1Chemistry 2C Lecture 20: May 17 th, )Introduction to Kinetics 2)Rate Laws 3)Orders and Reaction Constants 4)Initial Slopes 5)Zero th order reactions Lecture 20: Kinetics

2Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary Simple Reaction rate For the simple reaction we defined an instantaneous rate: Rate defined in terms of either gain of products or loss of reactants

3Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary Reaction rate Stoichiometrically more complicated reactions The rate must be expressed in an unambiguous manner! Both the ratios still express the rate of change for the reactant and product concentrations, however they are not equal anymore, because the reactant is used up twice as fast as the product appears.

4Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary For example: 2Fe 3+ + Sn 2+ -> 2Fe 2+ + Sn 4+ Fe 3+ disappears twice as fast as Sn 2+ disappears Fe 2+ appears twice as fast as Sn 4+ disappears The rate must be expressed in an unambiguous manner! Each of these equations represent the rate of reaction rate!!

5Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary 2Fe 3+ + Sn 2+ -> 2Fe 2+ + Sn 4+ Instantaneous a specific time Averaged Rate over a specific time interval Question: What is the averaged reaction rate for this reaction if the concentration of Fe 2+ is initially zero and then after 100s, is 0.05M ?

6Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary 2Fe 3+ + Sn 2+ -> 2Fe 2+ + Sn 4+ Question: What is the averaged reaction rate for this reaction if the concentration of Fe 2+ is initially zero and then after 100 s, is 0.05 M ? =0.05 M-0.00 M=0.05 M =100 s

7Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary Reaction rate In general the rate for a general reaction Is given by

8Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary 2A -> 3B Question: [A] drops from M to M in 2.50 min. What is the average rate for formation of B during this time interval ? Rate of formation of B is And in terms of A and t: = M/min

9Chemistry 2C Lecture 20: May 17 th, 2010 Measuring Rates How do we measure rates? 1)Need a timer 2)Method to monitor the concentration If a gas: can follow the pressure of collect in a buret and follow volume If colored, can follow in a visible regions using a spectrometer (Absorption is proportional to concentration) If charged, we can follow conductivity If slow, we can withdraw aliquots at different times and measure by titration If fast, we can use very fast laser pulses (~fs)

10Chemistry 2C Lecture 20: May 17 th, 2010 Using spectroscopy to identify Reaction kinetics The reaction of formic acid (HCO 2 H) and bromine (Br 2 ). As time passes (left to right), the red color of bromine disappears because Br2 is reduced to the colorless Br 2 ion. The concentration of Br 2 as a function of time, and thus the reaction rate, can be determined by measuring the intensity of the color.

11Chemistry 2C Lecture 20: May 17 th, 2010 Using spectroscopy to identify Reaction kinetics A sequence of photographs showing the progress of the reaction of hydrogen peroxide (H 2 O 2 ) and iodide ion (I – ). As time passes (left to right), the red color due to triiodide ion (I 3– ) increases in intensity.

12Chemistry 2C Lecture 20: May 17 th, 2010

13Chemistry 2C Lecture 20: May 17 th, N 2 O 5 (g) -> 4NO 2 (g) + O 2 (g) Time dependent Concentrations Increases four times faster than O 2 Conc. of N 2 O 5 decreasing

14Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary Reaction order The relation ship between the rate of a reaction and the concentrations of reactants and products is usually complex In most cases the rate can be expressed in a rate law of the following form: Where x and y are called the reaction order with respect to A and B, respectively. The sum of x and y is called the overall reaction order. The rate law and the reaction order can NOT be derived from the stoichiometric equation! There is in general NO connection between the stoichiometric coefficient and the reaction order! The reaction order can be zero, an integer or even a non-integer!

15Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Vocabulary Reaction order: An example NO! Experiment shows that: The reaction order and the rate law MUST be determined by experiment

16Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Non-Constant rates For the N 2 O 5 reaction, the slope rate is decreasing with time! Thus, the reaction rate is changing as the reaction proceeds. Instantaneous Rate: is the slope of the tangent at point t. Average Rate: is is over a specified interval of time  t.

17Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics Determination of the reaction Order and Rate Law Differential Method or I nitial rates method. We measure the reaction rate at several starting concentration of reactant. Using the general form of the rate law we can write: and The slope of a plot of log [A] vs. log the initial reaction rate gives us the reaction order

18Chemistry 2C Lecture 20: May 17 th, 2010 Determining reaction orders For example Rate=k [HgCl 2 ] m [C 2 O 4 2- ] n m and n must be determined experimentally. If m or n is 0, then reaction doesn’t depend on their concentration 2HgCl 2 (aq) + C 2 O > 2Cl - (aq) + 2CO 2 (g) + Hg 2 Cl 2 (s) Experiment[HgCl 2 ][C 2 O 4 2- ]Initial Rate (M/min) M0.15 M1.8 x M0.3 M7.1 x M0.3 M3.5 x 10 -5

19Chemistry 2C Lecture 20: May 17 th, 2010 Determining reaction orders Rate=k [HgCl 2 ] m [C 2 O 4 2- ] n Experiment[HgCl 2 ][C 2 O 4 2- ]Initial Rate (M/min) M0.15 M1.8 x M0.3 M7.1 x M0.3 M3.5 x By inspection: A)1 vs. 2: Double [C 2 O 4 2- ] with a constant [HgCl 2 ]: the rate increases by 4 Rate ~ [C 2 O 4 2- ] 2 B) 2 vs. 3: Halve [HgCl 2 ], with a constant [C 2 O 4 2- ]: the rate decreases by 2 Rate ~ [HgCl 2 ] 1 C) Combine to get Rate =[HgCl 2 ][C 2 O 4 2- ] 2 What is the order of reaction? 1 st order in

20Chemistry 2C Lecture 20: May 17 th, 2010 Determining reaction orders Rate=k [HgCl 2 ] 1 [C 2 O 4 2- ] 2 What is the order of reaction? 1 st order in HgCl 2 2 nd order in C 2 O rd order overall (1+2)

21Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Reactions of integral order Zero-Order Reactions ReactionRate Law k is the zero-order rate constant in M s -1 We want to be able to calculate the concentration of A or P at any time: We have to integrate the rate law! Integrated form of the zero order rate law

22Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Reactions of integral order Zero-Order Reactions In a zero-order reaction the rate is independent of the reactant concentration Reactions are not of zero-order under all conditions A common example are catalyzed reactions when the catalyst is saturated with substrate

23Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Reactions of integral order First-Order Reactions In a first-order reaction the rate depends only on the concentration of the reactant raised to the first power: k is the first-order rate constant in s -1 We get the integrated form of the rate law by integrating between t=0 and t=t Integrated form of first-order rate law

24Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Reactions of integral order First-Order Reactions First-order reactions are very common. Typical examples are: Radioactive decay of phosphorous Growth of E.Coli bacteria in culture Isomerization of Acetonitrile

25Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Reactions of integral order First-Order Reactions How long do I have to wait until the radioactivity of my samples has decayed enough to make it safe for disposal? How long does an antibiotic stay active in a patient? How much time does it take for the bacteria in my culture to double in cell mass? The rate describes the process of the reaction accurately and allows us to calculate the concentration of reactants or products at any given time. However, from a practical point of view we are often interested in questions like: The half-life of a reaction or process provides a convenient measure for this kind of question. The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease to half its original value.

26Chemistry 2C Lecture 20: May 17 th, 2010 Chemical Kinetics: Reactions of integral order First-Order Reactions The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease to half its original value. The half-life of a first-order reaction is independent of the original concentration! The half-life of a first-order reaction is constant! Measuring the half-life provides an easy way to determine k!