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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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**Rate is proportional to changes in A and B**

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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**It is an expression that shows the quantitative effect of concentration changes on reaction rate.**

Rate = k[A]x where: k rate constant [A] concentration of A x reaction order **The rate constant (k) and the order (x) can only be determined experimentally**

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**Temperature is the only factor to affect**

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

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Reaction Order

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**Each reactant can affect the rate differently**

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

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**Rate = k[A] 1 x First order reaction ( x = 1)**

The reaction rate is directly proportional to changes in reactant concentration. [A] is doubled - rate doubles 2 = 21 [A] is tripled - rate triples 3 = 31 x Rate = k[A] 1

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**Rate = k[A]2 Second order reaction (x = 2)**

The reaction rate is proportional to changes in reactant concentration squared. Rate = k[A]2 Doubling [A] - increase rate 4x 4 = 22 Tripling [A] - rate increase 9x = 32

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****NOT included in the rate law if determined**

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

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**Rate = k[A][B]2 1st order + 2nd order = 3rd order overall**

Overall order of reaction is the sum of the orders: x + y = overall reaction order 1st order + 2nd order = 3rd 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 =

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**= Using ratios: A + B → products same Rate = k[A]x[B] y**

Trial [A] (mol/L) [B] (mol/L) Initial Rate (mol/Ls) 1 0.10 0.20 2.0 2 0.30 18.0 3 0.40 16.0 same Rate = k[A]x[B] y Rate = k[A]x[B] y Rate2 k [A]2x [B]2y Rate1 k [A]1x [B]1y = α 9.0 α [3]x 1 9.0 α [3]x 18.0 α x 0.2 y 0.2 x = second order

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**= Using ratios: A + B → products 2 Rate = k[A]2[B] y 1**

Trial [A] (mol/L) [B] (mol/L) Initial Rate (mol/Ls) 1 0.10 0.20 2.0 2 0.30 18.0 3 0.40 16.0 Rate = k[A]2[B] y 1 Rate = k[A]x[B] y Rate3 k [A]3x [B]3y Rate1 k [A]1x [B]1y = α 8.0 α [2]2 [2]y 8.0 α [2]y 2.0 α [2]y 16.0 α 0.4 y 0.2 y = first order

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**Can’t have multiple answers…pick new trials.**

Using ratios: A + B → products 2 Trial [A] (mol/L) [B] (mol/L) Initial Rate (mol/Ls) 1 0.10 0.20 2.0 2 0.30 18.0 3 0.40 16.0 Rate = k[A]2[B] y You might pick bad trials Can’t have multiple answers…pick new trials. Rate2 α [A]2x [B]2y 9.0 α [3] [1]y 2 Rate [A]1x [B]1y 9.0 α 9 [1]y 1 α [1]y 18.0 α x 0.2 y 0.2 y = 0 or 1 or 2…..

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Common Sense Approach

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**x y 1 1 rate = k[H2O2] [HI] rate = k[H2O2] [HI] = 2x 2 same same**

Rate2 k [H2O2]2x [HI]2y Rate1 k [H2O2]1x [HI]1y 2.0 α 1 ּ [2]y = x y 1 1 rate = k[H2O2] [HI] 2.0 α [2]y α x 0.2 y 0.1 rate = k[H2O2] [HI] x = first order

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**x 1 y Rate = k[A] [B] 8.0 α [2]x [4]1 Rate α [A]x [B]y**

Tl [A]i mol/L [B]i Initial Rate (mol/Ls) 1 0.0100 0.0240 1.45 x 10−4 2 0.0120 7.25 x 10−5 3 0.0200 0.0480 5.80 x 10−4 x y Rate = k[A] [B] 1 8.0 α [2]x [4]1 Rate α [A]x [B]y 8.0 α [2]x 4 Rate3 α [A]3x [B]3y Rate [A]2x [B]2y 2.0 α [2]x x = first order α x 0.012

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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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**rate = k[A][B]2 = = 1 2 same same same same same same**

same same same same same same a. Write the rate law for this reaction. Rate2 k [A]2x [B]2y [C]2z Rate1 k [A]1x [B]2y [C]2z = Rate2 [A]2x Rate1 [A]1x = rate = k[A][B]2

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**rate = k[A][B]2 b. Calculate the value of the rate constant (k).**

To find the value of k, we use that data from ANY trial. Don’t include units for k.

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**rate = (200)(0.50 mol/L)(0.40 mol/L)2 rate = 16 mol/Ls**

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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AP Chemistry – Chemical Kinetics Black powder burns quickly, but the reaction is much slower than nitroglycerin detonating. 4 C 3 H 5 (NO 3 ) 3 → 12 CO.

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