The mathematical expression of the rate of reaction on concentration terms of reactants is known as rate expression or rate equation or rate law.

For reaction \(A + B \rightarrow Products\), the rate equation is

\[rate ­\propto [A] [B]\]

\[rate = K [A] [B]\]

K is known as specific rate constant or rate per unit concentration of the reactants.

Units of rate constant are \((mole)^{1−n} (litre)^{n−1} s^{−1}\).

Rate law for any reaction cannot be predicted by looking at the balanced chemical reaction, that is, theoretically but must be determined experimentally.

Several chemical reactions take place in a sequence

of steps and the overall rate of reaction is governed

by the slowest step.

In certain cases, the slowest or rate-determining step may involve the formation of an unstable intermediate

from the reactant molecules. The total number of reactant molecules taking part in the slowest step may involve the formation of an unstable intermediate. The total number of reactant molecules taking part in the slowest step or limiting step in the formation of intermediate species is known as the molecularity of the reaction.

Identify the false statement from the following

If the concentration units are reduced by n times, then the value of rate constant of first order will increase by n times

The correct answer is option 1. If the concentration units are reduced by n times, then the value of rate constant of first order will increase by n times.

Let us explain why the first statement is false and why the others are true.

Statement 1: If the concentration units are reduced by n times, then the value of the rate constant of the first order will increase by n times.

For a first-order reaction, the rate constant \( k \) has units of \(\text{time}^{-1}\) (e.g., \(\text{s}^{-1}\)). This means that the rate constant \( k \) is not affected by the units of concentration because it is inherently defined in terms of the inverse of time. Changing the units of concentration does not alter the numerical value of \( k \) for a first-order reaction. The rate constant \( k \) is independent of concentration units; it is only dependent on factors like temperature and the nature of the reaction. Therefore, reducing the concentration units by \( n \) times does not affect the value of \( k \), making this statement false.

Statement 2: Rate equation is the expression that gives the relation between rate of reaction and concentration of reactants.

The rate equation, also known as the rate law, defines how the rate of a chemical reaction depends on the concentration of the reactants. For example, for a reaction \( A \rightarrow B \), the rate law might be expressed as:

\(\text{rate} = k[A]^n\)

Here, the rate of the reaction is proportional to the concentration of \( A \) raised to the power \( n \), and \( k \) is the rate constant. This equation directly relates the rate to the concentration of reactants, making the statement true.

Statement 3: The rate constant of a reaction depends upon temperature.

The rate constant \( k \) is indeed temperature-dependent. According to the Arrhenius equation:

\(k = A e^{-\frac{E_a}{RT}}\)

\( k \) increases with temperature because the exponential term \( e^{-\frac{E_a}{RT}} \) becomes larger as \( T \) increases (since \( R \) and \( E_a \) are constants).

\( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. This temperature dependence makes the statement true.

Statement 4: The sum of the powers to which the concentration of substances appears in the rate expression is known as the order of reaction.

The order of a reaction is the sum of the exponents of the concentration terms in the rate law. For a generic reaction: \(\text{rate} = k[A]^m[B]^n \)

The overall order of the reaction is \( m + n \). Each exponent indicates the order with respect to each reactant, and their sum gives the total order of the reaction.

For example, if the rate law is \( \text{rate} = k[A]^2[B] \), the reaction is second-order with respect to \( A \), first-order with respect to \( B \), and third-order overall (2 + 1). This makes the statement true.

In summary, the false statement is the first one because it incorrectly implies that the rate constant for a first-order reaction is affected by changes in the concentration units, which it is not.