Problem 102 - A Complete Resource Book in Chemistry for JEE Main

Question

For a certain reaction, the activation energy is zero. What is the value of rate constant at \(300 \mathrm{~K}\), if \(\mathrm{K}=1.6\) \(\times 10^{\circ} \mathrm{s}^{-1}\) at \(280 \mathrm{~K} ?\) (a) \(1.6 \times 10^{6} \mathrm{~s}^{-1}\) (b) zero (c) \(4.8 \times 10^{4} \mathrm{~s}^{-4}\) (d) \(3.2 \times 10^{12} \mathrm{~s}^{-1}\)

Step-by-Step Solution

Answer

The rate constant at 300K is unchanged: \(1.6 \times 10^{\circ} \mathrm{s}^{-1}\).

Step 1: Understand Activation Energy and Rate Constant

Activation energy is the minimum energy required for a chemical reaction to occur. In this problem, the activation energy is zero, which means the rate constant does not change with temperature. The rate constant is given as \( K = 1.6 \times 10^{\circ} \mathrm{s}^{-1} \) at 280 K.

Step 2: Evaluate the Effect of Zero Activation Energy

With zero activation energy, the rate constant is independent of temperature. This means the rate constant remains the same at any temperature, including the temperature change from 280 K to 300 K.

Step 3: Determine the Rate Constant at 300 K

Given the rate constant at 280 K is \( K = 1.6 \times 10^{\circ} \mathrm{s}^{-1} \) and this value remains constant regardless of the temperature change, the rate constant at 300 K will also be \( K = 1.6 \times 10^{\circ} \mathrm{s}^{-1} \).

Key Concepts

Rate Constant

The rate constant ( K ) is a crucial parameter in understanding the rate at which a chemical reaction proceeds. It tells us how fast a reaction will occur under a given set of conditions. The rate constant is generally influenced by factors such as temperature and the presence of a catalyst.

• The larger the rate constant, the faster the reaction.
• It is typically determined from experimental data and expressed in specific units depending on the order of the reaction.

In many reactions, the rate constant increases with an increase in temperature, aligning with the Arrhenius equation. However, in some unique cases where the activation energy is zero, we find that the rate constant behaves differently. The rate constant in these cases is not affected by temperature changes, making the process easier to predict.

Chemical Reaction

A chemical reaction involves the transformation of reactants into products. This change involves breaking old bonds and forming new ones, leading to different substances at the end of the process.

• Reactions can be fast or slow, inversely depending on the size of the activation energy and the rate constant.
• Understanding chemical reactions is fundamental in fields such as chemistry, biology, and environmental science.

In the context of zero activation energy, a chemical reaction occurs effortlessly as there is no energy barrier to overcome. This lack of barrier means that as soon as the reactants collide with each other, they can transform into products instantly.

Temperature Dependence

Temperature is a significant factor affecting the rate of chemical reactions. In general, increasing the temperature accelerates the reaction rate. This change occurs because higher temperatures provide energy that helps reactants overcome the activation energy barrier more readily.

• The common rule is that for every 10°C increase in temperature, the reaction rate doubles.
• This is modeled by the Arrhenius equation, which ties temperature to reaction rates via the activation energy.

However, with zero activation energy, the reaction's rate constant is entirely temperature-independent. This unique situation simplifies calculations as the rate constant will remain consistent, no matter the temperature. Therefore, despite fluctuations in temperature, the reaction rate does not change.

Zero Activation Energy

Zero activation energy is a unique scenario in the study of chemical kinetics. It means that there is no minimum energy threshold that reactants must surpass to transform into products.

• With zero activation energy, the effect of temperature on reaction rate is nullified.
• This means the rate constant ( K ) remains constant regardless of temperature changes.

In practical terms, if a reaction has zero activation energy, it proceeds smoothly without any additional energy input requirements. This concept is somewhat rare but is important in understanding reactions that occur under specific conditions, such as in biological systems or particular industrial processes. For instance, in the given exercise, the rate constant remains at 1.6 even when the temperature changes from 280 K to 300 K, underlining the fascinating nature of this scenario.