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.

2A B The rate is directly proportional to reactant A The [A] determines the reaction speed. Rate Law helps us calculate the rate of a reaction. It is an expression that shows the quantitative effect of concentration on reaction rate.

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. Rate law is represented by the equation:

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.

Order Reaction

The order of a reaction ( x ) indicates how much each [reactant] affects the rate of a reaction. First order reaction ( x = 1) The reaction rate is directly proportional to changes in reactant concentration. Concentration of A is doubled - rate doubles. Concentration of A is tripled - rate triples. Rate = k[A] 1

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

Zero order reaction ( x = 0) The rate does not depend on the [A]. A change in [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

A + B Products Rate = k[A] x [B] y The rate may depend on both [A] and [B]. (Each reactant can affect the rate differently) Total order of reaction is the sum of the orders: x A + y B = overall reaction order

Calculating Rate Law

Several ways to determine the rate law: differential rate law - uses calculus integrated rate law - uses [ ] vs time graphs initial rates method

Determining rate law: Measure the effect of changes in concentration of one reactant on rate, while keeping the other reactant constant. H 2 O HI 2 H 2 O + I 2 Rate Law is related to stoichiometry. BUT… Usually cannot be determined from overall reaction.

rate = k[H 2 O 2 ] [HI] yx 11 1 H 2 O HI 2 H 2 O + I 2 2x Doesn’t agree with stoichiometry

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.

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

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 Don’t include units for k.

c. Calculate the rate for Trial #5. rate = k[A][B] 2 rate = (200)(0.50 mol/L)(0.40 mol/L) 2 rate = 16.0 mol/Ls

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

Using ratios: A + B → products Trial[A] (mol/L)[B] (mol/L)Initial Rate (mol/Ls) Rate = k[A] x [B] y Rate α [A] x  [B] y 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] x  [0.2] y 18.0 α 0.3 x  0.2 y  α [3]   [1] y y = 0 or 1 3x9x x 9.0 α 9   [1] y 1 α [1] y 22 You can’t have 2 answers…start over.

Using ratios: A + B → products Trial[A] (mol/L)[B] (mol/L)Initial Rate (mol/Ls) Rate = k[A] 2 [B] Rate α [A] x  [B] y Rate 3 α [A] 3 x  [B] 3 y Rate 1 [A] 1 x  [B] 1 y 16.0 α  0.4 y  0.2 y = first order 8.0 α [2] 2  [2] y 8.0 α 4  [2] y 2.0 α [2] y y1

Tl [A] i mol/L [B] i mol/L Initial Rate (mol/Ls) x 10 − x 10 − 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 α 0.2 x   x = first order 8.0 α [2] x  [4] α [2] x  α [2] x y 1 x

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