tangent line) of curve at that point**2 HI(g) H2(g) + I2(g)**Table 14.1 Data at 508 °C Initial rate • Average rate between first two data points**Rate at 100 s**(50,0.068) (150,0.044)**Rate at 300 s**2 HI(g) H2(g) + I2(g) Rate = tangent of curve at 300 s**Your Turn!**A reaction was of NO2 decomposition was studied. The concentration of NO2 was found to be 0.0258 M at 5 minutes and at 10 minutes the concentration was 0.0097 M. What is the average rate of the reaction between 5 min and 10 min? A. 310 M/min B. 3.2 × 10–3M/min C. 2.7 × 10–3M/min D. 7.1 × 10–3M/min**Concentration and Rate**Rate Laws • A + BC + D • Homogeneous reaction • Rate = k[A]m[B]n • Rate Law or Rate expression • m and n = exponents found experimentally • No necessary connection between stoichiometric coefficients (,) and rate exponents (m, n) • Usually small integers • Sometimes simple fractions (½, ¾) or zero**Rate Laws**Rate = k[A]m[B]n • k = Rate Constant • Dependence of rate on concentration is some power (m) of concentration [A] • All other factors (T, solvent) are included in k • Specific rate constant • k depends on T • Must specify T at which you obtained k. = k[A]m[B]n**Learning Check**The rate law for the reaction 2A +B → 3C is rate= 0.045 M–1s–1 [A][B] If the concentration of A is 0.2 M and that of B is 0.3 M, what will be the reaction rate? rate=0.045 M–1 s–1 [0.2][0.3] rate=0.0027 M/s 0.003 M/s**Rate Laws**Rate = k[A]m[B]n • Exponents specify the order of reaction with respect to each reactant • Order of Reaction • m = 1 [A]1 1st order in [A] • m = 2 [A]2 2nd order in [A] • m = 3 [A]3 3rd order in [A] • m = 0 [A]0 0th order in [A] • [A]0 = 1 means A doesn't affect rate • Overall order of reaction = sum of orders (m and n) of each reactant in rate law**Example 1: Determining Order of Reactions**5Br– + BrO3– + 6H+ 3Br2 + 3H2O • x = 1 y = 1 z = 2 • 1st order in [BrO3–] • 1st order in [Br –] • 2nd order in [H+] • Overall order = 1 + 1 + 2 = 4**Example 2: Determining Order of Reactions**• Sometimes n and m are coincidentally the same as stoichiometric coefficients 2HI(g) H2(g) + I2(g) • 2nd order in [HI] • 2nd order overall**Your Turn!**The following rate law has been observed: Rate = k[H2SeO][I–]3[H+]2. The rate with respect to I– and the overall reaction rate is: A. 6, 2 B. 2, 3 C. 1, 6 D. 3, 6**Calculating k from Rate Law**• If we know rate and concentrations, can use rate law to calculate k From Ex.2 at 508 °C • Rate= 2.5 × 10–4M/s • [HI] = 0.0558 M**How To Determine Exponents in Rate Law**Experiments • Method of initial rates • If reaction is sufficiently slow • or have very fast technique • Can measure [A] vs. time at very beginning of reaction • Before it slows very much, then • Set up series of experiments, where initial concentrations vary**Example 3: Method of Initial Rates**3A + 2Bproducts Rate = k[A]m[B]n • Convenient to set up experiments so • The concentration of one species is doubled or tripled • And the concentration of all other species are held constant • Tells us effect of [varied species] on initial rate**Reaction Order and Rate**• If reaction is 1storder in [X], • Doubling [X]1 21 • Doubles the rate • If reaction is 2ndorder in [X], • Doubling [X]2 22 • Quadruples the rate • If reaction is 0thorder in [X], • Doubling [X]0 20 • Rate doesn't change • If reaction is nthorder in [X] • Doubling [X]n 2n times the initial rate**Back to Example 3**• Comparing Expt. # 1 and 2 • Doubling [A] • Quadruples rate • Reaction 2ndorder in A = [A]2 2m = 4 or m = 2**Back to our Example 3**• Comparing Expt. # 2 and 3 • Doubling [B] • Rate does not change • Reaction 0thorder in B = [B]0 = 1 2n = 1 or n = 0**Ex. 3: Method of Initial Rates**• Conclusion: rate = k[A]2 • Can use data from any experiment to determinek • Let’s choose first experiment**Example 4: Method of Initial Rates**2 SO2 + O2 2 SO3 2 SO2 + O2 2 SO3 Rate = k[SO2]m[O2]n**Ex. 4: Compare Experiments 1 and 2**4 = 2mor m = 2**Ex. 4: Compare Experiments 2 and 4**3 = 3n or n = 1**Ex. 4 Find k**Rate = k[SO2]2[O2]1 • 1st order in [O2] • 2nd order in [SO2] • 3rd order overall • Can use any experiment to find k**Example 5: Method of Initial Rates**BrO3– + 5Br– + 6H+ 3Br2 + 3H2O**Ex. 5: Method of Initial Rates**Compare 1 and 2 Compare 2 and 3**Ex. 5: Method of Initial Rates**• First order in [BrO3–] and [Br–] • Second order in [H+] • Overall order = m + n + p = 1 + 1 + 2 = 4 • Rate Law is: Rate = k[BrO3–][Br–][H+]2 Compare 1 and 4**Your Turn!**Using the following experimental data, determine the order with respect to NO and O2 . A. 2, 0 B. 3,1 C. 2, 1 D. 1, 1**Concentration and Time**• Rate law tells us how speed of reaction varies with concentrations. • Sometimes want to know • Concentrations of reactants and products at given time during reaction • How long for the concentration of reactants to drop below some minimum optimal value • Need dependence of rate on time**Integrated Rate Law for First Order Reactions**• Corresponding to reactions • A products • Integrating we get • Rearranging gives • Equation of line y = mx + b**Plot ln[A]t (y axis) vs. t (x axis)**• Yields straight line • Indicative of first order kinetics • Slope = –k • Intercept = ln [A]0 • If we don't know already Slope = –k