Chemical Kinetics 2 PDF

MED-102 General Chemistry Chemical Kinetics 2  LOBs covered Discuss how the concentration changes with time for different reaction orders Calculate the concentration at a given time for different reaction orders Interpret kinetic data plots in order to identify react...

MED-102 General Chemistry Chemical Kinetics 2  LOBs covered Discuss how the concentration changes with time for different reaction orders Calculate the concentration at a given time for different reaction orders Interpret kinetic data plots in order to identify reaction order Determine the half-life from a plot of concentration versus time for a first-order reaction Explain how temperature affects the reaction rate Perform calculations related to temperature changes and the reaction rate Interpret Arrhenius plots to determine the activation energy Dependence of Concentration on Time There appears to be an exponential decrease of concentration as reaction time proceeds  Reaction Order and Time First-order reactions – Overall reaction order is 1 Second-order reactions – Overall reaction order is 2 Zeroth-order reactions – Constant rate that does not depend on concentration Dependence of Concentration on Time For the general first-order reaction A → Products Rate = k[A] −kt [A]t [A]t = [A]0 e ln = −kt [A]0 ln[A]t = ln[A]0 − kt = −kt + ln[A]0 y = mx + b (straight-line equation) y = ln[A]t m = slope = −k b = y -intercept = ln[A]0 First-order reaction plots ln[A]t = − kt + ln[A]0 y = mx + b  First-order reaction plots – Revision Slide ln[A]t = − kt + ln[A]0 y = mx + b If the reaction is first-order, a plot of [A] versus Time will not be linear, just like the plot on the left. A plot of ln[A] versus Time will produce a straight line if the reaction is first-order, just like the plot on the right. If the ln[A] versus Time plot is not linear, then it is not a first-order reaction. The slope of this straight line is equal to -k, so this gives us directly the value of the rate constant. The y-intercept (b) of this straight line will be equal to ln[A]0, from which we can obtain the initial concentration of the reactant as [A]0 = eb.  Half-Life Half-life is the time it takes for the reactant concentration to drop to one-half of its initial value [A]t 1 ln = −kt ln = − kt1/ 2 [A]0 2 ln 2 0.693 t1/ 2 = = k k This final equation shows very clearly that the half-life of a first-order reaction is constant throughout the reaction.  Half-life from graph This graph shows clearly that the half-life of a first-order reaction is constant throughout the reaction. Note we are plotting [A] versus Time.  Second-order reactions Rate law Rate = k[A]2 Integrated rate law 1 1 = kt +  At  A0 Second-order reaction plot 1 1 = kt +  At  A0 y = mx + b  Second-order reaction plot – Revision Slide 1 1 = kt +  At  A0 y = mx + b If the reaction is second-order, the [A] versus Time, and ln[A] versus Time plots will not give straight lines. The 1/[A] versus Time plot gives a straight line for a second-order reaction. The Slope of this straight line gives k directly, and the y-intercept is equal to 1/[A]0. Second-order reaction half-life 1 t1/2 = k  A 0  Second-order reaction half-life – Revision Slide 1 t1/2 = k  A 0 The half-life of a second-order reaction depends on concentration, and is not constant. Looking at the green plot above (second-order) we see from the red markings that the half-life of a second-order reaction continuously doubles. The first half-life is equal to the equation above, the second half-life is double the first one, and the third half-life is double the second half-life, etc.  Zeroth-order reactions These are relatively uncommon Rate = k[A] = k 0 Integrated rate law: At = −kt + A0 Half-life The half-life of a zeroth-order reaction continuously halves. Zeroth-order plots At = −kt + A0 y = mx + b  Zeroth-order plots – Revision Slide At = −kt + A0 y = mx + b The [A] versus Time plot gives a straight line, which means that we have a zero-order reaction. The ln[A] versus Time plot is not linear, which means that the reaction is not first-order. The 1/[A] versus Time plot is not linear, which means that the reaction is not second-order. For the zero-order plot, we see that Slope = k, and the y-intercept = [A]0.  Zeroth-order half-life For a zeroth-order plot, the half-life continuously halves. The second half-life is half of the first, and the third half-life is half of the second, etc.  