5.4.A.1 Rate Law of an Elementary Reaction and Stoichiometry:

1. Elementary Reactions and Molecularity:

Molecularity of a reaction is the number of reacting molecules (or ions) which come together and react in an elementary step. It is directly related to the rate law of the reaction, which is expressed in terms of the concentration of the reactants with the rate at which the reaction proceeds. Please see below:

i. Unimolecular Reaction (Molecularity = 1):
– Example: A → products
– In a unimolecular reaction, one reactant molecule decomposes or rearranges to produce products.
– Rate law: The reaction rate is directly proportional to the concentration of one reactant.
– Rate = k[A]
– Where k is the rate constant, and [A] is the concentration of reactant A.

ii. Bimolecular Reaction (Molecularity = 2):
– Example: A + B → products
– In a bimolecular reaction, two molecules (can be same or different) approach each other and react.
– Rate law: Rate of the reaction is proportional to the product of the concentration of both reactants.
– Rate = k[A][B]
– Where [A] and [B] are concentrations of reactant A and B, respectively.

iii. Termolecular Reaction (Molecularity = 3):
– Example: A + B + C → products
– Three molecules come together in one step in a termolecular reaction.
– These reactions are rare because the possibility of three molecules meeting simultaneously is very low.
– Rate law: The rate of the reaction is equal to the product of the concentration of all three reactants.
– Rate = k[A][B][C]

iv. Key Points:
– The molecularity of a step in a reaction is represented by the reaction stoichiometry in that single step of the reaction, not by the overall reaction.
– Order of the reaction relates to the rate law and depends on how the rate law is derived, while molecularity is merely the number of molecules in the step.

In general, molecularity of a reaction directly influences the rate law:
– Unimolecular → Rate depends on the concentration of 1 reactant.
– Bimolecular → Rate depends on the concentration of 2 reactants.
– Termolecular → Rate depends on the concentration of 3 reactants.

2. Collision Theory:

Collision theory explains the role of molecular collisions in affecting reaction rate. Reactant molecules must collide with each other in a way that they will be capable of breaking and forming new bonds for a reaction to occur. The rate of a reaction depends on the frequency, energy, and orientation of these collisions. This is how collisions affect reaction rates:

 i. Collision Frequency:
– The rate of reaction will be greater if the rate of collision between reactant molecules is higher. If more often, then the likelihood of successful reaction is greater.
– Collision frequency is determined by:
– Concentration of reactants: With higher concentrations of reactants, there are more molecules per unit volume, thus opportunities for collision become greater.
– Temperature: An increase in temperature makes molecules move faster, and this leads to an increase in the number of collisions.

ii. Collision Energy (Activation Energy):
– Not all collisions lead to a reaction; only those with sufficient energy can overcome the activation energy barrier. The activation energy (Ea) is the minimum energy that molecules need to collide for a reaction to take place.
– When the colliding molecules do not have enough energy, they will simply bounce off each other without reacting.
– With increasing temperature, the kinetic energy of the molecules also increases, hence more molecules gain enough energy to break through the activation energy.

iii. Collision Orientation:
– Even if molecules are coming in with the right amount of energy, they need to have the correct orientation as well for the reaction to occur.
– Successful collisions occur when the reacting molecules move in a way that their atoms or functional groups can approach and form new bonds.
– Randomly oriented molecules may possess enough energy for a collision but do not react because they cannot form or break necessary bonds.

iv. Rate of Reaction:
– Rate = Z * f where:
– Z is collision frequency (how often molecules collide with one another).
– f is fraction of effective collisions, in terms of energy and orientation.
– The rate of the reaction is therefore dependent on how often molecules collide and on how likely such collisions are to result in a chemical reaction.

3. Stoichiometry and Rate Law:

The rate law formulates a reaction rate as a function of concentrations of reactants raised to some power. The relationship between the rate law and the stoichiometric coefficients is based on whether the reaction is elementary or complex:

i. Elementary Reactions: The exponents of the rate law are identical to the stoichiometric coefficients.
– Unimolecular (A → products): Rate = k[A]
– Bimolecular (A + B → products): Rate = k[A][B]
– Termolecular (A + 2B → products): Rate = k[A][B]²

2. Complex Reactions: Experimentally, the rate law needs to be found out, as it need not always bear a direct proportion to the stoichiometric coefficients.

Experimental methods such as the initial rates method are utilized in order to determine the order with regard to each of the reactants for complex reactions.