Rate Laws

Determine the rate law from experimental data. Explain the effect of concentration on reaction rates. Derive rate law form a reaction mechanism. Predict a reaction mechanism from rate law.

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.

It is an expression that shows the quantitative effect of concentration 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**

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

Reaction Order

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.

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

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 9 = 32

**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**

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

Calculating Rate Law

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.

Common Sense Approach

1 x y 1 rate = k[H2O2] [HI] rate = k[H2O2] [HI] Doesn’t agree with stoichiometry 1 H2O2 + 2 HI 2 H2O + I2

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.

1 2 a. Write the rate law for this reaction. rate = k[A][B]2

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.

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

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

Ratio Approach 8 = 2  4 2 = 1 2 

Can’t have multiple answers…start over. Using ratios: A + B → products 2 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 3x 9x Rate = k[A]x[B] y Rate α [A]x  [B]y Rate = k[A]x[B] y Rate2 α [A]2x  [B]2y 18.0 α 0.3 x  0.2 y 2.0 0.1  0.2 Rate1 [A]1x  [B]1y Can’t have multiple answers…start over. 9.0 α [3]  [1]y x 18.0 α [0.3]x  [0.2]y 2.0 [0.1]x  [0.2]y 9.0 α 9  [1]y 1 α [1]y y = 0 or 1 or 2…..

Using ratios: A + B → products Rate = k[A]2[B] 1 y Rate α [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 Rate = k[A]2[B] 1 y Rate α [A]x  [B]y Rate3 α [A]3x  [B]3y Rate1 [A]1x  [B]1y 8.0 α [2]2  [2]y 8.0 α 4  [2]y 2.0 α [2]y 16.0 α 0.2 2  0.4 y 2.0 0.1  0.2 y = first order

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 Rate2 [A]2x  [B]2y 2.0 α [2]x x = first order 5.8 -4 α 0.2 x  0.048 1 7.25 -5 0.1  0.012

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

CAN YOU? / HAVE YOU? Determine the rate law from experimental data. Explain the effect of concentration on reaction rates. Derive rate law form a reaction mechanism. Predict a reaction mechanism from rate law.