Question

Write the rate law for the reaction a \(\mathrm{A} \rightarrow b \mathrm{B}\) if the reaction is third order in \(\mathrm{A}\) . [B] is not part of the rate law.

Short answer

The rate law for the reaction a A → b B, where the reaction is third order in A, and B is not part of the rate law, is given by the equation: \( \text{Rate} = k[\mathrm{A}]^3 \).

Step-by-step solution

Identify the Reaction Order

The reaction is third order in A, which means the rate of the reaction depends on the concentration of A to the power of 3. The reaction does not depend on the concentration of B, so it is not included in the rate law.

Write the Rate Law

Given the reaction order (3) and the reactant (A), we can now write the rate law for the reaction using the following formula: Rate = k[A]^n Where: Rate is the rate of the reaction k is the rate constant [A] is the concentration of reactant A n is the reaction order (which is 3 in this case) Plugging in the values, we get: Rate = k[A]^3 So, the rate law for the given reaction is: Rate = k[A]^3

Key concepts

Reaction Order

Reaction order is a crucial concept in understanding how different reactants impact the rate at which a chemical reaction proceeds. It tells us how the concentration of a reactant affects the reaction rate. The reaction order is determined by the exponent on the concentration of the reactant in the rate law.
Let's say we have a reaction: a \(\mathrm{A} \rightarrow b \mathrm{B}\). If it is stated that the reaction is third order in \(\mathrm{A}\), it means that the rate of reaction is proportional to the concentration of \(\mathrm{A}\) raised to the power of three. This means if the concentration of \(\mathrm{A}\) doubles, the rate of the reaction increases by a factor of eight \((2^3)\). If \(\mathrm{B}\) does not appear in the rate law, it means the concentration of \(\mathrm{B}\) does not influence the rate of the reaction.
The importance of reaction order is that it helps predict how changes in concentration affect the speed of a reaction. Understanding this can also guide chemists in controlling the reactions for desired outcomes.

Rate Constant

The rate constant, represented by the symbol \(k\), is a fundamental aspect of the rate law in chemical kinetics. Its value provides insight into the speed of a reaction under specific conditions. The rate constant is a proportionality factor in the rate equation:

• Rate = \(k[A]^n\)

Here, \(k\) does not depend on the concentration of the reactants. Instead, it varies with temperature and other factors such as the presence of a catalyst. Adjustments in these factors alter the speed of the reaction without changing the reaction order.
An important point to remember is that each reaction has its own unique rate constant. When you compare reaction rates under different conditions or between different reactions, the rate constant serves as a standard for these comparisons. Knowing \(k\) allows scientists to predict how fast a reaction will proceed, which is crucial in both laboratory and industrial chemistry.

Chemical Kinetics

Chemical kinetics is the area of chemistry that studies the speed of chemical reactions and the factors affecting this speed. By understanding chemical kinetics, we can predict how a reaction will occur over time, which is vital for fields ranging from biochemistry to engineering.

• It involves studying the reaction rates.
• It helps in establishing reaction mechanisms, which are detailed pathways from reactants to products.
• Temperature, concentration, and pressure are among the factors that influence reaction rates.

When considering chemical kinetics, we often discuss concepts like the rate law, which provides a mathematical description of how the reaction rate depends on the concentration of reactants, and how reaction orders determine these relationships.
The study of kinetics not only assists in understanding the behavior of chemical reactions but also in optimizing conditions to produce desired products more efficiently. It provides a deeper understanding of both fundamental and applied chemistry.