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Rate Laws

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Determine the rate law and order of a chemical reaction from experimental data. Include: various reaction orders, rate versus concentration graphs. Additional KEY Terms Ratio

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A + B C Rate is proportional to changes in A and B Rate Law helps us calculate the rate of a REACTION not a reactant.

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where:krate constant [A]concentration of A xreaction order Rate = k[A] x **The rate constant (k) and the order ( x ) can only be determined experimentally** It is an expression that shows the quantitative effect of concentration changes on reaction rate.

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Rate = k[A] x The rate constant (k) is specific for each reaction at a specific temperature. Temperature is the only factor to affect the rate constant.

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Order Reaction

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The orders of a reaction ( x and y ) indicate how much each [reactant] affects the rate of a reaction. A + B Products Rate = k[A] x [B] y Each reactant can affect the rate differently

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First order reaction ( x = 1) The reaction rate is directly proportional to changes in reactant concentration. [A] is doubled - rate doubles 2 = 2 1 [A] is tripled - rate triples 3 = 3 1 Rate = k[A] 1 x

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Second order reaction (x = 2) The reaction rate is proportional to changes in reactant concentration squared. Doubling [A] - increase rate 4x 4 = 2 2 Tripling [A] - rate increase 9x 9 = 3 2 Rate = k[A] 2

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Zero order reaction ( x = 0) The rate does not depend on the [A]. Changing [A] does NOT change the rate. Third order reaction ( x = 3) The reaction rate is proportional to changes in reactant concentration cubed. **NOT included in the rate law if determined to be zero order** Rate = k[A] 3 Rate = k

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Overall order of reaction is the sum of the orders: x + y = overall reaction order Rate = k[A][B] 2 1 st order + 2 nd order = 3 rd order overall

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Calculating Rate Law

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Several ways to determine the rate law: differential rate law - uses calculus integrated rate law – uses graphing software initial rates method – uses data tables Determining rate law: Measure the effect of changes in concentration of one reactant on rate, while keeping the other reactant constant.

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Ratio Approach 8 = 2 4 2 = 1 2

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Using ratios: A + B products Rate 2 k [A] 2 x [B] 2 y Rate 1 k [A] 1 x [B] 1 y 18.0 α 0.3 x 0.2 y 2.0 0.1 0.2 x = second order 9.0 α [3] x 1 9.0 α [3] x Trial[A] (mol/L)[B] (mol/L)Initial Rate (mol/Ls) 10.100.202.0 20.300.2018.0 30.200.4016.0 Rate = k[A] x [B] y α =

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Using ratios: A + B products Rate 3 k [A] 3 x [B] 3 y Rate 1 k [A] 1 x [B] 1 y 16.0 α 0.2 2 0.4 y 2.0 0.1 0.2 y = first order 8.0 α [2] 2 [2] y 2.0 α [2] y Trial[A] (mol/L)[B] (mol/L)Initial Rate (mol/Ls) 10.100.202.0 20.300.2018.0 30.200.4016.0 Rate = k[A] 2 [B] Rate = k[A] x [B] y α = 2 8.0 α 4 [2] y y 1

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Using ratios: A + B products Rate 2 α [A] 2 x [B] 2 y Rate 1 [A] 1 x [B] 1 y 18.0 α 0.3 x 0.2 y 2.0 0.1 0.2 9.0 α [3] [1] y y = 0 or 1 or 2….. 2 9.0 α 9 [1] y 1 α [1] y Cant have multiple answers…pick new trials. Trial[A] (mol/L)[B] (mol/L)Initial Rate (mol/Ls) 10.100.202.0 20.300.2018.0 30.200.4016.0 Rate = k[A] 2 [B] You might pick bad trials y 2

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Common Sense Approach

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2x2x Rate 2 k [H 2 O 2 ] 2 x [HI] 2 y Rate 1 k [H 2 O 2 ] 1 x [HI] 1 y 0.0152 α 0.1 x 0.2 y 0.0076 0.1 0.1 x = first order 2.0 α 1 ּ [2] y 2.0 α [2] y = 1 2 1 rate = k[H 2 O 2 ] [HI] yx 11

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Tl [A] i mol/L [B] i mol/L Initial Rate (mol/Ls) 10.01000.02401.45 x 10 4 20.01000.01207.25 x 10 5 30.02000.04805.80 x 10 4 Rate = k[A] [B] Rate α [A] x [B] y Rate 3 α [A] 3 x [B] 3 y Rate 2 [A] 2 x [B] 2 y 5.8 -4 α 0.2 x 0.048 1 7.25 -5 0.1 0.012 x = first order 8.0 α [2] x [4] 1 8.0 α [2] x 4 2.0 α [2] x y 1 x

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3 A (g) + B (g) + 2 C (g) 2 D (g) + 3 E (g) a. Write the rate law for this reaction. b. Calculate the value of the rate constant (k). c. Calculate the rate for Trial #5. d. Calculate the concentration of A in Trial #6.

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a. Write the rate law for this reaction. rate = k[A][B] 2 1 20 Rate 2 k [A] 2 x [B] 2 y [C] 2 z Rate 1 k [A] 1 x [B] 2 y [C] 2 z = Rate 2 [A] 2 x Rate 1 [A] 1 x =

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b. Calculate the value of the rate constant (k). To find the value of k, we use that data from ANY trial. rate = k[A][B] 2 Dont include units for k.

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c. Calculate the rate for Trial #5. rate = k[A][B] 2 rate = (200)(0.50 mol/L)(0.40 mol/L) 2 rate = 16 mol/Ls

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d. Calculate the concentration of A in Trial #6. rate = k[A][B] 2

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Conclusion: Everything in the Rate Law must be determined experimentally: 1.Write a basic rate law with all reactants 2.Determine the order for each reactant (1, 2, 0) 3.Re-write the rate law with the determined order of reaction for each 4.Solve any problems

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CAN YOU / HAVE YOU? Determine the rate law and order of a chemical reaction from experimental data. Include: various reaction orders, rate versus concentration graphs. Additional KEY Terms Ratio

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