Unit 2

Rate Law

The RATE LAW for a reaction describes the relationship between the rate (r) and the reactants’ concentrations raised to specific exponents. These exponents indicate how the rate depends on each reactant.

The slowest step in a reaction will have the largest activation energy

Rate law for a Reaction Mechanism

Given a reaction consisting of n elementary steps.
Your rate law is derived simply from the slowest of the n reactions.
so if one is $2N{o}_{2(g)}\rightleftharpoons N{O}_3+N{O}_g(slow)$ then the rate law would be $R=k[N{O}_2{]}^2$

WHEN YOU HAVE AN INTERMEDIARY PRODUCT IN THE RATE LIMITING REACTION

• Assuming the step producing the intermediary step is reversible, sub the reactants that produce the intermediary molecule.

Rate Law Equation

$$r=k[X_1{]}^{m_1}[X_2{]}^{m_2}\dots$$

or, using product notation:

$$r=\prod _{i=1}^{n}k[X_i{]}^{m_i}$$

The exponents ($m_i$) are called the orders of reaction with respect to each reactant, and their sum is the overall order of the reaction.

Note: For elementary reactions (reactions that occur in one step), the reaction orders are directly equal to the stoichiometric coefficients from the balanced equation.

Molecularity

The the number of reactant molecules (ions, atoms or molecules) involved in an elementary step or making up an activated complex.

• Unimolecular: steps involving 1 molecule
• Bimolecular: steps involving 2 molecules
• Termolecular: steps involving 3+ molecules

Lower Molecularity generally implies that the reaction will be faster

Additional Considerations

• Determining Orders: For non-elementary reactions, the orders are typically determined experimentally.
• Zero Order: A reactant can appear in the chemical equation yet have no effect on the rate (i.e., it is zero order with respect to that reactant).
• Simplification in Calculations: When writing out rate law problems, if terms cancel out, you can simplify the exponent calculations accordingly.