Question

The rate equation of a reaction is \(d x / d t=k[A]^{a}[B]^{b}\) for which the order of the reaction is (a) \(\mathrm{a}+b\) (b) \(a-b\) (c) a (d) \(b\)

Short answer

The order of reaction is \(a + b\), which matches with option (a).

Step-by-step solution

Understand the Reaction Order

The reaction order is defined as the sum of the exponents of the concentration terms in the rate equation. In this equation, the exponents are a and b.

Add the Exponents

Using the concept of reaction order, the sum of the exponents a and b is calculated. So, reaction order is \(a + b\).

Key concepts

Rate Equation

The rate equation, also known as the rate law, is a mathematical representation that links the rate of a chemical reaction to the concentration of the reactants. It takes on the form \( r = k[A]^m[B]^n \) where \( r \) is the rate of the reaction, \( k \) is the rate constant, and \( [A] \) and \( [B] \) are the concentrations of the reactants A and B, respectively. The exponents \( m \) and \( n \) represent the order with respect to each reactant.

This equation plays a crucial role in determining how a change in concentration affects the rate of the reaction. If the order is zero (\( m = 0 \) or \( n = 0 \) ), changes in the concentration of that reactant do not affect the rate. If the order is one (\( m = 1 \) or \( n = 1 \) ), the rate varies linearly with changes in concentration. For orders greater than one, the rate responds more than proportionally to changes in concentration.

It's essential to recognize that the reaction order can only be determined by experimental data and does not necessarily correspond to the stoichiometric coefficients in a balanced chemical equation. Understanding how to apply and interpret rate equations can help predict reaction behavior under different conditions, which is fundamental in chemical kinetics.

Chemical Kinetics

Chemical kinetics is the branch of physical chemistry that studies the rates at which chemical reactions occur and the factors that affect these rates. The heart of chemical kinetics is understanding how different variables such as temperature, pressure, concentration, and presence of catalysts influence the speed of a reaction.

In-depth knowledge of chemical kinetics can allow chemists and engineers to design processes that optimize reaction conditions for maximum efficiency. For example, by controlling the concentration of reactants based on the rate equation, one can achieve desired reaction rates.

Temperature is another critical factor; according to the Arrhenius equation, the higher the temperature, the faster the reaction rate, which is due to an increased number of molecules having sufficient energy to overcome the activation barrier. Chemical kinetics blends the theoretical and experimental aspects of chemistry to improve our capability to manipulate chemical reactions, crucial for everything from industrial manufacturing to pharmacology.

Reaction Mechanism

The reaction mechanism is a detailed description of the step-by-step sequence of elementary reactions or processes that lead to the overall chemical change. It provides a microscopic view of which bonds break and form and how the reactants transform into products during the course of a reaction.

An accurate reaction mechanism can tell us the rate-determining step, which is the slowest step within the mechanism and thus dictates the overall reaction rate. This information is immensely useful in chemical kinetics, as it allows researchers to understand not just the 'how fast' but also the 'why' and 'how' of reactant conversion.

Moreover, through studying mechanisms, chemists can design catalysts that speed up certain steps within a reaction, leading to more efficient processes. Each step in a mechanism has its own rate equation and order, and the overall reaction order is a composite of these steps, rather than derived from the balanced equation for the overall reaction. By piecing together these details, scientists can build up an accurate picture of the reaction's kinetics.