Entry Task: Nov 5th Wednesday Sign off on Expression and Law ws Grab Integrated Law notes by door MAYHAN

Agenda: Go through Expression and Law ws Walkthrough NOTES Ch. 14 sec 3 – The change in concentration with time (integrated – graph) Integrated Rate Law ws MAYHAN

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A decreases twice as fast 1. Given the reaction: 2A (g) --->B (g) + C (g) a. Express the rate of reaction in terms of the change in concentration of each of the reactants and products. Δ[B] Δt 1 Δ[C] Δt - 1 2 Δ[A] Δt 1 = = b. When [C] is increasing at 2.0 mol.L–1.s–1 , how fast is [A] decreasing? SHOW WORK! Δ[A] Δt 1 Δ[2.0] Δt - 1 2 = 2 1 Δ[2.0] Δt Δ[A] Δt 4 mol.L-1s-1 = = A decreases twice as fast MAYHAN

Δ[F] Δt 1 2 Δ[G] Δt Δ[H] Δt Δ[D] Δt -1 3 Δ[E] Δt -1 1 1 - 1 2 = = = = 2. Given the reaction: 2D (g) + 3E (g) + F (g) ----> 2G (g) + H (g) a. Express the rate of reaction in terms of the change in concentration of each of the reactants and products. Δ[F] Δt 1 2 Δ[G] Δt Δ[H] Δt Δ[D] Δt -1 3 Δ[E] Δt -1 1 1 - 1 2 = = = = b. When [E] is decreasing at 0.10 mol.L–1.s–1, how fast is [G] increasing? SHOW WORK! - 1 3 Δ[0.10] Δt 1 2 Δ[G] Δt = 2 3 Δ[0.10] Δt Δ[G] Δt 0.067 mol.L-1s-1 = = 2/3 as fast MAYHAN

Double the concentration of H3PO4 or I- 3. For the reaction 3 ClO – (aq) → ClO3 – (aq) + 2 Cl – (aq) doubling the concentration of ClO – quadruples the initial rate of formation of ClO3-. What is the rate law for the reaction? Rate = k [ClO –]2 4. The reaction C6H5N2Cl (aq) + H2O (l) → C6H5OH (aq) + N2 (g) + HCl (aq) is first order in C6H5N2Cl and zero order in H2O. What is the rate law for this reaction? Rate = k [C6H5N2Cl] 5. For the reaction H3PO4 (aq) + 3I – (aq) + 2 H+ (aq) → H3PO3 (aq) + I3- (aq) + H2O (l) the rate law under certain conditions is given by Rate = k[H3PO4][I -][H+]2. What method(s) could be used if you want to double the reaction rate? Double the concentration of H3PO4 or I- MAYHAN

NO is a second order Cl2 is 1st order Rate = k [NO]2[Cl2] 6. What is the overall order of reaction for each of the following? a) Rate = k[NO2]2 _______ b) Rate = k _______ c) Rate = k[Br2] _______ d) Rate = k[NO]2[O2] ______ 2nd Zero 1st 3rd 7. For the reaction 2 NO (g) + Cl2 (g) → 2 NOCl (g) If the concentration of NO is tripled, the rate of the reaction increases by a factor of nine. If the concentration of Cl2 is cut in half, the rate of the reaction is decreased to half the original rate. Find the order of reaction for each reactant and write the rate law for the reaction. NO is a second order Cl2 is 1st order Rate = k [NO]2[Cl2] MAYHAN

Rate would increase by a factor of 9 8. In the decomposition of ammonia on a platinum surface at 856°C , 2 NH3 (g) → N2 (g) + 3 H2 (g) , changing the concentration of NH3 has no effect on the rate. Write the rate law for the reaction. Rate = k 9. A reaction has the experimental rate law of Rate = k[A]2. a) What happens to the rate if the concentration of A is tripled? b) What happens to the rate if the concentration if A is reduced to one third the initial concentration? Rate = k [3]2 Rate would increase by a factor of 9 Rate = k [1/3 ]2 Rate would decrease by a factor of 1/9 MAYHAN

A would be 1st order and B is zero order 10. For the reaction 2 A + B → C + D, if the concentration of A is doubled, the reaction rate doubles. If the concentration of B is halved, there is no change in the reaction rate. Determine the order of reaction with respect to each reactant and the overall order of reaction. Write the rate law for the reaction. A would be 1st order and B is zero order Rate = k [A] MAYHAN

