Problem 1 - A Complete Resource Book in Chemistry for JEE Main

Question

The unit of specific reaction rate constant for a firstorder (if the concentration is expressed in molarity) would be (a) \(s^{-1}\) (b) mole \(\mathrm{s}^{-1}\) (c) mole \(L^{-1} s^{-1}\) (d) mole \(L^{-1}\)

Step-by-Step Solution

Answer

The unit of the specific reaction rate constant for a first-order reaction is \( s^{-1} \) (Answer: a).

Step 1: Understanding the first-order reaction

For a first-order reaction, the rate law is given by \( rate = k[A] \), where \( [A] \) is the concentration of the reactant in molarity (\( mol/L \)). The rate is usually expressed in \( mol/(L \, s) \).

Step 2: Defining the rate constant

The specific reaction rate constant \( k \) for a first-order reaction must make the equation dimensionally consistent. So, \( rate = k[A] \) tells us that the units of \( k \) should ensure that the product of \( k \) and \( [A] \) has units of rate.

Step 3: Determining the units of the rate constant

From the equation \( mol/(L \, s) = k \times mol/L \), we need \( k \) such that when multiplied by \( mol/L \) it results in \( mol/(L \, s) \). This means \( k \) must have units of \( s^{-1} \).

Step 4: Answering the question

With the determined unit for \( k \) being \( s^{-1} \), we can identify the correct choice from the options provided.

Key Concepts

Reaction Rate Constant

The reaction rate constant, often denoted by the symbol \( k \), is a crucial element in chemical kinetics that defines the speed of a chemical reaction. For any reaction, the rate constant provides a proportional relationship between the concentration of reactants and the rate of the reaction itself. In the case of a first-order reaction, the rate constant is particularly simple. The reaction rate equation is expressed as:

• \( rate = k[A] \)

where \( [A] \) represents the concentration of the reactant. The beauty of the reaction rate constant in a first-order reaction lies in its direct correlation to the amount of reactant available. It remains unchanged, meaning it does not vary with changes in concentration or time during the reaction. This consistency helps chemists to predict reaction behaviours accurately over time.

Rate Law

Rate law is the mathematical relationship between the concentration of reactants and the rate of a reaction. For first-order reactions, the rate law is particularly straightforward. It takes the form:

• \( rate = k[A] \)

This equation illustrates that the reaction rate is directly proportional to the reactant concentration. In a first-order reaction, if the concentration of \( [A] \) doubles, the reaction rate also doubles. The simplicity of the first-order rate law lies in its linearity. This linear relationship helps in predicting how the reaction will proceed with time and is foundational in chemical kinetics. By understanding the rate law, students can easily determine how changing reactant concentrations influence the speed of chemical reactions.

Molarity

Molarity is a common unit used in chemistry to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution and is represented by the symbol \( M \). For a first-order reaction, molarity is used to quantify the reactant concentration in the rate law:

• \( [A] = \text{moles of solute} / \text{liter of solution} \)

This unit is pivotal for accurately measuring reactant concentrations in a reaction. In a laboratory setting, molarity allows chemists to prepare solutions with precise concentrations, which in turn enables them to predict and analyze the rate and outcome of reactions. Mastering molarity is essential for students to navigate problems related to solution concentrations in first-order reactions.

Units of Measurement

Units of measurement are fundamental in ensuring clarity and precision in scientific communication. In the context of determining the reaction rate constant for a first-order reaction, units play a pivotal role. To ensure dimensionality consistency in the rate law \( rate = k[A] \), the units of each component need to balance perfectly. The rate of reaction is expressed in \( mol/(L \, s) \), and the concentration is given in \( mol/L \). Therefore, since the rate law needs to equate these units, the reaction rate constant \( k \) for a first-order reaction must have the units \( s^{-1} \). This ensures that when \( k \) is multiplied by the concentration \([A]\), the result aligns dimensionally with the rate of reaction.