Problem 35 - A Complete Resource Book in Chemistry for JEE Main

Question

For a chemical reaction which can never be a fractional number. (a) order (b) half-life (c) molecularity (d) rate constant

Step-by-Step Solution

Answer

Molecularity can never be a fractional number.

Step 1: Understanding the Options

First, we need to understand what each term means in the context of chemical reactions. The 'order' of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. 'Half-life' is the time required for half the reactant to be consumed. 'Molecularity' refers to the number of molecules that come together to react, and 'rate constant' is the proportionality constant in the rate law.

Step 2: Identifying the Key Characteristic

We need to identify which characteristic can never be a fractional number. Reaction order and rate constant can be fractional in many reactions. Half-life is a measurable time duration, which can be fractional. However, molecularity refers to the number of reacting species and must represent an actual, countable number of molecules.

Step 3: Determining the Correct Answer

Since molecularity involves a count of molecules that collide to react, it is always a whole number. It cannot be fractional because we can't have a fraction of a molecule participating in a reaction.

Key Concepts

Chemical Reaction Order

The order of a chemical reaction is a key concept in understanding how different factors affect the rate of the reaction. This term refers to the sum of the powers to which the concentration terms are raised in the rate law equation. In simple terms, it tells us how the concentration of a reactant influences the speed of the reaction.
Let's assume a rate law for a reaction is expressed as \( \text{Rate} = k[A]^m[B]^n \),where:

• \(k\) is the rate constant,
• \([A]\) and \([B]\) are the concentrations of reactants,
• \(m\) and \(n\) are the orders with respect to each reactant.

The overall reaction order is then \(m + n\). Reaction orders can be zero, positive, or negative, and they are not necessarily related to the stoichiometric coefficients of the balanced equation. This means the reaction order could even be a fractional or zero, as it is based on experimental observations rather than theoretical prediction. Understanding reaction order helps predict how changes to the concentration of reactants will affect the rate of reaction, making it a crucial aspect of chemical kinetics.

Half-Life in Reactions

In kinetics, the half-life of a reaction is a valuable concept, particularly when dealing with first-order reactions. It is defined as the time required for the concentration of a reactant to decrease to half of its initial value. The half-life is represented by \(t_{1/2}\) and varies depending on the order of the reaction.
For first-order reactions, the half-life is independent of the initial concentration and is given by the equation:\[ t_{1/2} = \frac{0.693}{k} \]where:- \(k\) is the rate constant.
This property makes predicting the time course of reactions easier, as you know exactly when the reactant concentration will reach half its starting amount. It remains constant throughout the reaction in first-order kinetics. In contrast, for reactions of higher orders, half-life depends on the initial concentration, which makes the calculation a bit more complex.
Understanding the half-life is crucial for applications in both chemical manufacturing and natural processes, such as radioactive decay and pharmacokinetics.

Rate Constant in Kinetics

The rate constant is an integral component of the rate law in kinetics and is symbolized as \(k\). It provides a proportional measure that helps us understand the speed of a chemical reaction under given conditions. The value of \(k\) can significantly vary, as it is affected by factors like temperature, the presence of catalysts, and pressure.
In the rate equation \( \text{Rate} = k[A]^m[B]^n \), the rate constant \(k\) links the rate of reaction with the concentration of the reactants raised to certain powers (order of the reaction). The units of \(k\) also vary depending on the overall reaction order. For example, if the reaction order is zero, then the units of \(k\) are the same as rate, while for first-order reactions, \(k\) usually has the unit \(\min^{-1}\) or \(\sec^{-1}\).
Knowing the rate constant is essential for predicting how quickly a reaction will proceed and can assist in scaling reactions from laboratory experiments to industrial applications.