Determining order of reaction Given [A]t versus Time plot If this is linear then zeroth-order If not linear then either first or second order Obtain ln[A]t and 1/[A]t Plot ln[A]t versus Time (first-order) – If this is linear, then the reaction is first-order Plot 1/[A]t versus Time (second-order) – If this is linear, then the reaction is second-order Exercise Exercise 5-Minute Break Reaction rates and temperature We know that chemical reactions occur faster at higher temperatures Milk spoils faster outside of a fridge Food cooks faster at a higher oven T Humans age faster in a warmer environment  Collision theory model Reactions take place because reactant molecules undergo successful collisions Successful collisions: – Minimum amount of energy (reactants must exceed activation energy) – Correct orientation (reactants must collide together with the appropriate orientation with respect to each other – see example below)  Reaction Energy Diagrams Consider both exergonic (G < 0) and endergonic (G > 0) cases Ea is called the Activation Energy. The higher it is, the slower the chemical reaction  Activation energy and Boltzmann distributions We have discussed Boltzmann distributions with regard to chemical kinetics in the Chemical Kinetics 1 presentation  Arrhenius Equation for the Rate Constant m n Rate = k[A] [B] Svante Arrhenius (1889) gave his expression for the rate constant − Ea / RT k = Ae What happens when T is varied? What happens when the activation energy is varied?  Uses of Arrhenius Equation Main use: experimental determination of activation energy Measure the Rate Constant, k, at different temperatures Ea ln k = ln A − RT  − Ea  1  ln k =     + ln A  R  T  y = mx + b We will make a plot of ln k on the y-axis and 1/T on the x-axis. This will give a straight line with Slope = -Ea/R and y-intercept = ln A. T must be in degrees Kelvin, and R = 8.314 J/mol K. Arrhenius Plot  − Ea  1  ln k =     + ln A  R  T  y = mx + b  Arrhenius Equation Another form: two k measurements at two different T  k2   − Ea   1 1  ln   =   −   k1   R   T2 T1   Catalysis A catalyst is a substance that speeds up a chemical reaction It is not consumed in the reaction It is fully recovered at the end of the reaction Does this mean that it does not participate?? – It has to participate! – It changes form during the reaction – It returns to its original form by the end of the reaction  Uses of catalysts Speed up industrial reactions More product in less time In industry time = money Car catalytic converters Biological catalysts = enzymes  How does a catalyst work? Alternative pathway Smaller Ea Increases frequency factor A in the Arrhenius equation  Types of catalysts Homogeneous catalyst – exists in the same phase as the reactants e.g. I-(aq) ions speed up decomposition of H2O2(aq) Heterogeneous catalyst – exists in a different phase than the reactants e.g. Iron metal catalyzes the production of ammonia from its elements (H2(g) and N2(g))  Summary for Revision-1 We consider zeroth-order, first-order and second-order reactions only. Equations have been provided for all three orders considered that enable us to calculate the concentration of the reactant during the reaction. If we are given a plot of [A] versus Time, if it is linear then we know that the reaction is zeroth-order. If this plot gives a curve, then it is not a zeroth-order reaction. We make a plot of ln[A] versus Time. If this plot gives a straight line, then the reaction is first-order. If it gives a curve, then the reaction is not first-order. We make a plot of 1/[A] versus Time. If this plot gives a straight line, then the reaction is second- order. If it gives a curve, then the reaction is not second-order. The half-life of a reaction is the time it takes to halve the concentration. The half-life of a first-order reaction is constant throughout the reaction. The half-life of a second-order reaction doubles continuously during the reaction. The half-life of a zeroth-order reaction halves continuously during the reaction. WATCH: https://www.youtube.com/watch?v=QfS1DSOw3Og  Summary for Revision-2 The rate of a chemical reaction increases when the temperature is increased. This observation is explained by using the Collision Theory model. This states that as the temperature increases, reactants gain kinetic energy and undergo more successful collisions, giving more product in less time. Collisions must have the correct orientation, and a minimum of energy (activation energy). Reaction energy diagrams can be made for both endergonic (non-spontaneous) and exergonic (spontaneous) reactions. The Arrhenius equation is a mathematical expression for the rate constant k. It involves the frequency factor A, the activation energy, and the Kelvin temperature. We can take the logarithm of the Arrhenius equation, giving an equation that can lead to a straight line plot. We make several measurements of the rate constant k at different temperatures. We plot ln k on the y-axis and 1/T on the x-axis, and from the slope of the straight line we can obtain the activation energy. Catalysts are substances that help speed up a chemical reaction. They take the reactants through a different pathway with lower activation energy. A catalyst is fully recovered at the end of the reaction. There are two types of catalysts, homogeneous and heterogenous.