Problem 32 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Read the following assertion and statement and answer as per the options given below: Assertion : For each ten degree rise of temperature the specific rate constant is nearly doubled. Statement : Energy-wise distribution of molecules in a gas is an experimental function of temperature. (a) If both assertion and statement are correct and statement is an explanation of assertion. (b) If assertion is correct and statement is wrong, statement is not an explanation of assertion. (c) If assertion is wrong and statement is correct, statement is not an explanation of assertion. (d) If both assertion and statement are wrong and statement is not explanation of assertion.

Step-by-Step Solution

Answer

(a) Both assertion and statement are correct and statement is an explanation of assertion.

Step 1: Understand the Assertion

The assertion states that for every ten-degree increase in temperature, the specific rate constant approximately doubles. This is generally true because of the Arrhenius equation, which shows that an increase in temperature results in an increase in reaction rates due to more molecules having sufficient energy to overcome the activation barrier.

Step 2: Understand the Statement

The statement indicates that the energy distribution of molecules in a gas is an experimental function of temperature, matching the Maxwell-Boltzmann distribution. This distribution indeed depends on temperature, affecting how energy levels are populated among molecules.

Step 3: Evaluate the Relationship

Both the assertion and the statement are correct: the assertion about the rate constant doubling due to increased molecular energy, and the statement on energy distribution tied to temperature. Therefore, the statement correctly explains the assertion, as a higher temperature broadens the energy distribution, allowing more molecules to reach the requisite energy to react.

Step 4: Select the Correct Option

Given that both the assertion and statement are accurate and the statement explains the assertion, option (a) is the correct choice. The necessity for more energy to overcome reaction barriers is explained by energy distribution which depends on temperature.

Key Concepts

Specific Rate Constant

In chemical kinetics, the specific rate constant plays a significant role in determining how fast a reaction proceeds. It is part of the Arrhenius equation, which is used to express the dependence of reaction rates on temperature and activation energy.The Arrhenius equation is:\[k = A \exp\left(-\frac{E_a}{RT}\right)\]where:

• \(k\) is the specific rate constant.
• \(A\) is the pre-exponential factor, which is specific to each reaction.
• \(E_a\) is the activation energy required for the reaction to occur.
• \(R\) is the universal gas constant.
• \(T\) is the temperature in Kelvin.

The specific rate constant \(k\) is sensitive to temperature changes. It does not remain constant with varying temperature, which is why for many reactions, each 10-degree Celsius rise in temperature can roughly double \(k\). This happens because more molecules reach the activation energy required for the reaction as thermal motion increases. Thus, understanding \(k\) is crucial for predicting how quickly a reaction will occur under different conditions.

Temperature Effect on Reactions

Temperature is a critical factor affecting the rates of chemical reactions. Generally, as temperature increases, the speed of the reaction also goes up. The reason lies in the increased kinetic energy of the molecules.Higher temperatures provide energy that enables more molecules to surpass the activation energy threshold needed for reactions. Here’s why temperature has such an effect:

• It increases molecular movement, causing more frequent collisions between reactant molecules.
• It enhances the energy of collisions, making chemical bonds break and new bonds form more likely.
• This increased energy can lead to more effective collisions that result in a reaction.

Due to these points, reactions are often quicker at higher temperatures. This is reflected in the Arrhenius equation, which shows that reaction rates and the specific rate constant \(k\) rise with temperature, following an exponential trend. Understanding how temperature influences reactions helps predict and control reactions in industrial and laboratory settings.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution explains how energy is distributed among molecules in a gas. It shows that not all molecules in a gas possess the same energy, leading to a range of molecular speeds and energies. This distribution is significant because it directly affects reaction rates and is temperature-dependent. It is generally depicted graphically where:

• The x-axis represents molecular speed or energy.
• The y-axis represents the number of molecules having a particular speed or energy.
• The peak of the curve shows the most probable speed.

As temperature increases, the curve flattens and shifts to the right, indicating higher energies and speeds. More molecules possess enough energy to surpass the activation barrier in this scenario, explaining why reactions tend to proceed faster at higher temperatures. The Maxwell-Boltzmann distribution is essential to understanding why temperature changes impact how many molecules have sufficient energy to participate in reactions. It supports the idea that temperature is a critical component in determining reaction rates as it widens the range of energies present among molecules, making successful collisions more probable.