Question

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): Arrhenius equation explains the temperature dependence of rate of a chemical reaction. (R): Plots of log \(\mathrm{K}\) vs \(1 / \mathrm{T}\) are linear and the energy of activation is obtained from such plots.

Short answer

Both A and R are correct, and R is the correct explanation of A (option a).

Step-by-step solution

Understanding Assertion (A)

The Assertion (A) states that the Arrhenius equation explains the temperature dependence of the rate of a chemical reaction. This is correct because the Arrhenius equation \( k = Ae^{-Ea/RT} \) gives the relationship between the rate constant \( k \) and temperature \( T \), where \( A \) is the pre-exponential factor, \( Ea \) is the activation energy and \( R \) is the universal gas constant. So, A is true.

Understanding Reason (R)

The Reason (R) asserts that plots of \(\log K\) versus \(1/T\) are linear and allow calculation of the energy of activation. This is true based on the Arrhenius equation. By taking the logarithm of both sides of the Arrhenius equation, we get \( \log k = \log A - Ea/(RT) \). This is a linear equation (equation of a straight line) with \( \log k \) as the vertical axis and \( 1/T \) as the horizontal axis. Hence, R is also true.

Evaluating the connection

Now that we've established both A and R are true, we examine if R is the correct explanation for A. The Reason (R) effectively describes how the Arrhenius equation is used in practice to determine the activation energy and shows the temperature dependency of reaction rates, thus directly explaining Assertion (A). As the linear plots are a result of the Arrhenius equation, R is indeed the correct explanation for A.

Key concepts

Temperature Dependence

The Arrhenius equation is fundamental to understanding temperature dependence in chemical reactions. It links temperature to the rate at which a reaction occurs, demonstrating that reactions generally proceed faster at higher temperatures. This is because as temperature increases, molecules gain more energy, increasing the likelihood of them colliding with enough energy to surpass the activation barrier needed for the reaction.

The equation is presented as \( k = Ae^{-Ea/RT} \), where

• \( k \) is the rate constant, representing how fast a reaction proceeds,
• \( A \) is the pre-exponential factor or frequency factor, indicating the frequency of collisions with the correct orientation,
• \( Ea \) is the activation energy, the minimum energy necessary to initiate a reaction,
• \( R \) is the gas constant, and
• \( T \) represents the temperature in Kelvin.

The exponential term \( e^{-Ea/RT} \) quantifies the fraction of molecules with sufficient energy to overcome the activation energy, showing why there's a temperature dependence.

Rate of Chemical Reaction

The rate of a chemical reaction is influenced by several factors, with temperature being a key one according to the Arrhenius equation. The rate constant \( k \), derived from this equation, is directly tied to how quickly reactants are converted into products in a given time frame.

When plotting the rate of reaction on a graph against temperature, one typically observes that reaction rates increase with an increase in temperature. This manifests from the Arrhenius equation as a higher temperature leads to a larger rate constant \( k \), explaining why certain reactions that are sluggish at room temperature might proceed rapidly when heated.

Other elements such as concentration, surface area, and catalysts affect reaction rates, but temperature plays a uniquely consistent role as shown through the Arrhenius framework.

Activation Energy

Activation energy \( Ea \) is the energy barrier that must be overcome for a chemical reaction to proceed. It is a critical concept within the Arrhenius equation, reflecting the minimum energy that reactant molecules need to acquire before transforming into product molecules.

This energy is the reason why not all molecular collisions result in a reaction. Only those collisions that provide sufficient energy to break the bonds of reactants allow the formation of products. Hence, a lower activation energy typically means a faster reaction under the same conditions, as more molecules will have the required energy to react.

Activation energy can also be derived from experimental data using the Arrhenius formula. By determining the slope from a plot of \(\log k\) against \(1/T\), one can calculate \(Ea\) through the relationship:

• \( \log k = \log A - \frac{Ea}{RT} \)
• The slope equates to \(-Ea/R\), allowing \(Ea\) to be derived.

Logarithmic Plots

Logarithmic plots are a powerful tool for extracting information from the Arrhenius equation. By rearranging the equation to a logarithmic form, one can utilize plot analysis to determine activation energy and assess the effect of temperature on reaction rates.

The transformation of the Arrhenius equation into a linear form **\( \log k = \log A - Ea/(RT) \)** allows for straight-line plotting of \( \log k \) versus \(1/T\), where the slope of this line is \( -Ea/R \). This slope reveals the activation energy \( Ea \) in an easily measurable fashion from experimental data.

Use of these logarithmic plots simplifies the complexity involved in extracting quantitative measures of a chemical reaction's responsiveness to temperature, making it an essential practice in kinetics studies and applications. By understanding the graphical representation, the entire dynamic between energy, reaction rates, and temperature becomes clearer and more approachable.