Problem 17 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The rate law for the reaction below is given by the expression \(\mathrm{k}[\mathrm{A}]\) [B] \(\mathrm{A}+\mathrm{B} \rightarrow\) Product If the concentration of \(\mathrm{B}\) is increased from \(0.1\) to \(0.3 \mathrm{~mole}\), keeping the value of \(A\) at \(0.1\) mole, the rate constant will be: [Main Online April 10, 2016] (a) \(3 k\) (b) \(9 k\) (c) \(k / 3\) (d) \(k\)

Step-by-Step Solution

Answer

(d) k

Step 1: Understand the Rate Law

The rate law for the reaction is given by \( ext{Rate} = k[A][B] \). Here, \( k \) is the rate constant, \([A]\) and \([B]\) are the concentrations of reactants A and B respectively.

Step 2: Initial Rate Calculation

Initially, the concentrations are \([A] = 0.1 \) mole and \([B] = 0.1 \) mole. The initial rate is given by: \[ ext{Rate}_{1} = k imes 0.1 imes 0.1 = 0.01k\]

Step 3: New Rate Calculation After Increase in [B]

The concentration of \(B\) is increased to \(0.3\) moles while \( A \) remains at \(0.1\) mole. The new rate is calculated as: \[ ext{Rate}_{2} = k imes 0.1 imes 0.3 = 0.03k\]

Step 4: Determine Effect on Rate Constant

The rate constant \( k \) itself is independent of concentrations and depends only on temperature and the nature of the reactant. Therefore, changes in concentrations do not affect \( k \).

Step 5: Conclusion

Since the rate constant \( k \) does not change with changes in concentration, the value of \( k \) remains the same despite the change in \([B]\). Hence, the correct answer is \(d\), which is \(k\).

Key Concepts

Chemical Kinetics

Chemical kinetics explores how chemical reactions occur and the factors affecting their speed. These reactions happen at different rates, depending on various conditions.
This study helps chemists understand reactions better and optimize them for industrial or laboratory purposes. It's like having a recipe and knowing exactly how long each step will take.
In chemical kinetics, the reaction rate is vital. It measures how fast reactants turn into products.

• Temperature: Changes can increase or decrease reaction rates.
• Concentration: More reactant particles usually result in faster reaction.
• Catalysts: These substances speed up reactions without being consumed themselves.

All these elements define how a reaction proceeds, helping predict and control it effectively.

Rate Constant

The rate constant, denoted as \( k \), is a crucial part of the rate law and indicates the reaction's speed at a given temperature.
In mathematical terms, it is the proportionality factor in the rate equation. For instance, in a rate law like \( \text{Rate} = k[A][B] \), \( k \) links the concentration of reactants \([A]\) and \([B]\) to the reaction rate.
Here are some key characteristics of the rate constant:

• Specific to a particular reaction and set of conditions.
• Units depend on the overall order of reaction.
• Unchanged by altering reactant concentrations.

A constant temperature means \( k \) remains unchanged, making it a reliable measurement for comparing reaction speeds.

Reaction Order

The reaction order is another critical aspect in understanding rate laws.
It describes how the rate is affected by the concentration of each reactant. This gives insight into the mechanism of the reaction and helps in predicting reaction behavior.
The reaction order isn't always the same as the stoichiometric coefficients in the balanced equation. It can be:

• Zero order: Rate doesn't depend on reactant concentration.
• First order: Rate directly proportional to one reactant's concentration.
• Second order: Rate proportional to either the square of one reactant's concentration or the product of two reactants' concentrations.

To determine the overall reaction order, add the orders of all reactants in the rate law. This information is pivotal for predicting how a reaction will respond to changes in concentration or other conditions.