Calculating Reaction Rates. Mechanism: Change in concentration For the following reaction: A(g) + B(g) → AB(g) The reaction rate can be determined by measuring how fast the concentration of A or B decreases, or by how fast the concentration of AB increases. Change in concentration Ave. Reaction rate = = Reaction time

Example: During the reaction of carbon monoxide with nitrogen dioxide a total of 0.010 mol of nitrogen monoxide were formed after 2.00 seconds (the volume of the container is 1.00 L). Calculate the reaction rate. CO(g) + NO2(g) → CO2(g) + NO(g) Ave. Reaction rate = = Initial [NO] = 0.00 M (mol/L) at t = 0.00 s Final [NO] = 0.010 M (mol/L) at t = 2.00 s Ave. Reaction rate = = = = 0.0050 M/s = 0.0050 mol/(L.s)

Experimental data for H2 + Cl2 → 2 HCl Practice Problems: Use the data in the following table to calculate the average reaction rates: 1. Calculate the average reaction rates: a) Expressed in moles H2 consumed per liter per second. b) Expressed in moles Cl2 consumed per liter per second. c) Expressed in moles HCl produced per liter per second. Experimental data for H2 + Cl2 → 2 HCl Time (s) [H2] (M) [Cl2] (M) [HCl] (M) 0.00 0.030 0.050 0.000 4.00 0.020 0.040 - 0.0025 mol/(L.s) - 0.0025 mol/(L.s) 0.0050 mol/(L.s)

Reaction Rate Laws: The equation that expresses the mathematical relationship between the rate of a chemical reaction and the concentration of reactants is called a Rate Law. For example, for the reaction A → B the rate law is expressed as: Rate = k [A] k is the specific rate constant which depend on the temperature & is unique for each reaction. The k values are determined experimentally.

Rate = k [A] A large value of k means that A reacts rapidly to form B. Reaction Order: For a reactant defines how the rate is affected by the concentration of that reactant. For example in the equation above [A] means the same as [A]1 . For reactant A the exponent 1 is called the reaction order. In other words, the reaction is the first order in A.

For mA + nB → products The general rate law for such reaction is: Rate = k [A]m [B]n m & n are the reaction orders for A & B respectively. The reaction is the m order in A and n order in B The overall order for the reaction is m + n. The overall reaction order of a chemical reaction is the sum of the orders for the individual reactants in the rate law.

Example: 2NO(g) + 2H2(g) → N2(g) + 2H2O(g) The rate law, determined experimentally is: Rate= k [NO]2 [H2] The reaction is described as second order in NO, first order in H2 and third order overall. The rate depend on the concentration of the reactants as follows: If [NO] doubles the rate quadruples. If [H2] doubles the rate doubles

NO2(g) + CO(g) → NO(g) + CO2(g) The rate law, determined experimentally is: Rate= k [NO2]2 The experimental rate law does not match our predicted rate law, so the reaction must involve more than one step. Reaction mechanism: Describes the sequence of elementary steps that occur to go from reactants to products.

1) 2 NO2(g) → NO(g) + NO3(g) Elementary step (slow) Reaction mechanism: 1) 2 NO2(g) → NO(g) + NO3(g) Elementary step (slow) 2) NO3(g) + CO (g) → NO2(g) + CO2(g) Elementary step (fast) NO2(g) + CO (g) → NO(g) + CO2(g) Overall reaction NO3​(g) is a reaction intermediate (it is produced in one step and consumed in later step). The slowest step in a reaction mechanism is called the rate determining or rate limiting step. Second order in NO2 That’s why the rate law for this reaction is: & Rate= k [NO2]2 Second order overall

Energy Diagram: Slowest step Fastest step ∆H Exothermic reaction

Practice: Consider the proposed reaction mechanism below: 2 NO → N2O2 Elementary step (fast) N2O2 + H2 → N2O + H2O Elementary step (slow) N2 + H2 → N2 + H2O Elementary step (fast) Based on this information, try answering the following questions. 1. What is the overall reaction? 2. What is the rate determining step? 3. What are the intermediates in this reaction? 4. What is its rate law expression? 2 NO + 2H2 → N2O + 2H2O The second step N2O2 Rate= k [NO]2 [H2] (Because N2O2 is not in the overall reaction & it was formed from 2 NO)