Rate Laws

Rate Laws Chemists conduct experiments to determine the rate law for a chemical reaction. A RATE LAW is a mathematical equation that shows how the reaction rate is related to the concentration of the reactants.

Rate = k [reactant A]m [reactant B]n Rate Constant (k) From collision theory, you know that one way to speed up a reaction is to increase reactant concentrations. For two reactants, a rate law has this form: Rate = k [reactant A]m [reactant B]n The term k is the rate constant it is unique to each reaction; changes with catalyst determined experimentally at specific temperature

Order of Reaction The exponents m and n indicate the order of each reactant in the reaction. For example, an exponent of 1 means the reaction is first order with respect to the given reactant. Higher order, greater effect on reaction rate. The sum of m + n gives the order of the overall reaction.

Reaction Order 2NO (g) + O2 (g)  2NO2 (g) Has rate equation: rate = k[NO]1[O2]1 Describe reaction Describe reactants

Reaction Order 2NO (g) + Cl2 (g)  2NOCl (g) Has rate equation: rate = k[NO]2[Cl2] Describe reaction Describe reactants

CH3CHO (g)  CH4 (g) + CO (g) Exp’t [CH3CHO ]0 Initial Rate (mole/l-s) 1 0.100 M 0.18 2 0.200 M 0.72 3 0.300 M 0.29 Exp't Data

Rate Law Using the data from the decomposition of acetaldehyde, CH3CHO, the order fo the reaction is determined in the following way: Rate = [CH3CHO]m To determine the value of m, write a ratio of the rate expressions for two different concentrations.

NO (g) + ½ Cl2 (g)  NOCl (g) Two Reactants NO (g) + ½ Cl2 (g)  NOCl (g) Exp’t [NO]0 (moles/L) [Cl2]0 Initial Rate (moles/L-s) 1 0.250 1.43 X 10-6 2 0.500 2.86 X 10-6 3 11.4 X 10-6

NH4+ (aq) + NO2- (aq)  N2 (g) + 2 H2O (l) Exp’t [NH4+]0 [NO2-]0 Initial Rate (M/s) 1 0.100 M 0.0050 M 1.35 X 10-7 2 0.010 M 2.70 X 10-7 3 0.200 M 5.40 X 10-7

Compare how the rate changes with concentration to find m, n Compare expt’s 1 & 2 [NH4+] is constant, doubled [NO2-] The rate doubled Compare expt’s 2 & 3 [NO2-] is constant, doubled [NH4+]

Or, take Ratio of Rates Rate2 = k[NH4+]n[NO2-]m = k[0.100]n[0.010]m 2.70 X 10-7 = [0.010]m 1.35 X 10-7 = [0.005]m 2.00 = (2.0)m m = 1

Write a Rate Law Refer to balanced equation for the rate-determining step. Write a rate constant, k. Write the formula of each reactant in brackets. Write the equation coefficient of each reactant as an exponent (only if a single event).

Example: Write a Rate Law Step 1: NO + Cl2  NOCl2 (fast) Step 2: NOCl2 + NO  2NOCl (slow) Determine the overall balanced equation. What is the intermediate? Which step is rate-determining? What is the rate law for the rate-determining step? What is the order of the reaction with respect to NO and Cl2?