Rate and Order of Reaction Quiz

Rate and Order of Reaction

Introduction

The reaction rate is the velocity at which a reaction converts reactants into products. Reactions can be classified based on the order of reaction, which is the number of reacting species whose concentration determines the reaction rate. The most common orders of reaction are zero, first, and second order.

Zero Order Reaction

A zero order reaction is characterized by a reaction rate that is independent of the concentration of any of the reactants. The rate of a zero order reaction is described by the rate law:

[ \text{rate} = k ]

where (k) is the rate constant. The rate constant is independent of the reactant concentrations but does vary with temperature.

First Order Reaction

A first order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration. The differential rate law for a first-order reaction is:

[ \text{rate} = - \frac{d[A]}{dt} = k[A] ]

where [A] is the concentration of the reactant, and (k) is the rate constant. The integral form of the rate law is:

[ [A] = [A]_{\text{o}}e^{- kt} ]

where [A] is the concentration at time (t), [A]o is the concentration at time 0, and (k) is the first-order rate constant. The half-life of a first-order reaction is independent of the initial concentration of reactant.

Second Order Reaction

A second order reaction is a reaction that proceeds at a rate that depends on the concentrations of two reactants. The differential rate law for a second-order reaction is:

[ \text{rate} = - \frac{d[A]}{dt} = k[A][B] ]

where [A] and [B] are the concentrations of the reactants, and (k) is the rate constant. The integral form of the rate law is:

[ [A] = [A]_{\text{o}} - k[B][A]t ]

where [A] is the concentration at time (t), [A]o is the concentration at time 0, [B] is the concentration of the second reactant, and (k) is the second-order rate constant.

Rate Laws

Rate laws, also known as differential rate laws or rate equations, are mathematical expressions that describe the relationship between the rate of a reaction and the concentrations of its reactants. The rate law for a reaction is written as:

[ \text{rate} = k[A]^{m}[B]^{n} ]

where [A] and [B] are the concentrations of the reactants, (k) is the rate constant, and (m) and (n) are the reaction orders with respect to reactants A and B, respectively. The overall reaction order is simply the sum of the orders for each reactant.

Writing Rate Laws from Reaction Orders

To write a rate law from reaction orders, the following steps can be followed:

1. Identify the reactants and their balanced reactions.
2. Determine the reaction orders of each reactant by observing how the rate of the reaction changes with changes in their concentrations.
3. Write the rate law using the reaction orders and the rate constant.

Determining a Rate Law from Initial Rates

The method of initial rates is commonly used to determine rate laws. In this approach, reaction rates are measured for multiple experimental trials carried out using different initial reactant concentrations. Comparing the measured rates permits determination of the reaction orders and, subsequently, the rate constant, which together are used to formulate a rate law.

Conclusion

Understanding the rate and order of a reaction is crucial in chemical kinetics. By studying the rate laws and applying the appropriate experimental methods, researchers can determine the reaction orders and rate constants, which provide valuable insights into the reaction mechanism and help optimize reaction conditions.