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): The rate of a reaction normally increases by a factor of 2 or 3 for every \(10^{\circ c}\) rise in temperature. (R): Increase in temperature increases the number of collisions.

Short answer

b. Both A and R are correct but R is not the correct explanation of A.

Step-by-step solution

Understanding the Assertion

The Assertion (A) states that the rate of a reaction generally increases by a factor of 2 or 3 with a rise in temperature by 10°C. This is a well-known observation in chemistry, explained by the Arrhenius equation, which shows that reaction rate constants increase exponentially with temperature.

Understanding the Reason

The Reason (R) given is that an increase in temperature increases the number of collisions. This is true because higher temperatures provide more energy to molecules, causing them to move faster, leading to more frequent collisions.

Analyzing the Connection

Now, assess whether (R) is the correct explanation for (A). While increasing the number of collisions is a factor in increasing reaction rates, the more direct reason for the increase is that more molecules have kinetic energy greater than the activation energy, thus increasing the rate significantly. Thus, (R) is a partial, but not full, explanation for (A).

Selecting the Answer

Both the Assertion (A) and the Reason (R) are true based on scientific principles. However, (R) is not the complete explanation of (A), since the activation energy and distribution of molecular energies are better predictors. Therefore, the correct answer is option (b).

Key concepts

Arrhenius Equation

The Arrhenius equation is fundamental in chemical kinetics. It's a mathematical formula that helps us understand the effect of temperature on the rate of a chemical reaction. The equation is expressed as:

1.   k = A \cdot \exp \left( \frac{-E_a}{RT} \right)

where:

• \(k\) is the rate constant of the reaction,
• \(A\) is the pre-exponential factor, which accounts for the frequency of collisions with proper orientation,
• \(E_a\) is the activation energy,
• \(R\) is the universal gas constant,
• \(T\) is the temperature in Kelvin.

This equation shows how the reaction rate can exponentially increase with an increase in temperature. The rate constant \(k\) becomes larger as the temperature rises, due to the exponential nature of \(\exp\left(\frac{-E_a}{RT}\right)\). The significance of the Arrhenius equation is in predicting how changes in temperature affect the speed of reactions, a crucial aspect when considering reaction efficiency in industrial processes as well as in laboratory settings.
Understanding the Arrhenius equation allows chemists to manipulate conditions to optimize reactions, for example, by adjusting the temperature to achieve faster reaction rates without compromising safety or product yield.

Reaction Rate

The reaction rate measures how fast a reaction occurs, essentially quantifying how quickly reactants turn into products. Understanding reaction rates is essential for controlling industrial processes and for research in chemistry.
There are different ways to express reaction rates:

• Rate of disappearance of reactants.
• Rate of appearance of products.
• Using changes in concentration over time: \( \frac{\Delta [{Products}]}{\Delta t} \) or \( - \frac{\Delta [Reactants]}{\Delta t} \).

Factors affecting reaction rates include temperature, concentration of reactants, surface area of reactants, presence of a catalyst, and the nature of the reactants. Increasing the temperature generally leads to faster reaction rates, which aligns with the assertion in the exercise that a 10°C increase can double or triple the reaction rate.
This acceleration occurs because higher temperatures increase the energy and movement of molecules, thus increasing the frequency and energy of collisions among reactant molecules. However, merely increasing collisions isn't sufficient; these collisions must also have adequate energy to surpass the activation energy barrier, which is critical for successful reactions.

Activation Energy

Activation energy is the minimum energy necessary for reactants to transform into products. It is an essential concept in chemical kinetics, representing the energy barrier that a reaction must overcome for the process to proceed.
Every chemical reaction involves a transition state, which is a high-energy state between reactants and products. The activation energy \(E_a\) is the energy difference between the reactant state and this transition state. Not all molecular collisions lead to a reaction; only those with enough energy to overcome the activation energy will result in the formation of products.

• Lower activation energies imply faster reactions as more molecules have sufficient energy to reach the transition state.
• Higher activation energies lead to slower reactions since fewer molecules can surpass the energy threshold.

The Arrhenius equation highlights this by showing that even a small increase in temperature can significantly increase the number of molecules with kinetic energy exceeding this barrier. Activation energy can also be influenced by catalysts, which lower the energy barrier, increasing reaction rates without being consumed in the process.
Thus, understanding activation energy helps predict how changes in conditions such as temperature and catalysts affect a reaction, a knowledge invaluable for developing efficient and effective chemical processes.