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I can… Graph the relationship of time with amount of reactant concentrations and integrate this with rates of reactions. Determine the graphical relationship between time and the rate order. MAYHAN

Equation Sheet Under thermochemistry and kinetics 1st order 2nd order MAYHAN

Two Types of Rate Laws Differential- Data table contains RATE AND CONCENTRATION DATA. Uses “table logic” or algebra to find the order of reaction and rate law Integrated- Data table contains TIME AND CONCENTRATION DATA. Uses graphical methods to determine the order of the given reactant. K=slope of best fit line found through linear regressions MAYHAN

Integrated Rate Law Can be used when we want to know how long a reaction has to proceed to reach a predetermined concentration of some reagent MAYHAN

Graphing Integrated Rate Law Time is always on x axis Plot concentration on y axis of 1st graph Plot ln [A] on the y axis of the second graph Plot 1/[A] on the y axis of third graph You are in search of a linear graph MAYHAN

Zero order Reactions- Use A  B as an example. What happens when we double [A], what happens to the rate of reaction that is zero order? So does the concentration affect rate? Y/N____ What would the rate law be for a zero order? The rate of reaction does not change No Rate = k MAYHAN

Sketch a graph with rate on Y and concentration on X axis- Label axis!! As concentration increases, the rate of reaction remains the same. MAYHAN

Sketch a graph with concentration on Y and time on X axis- Label axis!! Integrated Rate laws We look for straight lines. This provides a “clean” visual about the relationship of concentration and time. MAYHAN

Sketch a graph with concentration on Y and time on X axis- Label axis!! So when we plot our data table and get a negative straight line it is ____________order! Slope is negative (-k) Zero MAYHAN

First Order Reactions AB in a reaction. ① Write the rate expression for reactant A. (sec. 1 stuff) Rate = - ∆[A] ∆t MAYHAN

14.3- The Change of Concentration with Time ② Write the rate law for reactant A. (sec 2 stuff) Rate = k[A]1 MAYHAN

14.3- The Change of Concentration with Time Describe a First Order reaction. Double the concentration the reaction doubles. Low amount of reactant = low rate of reaction MAYHAN

Sketch a graph with rate on Y and concentration on X axis- Label axis!! As we double our concentration , the rate doubles. It’s a direct relationship. MAYHAN

Sketch a graph with concentration on Y and time on X axis- Label axis!! Integrated Rate laws We look for straight lines. This provides a “clean” visual about the relationship of concentration and time. This does not provide a straight line MAYHAN

Natural log x Concentration Sketch a graph with concentration on Y and time on X axis- Label axis!! Integrated Rate laws We can manipulate the data to provide a straight line plot. Change how we plot concentration. Natural log x Concentration In [A] Slope is negative (-k) MAYHAN

14.3- The Change of Concentration with Time Take equations ① and ② and smash them together. Rate = - ∆[A] ∆t = k[A] MAYHAN

14.3- The Change of Concentration with Time How do you use this equation to solve for concentration? Using calculus to integrate the rate law for a first-order process gives us ln [A]t [A]0 = −kt Where [A]0 is the initial concentration of A. [A]t is the concentration of A at some time, t, during the course of the reaction. MAYHAN

Integrated Rate Laws Manipulating this equation produces… ln [A]t [A]0 = −kt ln [A]t − ln [A]0 = − kt ln [A]t = − kt + ln [A]0 …which is in the form y = mx + b MAYHAN

First-Order Processes Relate this equation to the slope. ln [A]t = -kt + ln [A]0 Therefore, if a reaction is first-order, a plot of ln [A] vs. t will yield a straight line, and the slope of the line will be -k. MAYHAN

Sample Exercise 14.5 Using the Integrated First-Order Rate Law The decomposition of a certain insecticide in water at 12 C follows first-order kinetics with a rate constant of 1.45 yr1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0  107 g/cm3. Assume that the average temperature of the lake is 12 ºC. (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the insecticide concentration to decrease to 3.0  10–7 g/cm3? PLUG & CHUG k = 1.45 yr-1 ln [A]0 = [5.0 x 10-7g/cm3] SET IT UP ln [insecticide]t-1yr = [X] t = 1 year ln [insectacide]t-1yr = -(1.45 yr-1) (1 year) + ln [5.0 x 10-7g/cm3] ln[insecticide]t -1 yr = 1.45 + (14.51) ln[insecticide]t - 1 yr = 15.96 Get rid of ln by ex on both sides [insecticide]t = 1 yr = e15.96 = 1.2  107 g/cm3 MAYHAN

