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

The chemical property that can never be a fractional number is molecularity.

Step 1: Understanding the Question

The question asks which property of a chemical reaction can never be a fractional number. We will analyze each option to determine which one is always an integer.

Step 2: Analyzing Order of Reaction

The order of a reaction can be a fractional number. An example is a reaction with rate law \[ R = k[A]^{0.5} \, \], which has an order of 0.5, indicating fractional order is possible.

Step 3: Analyzing Half-Life

Half-life is the time required for a concentration of reactant to fall to half its initial value. This is usually expressed in units of time and can have fractional values.

Step 4: Analyzing Molecularity

Molecularity is defined as the number of molecules or atoms participating in an elementary reaction step. Since you cannot count half or a fraction of a molecule or atom, molecularity cannot be fractional. It is always an integer value.

Step 5: Analyzing Rate Constant

Rate constant, denoted as \( k \), is a proportionality factor in the rate equation. It can have fractional values depending on the order of reaction and units used. Therefore, it is not restricted to being an integer.

Step 6: Conclusion

Among the given options, molecularity is the one that can never be fractional because it represents a count of molecules involved in a collision or reaction step.

Key Concepts

Order of reaction

In chemical kinetics, the order of a reaction reflects how the rate of reaction is affected by the concentration of reactants. The order is determined from the rate equation: \[ R = k[A]^x[B]^y \]where \( k \) is the rate constant, \( [A] \) and \( [B] \) are the concentrations of reactants, and \( x \) and \( y \) are the respective reaction orders with respect to each reactant.

• If the reaction order is zero, this implies the reaction rate is independent of the concentration of that reactant.
• First-order reactions mean the rate is directly proportional to one reactant.
• Second-order may involve one reactant at a power of two, or two first-order reactants.

It is essential to note that the overall order of a reaction is the sum of the individual orders. Uniquely, reaction orders can be fractional. Thus, it's not uncommon to see reactions like a half-order, such as 0.5, reflecting complex reaction mechanisms.

Rate constant

The rate constant, denoted as \( k \), is a pivotal factor in determining the speed of a reaction. It appears in the rate law equation:\[ R = k[A]^x \]Here, \( k \) is an inherent property of the reaction, unaffected by the concentration of reactants or products but influenced by temperature and catalysts.

• The units of \( k \) vary. For a first-order reaction, \( k \) has units of s^-1, whereas for a second-order reaction, it is M^-1s^-1.
• Alterations in \( k \) with temperature changes are expressed through the Arrhenius equation \( k = Ae^{-E_a/RT} \).

The rate constant indicates the velocity of a reaction: a larger \( k \) means a faster reaction. Its value can be non-integer, which is often the case.

Half-life

Half-life in kinetics refers to the time needed for the concentration of a reactant to diminish to half its original value. It provides an easy way to characterize how fast a reaction progresses, especially with first-order reactions.For first-order reactions, half-life, \( t_{1/2} \), is calculated by:\[ t_{1/2} = \frac{0.693}{k} \]Interestingly, in first-order reactions, the half-life remains constant and does not depend on the initial concentration of the reactants. However, for reactions of other orders, the half-life depends on initial concentrations and can vary.

• In zero-order reactions, the half-life decreases as the concentration decreases.
• In second-order reactions, the half-life increases with the decrease in reactant concentration.

Half-life can be expressed in any time unit, such as seconds, minutes, or years, and it can certainly be a fractional time value, showcasing the nature of continuously progressing reactions.