Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

The basic theory of Arrhenius equation is that (1) activation energy and pre-exponential factors are always temperature independent (2) the number of effective collisions is proportional to the number of molecule above a certain thresh old energy. (3) as the temperature increases, the number of molecules with energies exceeding the threshold energy increases. (4) the rate constant in a function of temperature (a) 2,3 and 4 (b) 1,2 and 3 (c) 2 and 3 (d) 1 and 3

Step-by-Step Solution

Answer

(a) 2, 3 and 4

Step 1: Understanding the Arrhenius Equation

The Arrhenius equation is a formula that gives us the temperature dependence of reaction rates. It is given by the formula \( k = A e^{-E_a / (RT)} \), where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Step 2: Interpreting Statement 1

Statement 1 mentions that activation energy and pre-exponential factors are temperature independent. In the context of the Arrhenius equation, this is generally true; \( E_a \) and \( A \) are considered independent of temperature for a given reaction.

Step 3: Interpreting Statement 2

Statement 2 suggests that the number of effective collisions is proportional to the number of molecules above a certain threshold energy. This aligns with the theory that only molecules exceeding a certain energy (i.e., activation energy) will react, which correlates to effective collisions.

Step 4: Interpreting Statement 3

Statement 3 indicates that the number of molecules with energies exceeding the threshold energy increases as temperature increases. This is true, as increasing temperature raises the average kinetic energy of molecules, allowing more of them to exceed the threshold energy.

Step 5: Interpreting Statement 4

Statement 4 claims the rate constant is a function of temperature. This is accurate, as the Arrhenius equation explicitly shows that \( k \) varies with \( T \).

Step 6: Compare Options with Interpretations

Compare each option against the interpretations of the statements. Options - (a): Statements 2, 3, and 4 are all accurate. - (b): Only Statements 1, 2, and 3; in actuality, 1, 2, and 3 are all valid. - (c): Statements 2 and 3 are accurate. - (d): Statements 1 and 3 are accurate.

Step 7: Identify the Correct Answer

Option (a) includes Statements 2, 3, and 4, which are fully consistent with the Arrhenius theory. Hence, option (a) is the correct choice.

Key Concepts

Activation Energy

Activation energy is a crucial concept in understanding why certain reactions occur. It is the minimum energy required for reactant molecules to transition into products. You can think of it as the energy barrier a reaction must overcome for it to proceed. This concept is derived from the Arrhenius equation and helps explain why some reactions are slow at room temperature but much faster at higher temperatures.

In the equation, activation energy is represented as \( E_a \). This value determines how sensitive the reaction rate is to temperature changes. Lower activation energies mean that molecules need less energy to react, resulting in faster reactions at any given temperature.

• This concept helps chemists control reaction speeds by either altering temperature or using catalysts to lower the activation energy.
• Many reactions in biological systems occur at specific rates to maintain life, thanks to enzymes which act as catalysts.

Reaction Rates

Reaction rates describe how quickly a reaction occurs. The rate can vary significantly depending on several factors, including the activation energy, temperature, and concentration of reactants. In the Arrhenius equation, the rate constant \( k \) represents the speed of the chemical reaction. This constant is calculated using the formula \( k = A e^{-E_a / (RT)} \), showcasing the interaction between various factors influencing reaction speed.

Reaction rates increase with:

• Higher temperatures, as it provides molecules with the kinetic energy needed to exceed the activation energy.
• Increased concentration of reactants, which raises the chances of collision and subsequent reaction.
• Presence of a catalyst, which lowers the activation energy.

Understanding reaction rates is essential in fields ranging from industrial synthesis to biological processes.

Temperature Dependence

The relationship between temperature and reaction rates is a vital concept in chemistry. According to the Arrhenius equation, as temperature rises, the rate constant \( k \) increases, leading to faster reaction rates. This occurs because higher temperatures boost the kinetic energy of molecules, making it more likely for them to overcome the energy barrier and react.

For practical applications:

• Refrigeration slows down reactions, prolonging the shelf-life of perishable goods.
• Some reactions are deliberately carried out at high temperatures to increase yield and efficiency.

The temperature dependence of reaction rates highlights the importance of controlling environmental factors in optimizing chemical processes.

Pre-exponential Factor

The pre-exponential factor, also known as the frequency factor, is denoted by \( A \) in the Arrhenius equation. It can be understood as the frequency with which a correctly oriented collision occurs between reactant molecules. While activation energy sets the minimum threshold for a reaction to occur, the pre-exponential factor relates to the frequency and orientation of these collisions.

The significance of the pre-exponential factor:

• It accounts for the probability of reactant particles encountering each other in a manner that will lead to a reaction.
• This factor remains relatively constant for a specific reaction, even as temperature changes, helping maintain a baseline frequency of effective collisions.

By understanding this concept, chemists can better predict how often reactions can take place under certain conditions, which is key to designing efficient chemical reactions.