Sample Exercise 14.5 Using the Integrated First-Order Rate Law The decomposition of a certain insecticide in water at 12 C follows first-order kinetics with a rate constant of 1.45 yr1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0  107 g/cm3. Assume that the average temperature of the lake is 12 ºC. (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the insecticide concentration to decrease to 3.0  10–7 g/cm3? PLUG & CHUG k = 1.45 yr-1 ln [A]0 = [5.0 x 10-7g/cm3] SET IT UP ln [3.0 10-7]t = ln [3.0 10-7]t = -(1.45 yr-1) X + ln [5.0 x 10-7g/cm3] t = X Get X by itself- move to left side -15.02 - -14.51 ln [3.0 10-7]t - ln [5.0 x 10-7g/cm3] =X =0.35 years -1.45 yr -1.45 yr-1 MAYHAN

Sample Exercise 14.5 Using the Integrated First-Order Rate Law Continued Practice Exercise The decomposition of dimethyl ether, (CH3)2O, at 510 ºC is a first-order process with a rate constant of 6.8  10–4 s–1: (CH3)2O(g)  CH4(g) + H2(g) + CO(g) If the initial pressure of (CH3)2O is 135 torr, what is its pressure after 1420 s? k = 6.8 x 10-4-s-1 ln [A]0 = [135 torr] SET IT UP ln [X torr]t = [X] t = 1420 s ln [X torr]t = -(6.8 x 10-4) (1420 s) + ln [135 torr] ln[torr]t = 0.9656 + (4.91) ln[torr]t = 3.94 Get rid of ln by ex on both sides [torr]t = e3.94= 51.4 torr MAYHAN

14.3- The Change of Concentration with Time Describe a second-order reaction. When you double the reactant the rate increases by a power of 2, to quadruple the rate MAYHAN

Sketch a graph with rate on Y and concentration on X axis- Label axis!! The relationship is more pronounced. Double your concentration and the rate goes up by the power of 2. Hence- second order. MAYHAN

Sketch a graph with concentration on Y and time on X axis- Label axis!! Integrated Rate laws We look for straight lines. This provides a “clean” visual about the relationship of concentration and time. This does not provide a straight line MAYHAN

Sketch a graph with concentration on Y and time on X axis- Label axis!! Integrated Rate laws We can manipulate the data to provide a straight line plot. Change how we plot concentration. 1 divided by Concentration 1/[A] And the slope is positive (k) MAYHAN

Second-Order Processes Provide the second order equation. Similarly, integrating the rate law for a process that is second-order in reactant A, we get 1 [A]t = kt + [A]0 also in the form y = mx + b MAYHAN

Second-Order Processes 1 [A]t = kt + [A]0 So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line, and the slope of that line is k. MAYHAN

14.3- The Change of Concentration with Time What does second order reactions depend on? A second order reaction is one whose rate depends on the initial reactant concentration MAYHAN

Second-Order Processes The decomposition of NO2 at 300°C is described by the equation NO2 (g) NO (g) + 1/2 O2 (g) and yields data comparable to this: Time (s) [NO2], M 0.0 0.01000 50.0 0.00787 100.0 0.00649 200.0 0.00481 300.0 0.00380 MAYHAN

Second-Order Processes Graphing ln [NO2] vs. t yields: The plot is not a straight line, so the process is not first-order in [A]. Time (s) [NO2], M ln [NO2] 0.0 0.01000 −4.610 50.0 0.00787 −4.845 100.0 0.00649 −5.038 200.0 0.00481 −5.337 300.0 0.00380 −5.573 MAYHAN

Second-Order Processes Graphing ln 1/[NO2] vs. t, however, gives this plot. Because this is a straight line, the process is second-order in [A]. Time (s) [NO2], M 1/[NO2] 0.0 0.01000 100 50.0 0.00787 127 100.0 0.00649 154 200.0 0.00481 208 300.0 0.00380 263 MAYHAN

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Practice with graphs- After creating regression graphs of various reactions, provide the rate order for each graph. What order is this reaction and what formula would I use to calculate various times/concentrations? First order and MAYHAN

Practice with graphs- After creating regression graphs of various reactions, provide the rate order for each graph. What order is this reaction and what formula would I use to calculate various times/concentrations? Zero order and MAYHAN

Practice with graphs- After creating regression graphs of various reactions, provide the rate order for each graph. What order is this reaction and what formula would I use to calculate various times/concentrations? Second order and MAYHAN

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