Chemical Kinetics

2 = 4ⁿ → n = 1/2, so order is 1/2.

Rate law for the reaction can be expressed as: Where is the order with respect to NO and is the order with respect to .
(a) Determining the order with respect to NO ( ) Compare experiments 1 and 2 to eliminate the effect of concentration and find . From experiments 1 and 2: Determining the order with respect to ( ) Compare experiments 1 and 3 to eliminate the effect of NO concentration and find . From experiments 1 and 3: Thus, the order with respect to NO is 2 and the order with respect to s is 1.
(b) Calculating the rate constant (k) Use the rate law and the data from any experiment to solve for . Using experiment 1:
Determining the rate when the concentrations of NO and are 0.4 M and 0.2 M Now that we have the value of , we can use it to calculate the rate when [NO] = 0.4 M and [ ] = 0.2 M.

(a) Predict the Order of Reaction

The graph shows a linear relationship between log |R₀| and time. This suggests a first-order reaction.

In a first-order reaction, the concentration of the reactant decreases exponentially over time. This means:

Taking the logarithm (base 10) of both sides also gives a linear equation, which justifies that a plot of versus time is a straight line.

(b) What is the Slope of the Curve?

For a first-order reaction, the slope of the vs time graph is equal to , where is the rate constant.

So, the slope of the graph is:

To solve the problem, we need to evaluate the Assertion (A) and Reason (R) regarding the effect of doubling the reactant concentration on the half-life of a first order reaction and determine their validity and relationship.

1. Analyzing the Assertion (A):
Assertion (A) states that in a first order reaction, if the concentration of the reactant is doubled, its half-life is also doubled. For a first order reaction, the rate law is Rate = k[A], where k is the rate constant and [A] is the reactant concentration. The half-life (t ) of a first order reaction is given by the formula:


This formula shows that the half-life depends only on the rate constant k and is independent of the initial concentration [A] . If the initial concentration is doubled, the half-life remains the same because k does not change. Therefore, the assertion that doubling the concentration doubles the half-life is false, as the half-life stays constant.

2. Analyzing the Reason (R):
Reason (R) states that the half-life of a first order reaction does not depend upon the initial concentration of the reactant. As derived above, the half-life formula confirms that t is a function of k only and does not involve [A] . This is a characteristic feature of first order reactions, unlike zero or second order reactions where half-life depends on concentration. Thus, the reason is true.

3. Evaluating the Relationship:
The assertion is false because doubling the reactant concentration does not affect the half-life in a first order reaction. The reason is true and directly contradicts the assertion, as it correctly states that the half-life is independent of initial concentration. In assertion-reason questions, if the assertion is false, the reason’s truth does not make the assertion true. However, the reason explains why the assertion is incorrect, as the independence of half-life from concentration means doubling the concentration cannot double the half-life.

4. Conclusion:
- Assertion (A) is false because the half-life of a first order reaction does not change when the reactant concentration is doubled.
- Reason (R) is true because the half-life of a first order reaction is independent of the initial concentration.
- The reason explains why the assertion is false, as the concentration independence of the half-life contradicts the claim that doubling concentration doubles the half-life.

Final Answer:
Assertion (A) is false, Reason (R) is true.

To solve the problem, we need to determine what the number of molecules that react with each other in an elementary reaction measures.

1. Understanding Elementary Reactions:
An elementary reaction is a single-step chemical reaction where molecules collide and react directly to form products. The number of molecules that come together in this step defines a specific characteristic of the reaction.

2. Identifying the Term:
The number of molecules that react in an elementary reaction is referred to as the molecularity of the reaction. Molecularity indicates whether the reaction is unimolecular (one molecule), bimolecular (two molecules), or termolecular (three molecules).

Final Answer:
The number of molecules that react with each other in an elementary reaction is a measure of the molecularity.

To solve the problem, we need to identify which among the given statements about reaction kinetics is false.

1. Analyzing Statement (A):
Rate of a zero-order reaction is independent of the initial concentration of reactant. For a zero-order reaction, the rate law is , which does not depend on concentration. This statement is true.

2. Analyzing Statement (B):
Half-life of a zero-order reaction is inversely proportional to the rate constant. The half-life for a zero-order reaction is given by , where is the initial concentration. The half-life depends on and , but the statement claims it’s inversely proportional to the rate constant . Since , this statement is true.

3. Analyzing Statement (C):
Molecularity of a reaction may be zero. Molecularity represents the number of molecules colliding in an elementary reaction step and must be a positive integer (1, 2, or 3). It cannot be zero, as that would imply no molecules are involved, which is not possible for a reaction. This statement is false.

4. Analyzing Statement (D):
For a first-order reaction, . For a first-order reaction, the half-life is , which matches the given formula. This statement is true.

Final Answer:
The false statement is (C) Molecularity of a reaction may be zero.

1. Calculation of Activation Energy (Ea) for the First-Order Reaction:

Given Data:
- Reaction is 50% complete in 20 minutes at 300 K and 50% complete in 5 minutes at 350 K.
-
-

Step 1: Use the Arrhenius Equation:
The Arrhenius equation relates the rate constant to the temperature and activation energy :
where is the pre-exponential factor, is the activation energy, is the gas constant, and is the temperature in Kelvin. We can use the two given temperatures to find the activation energy.

Step 2: Use the Integrated Rate Law for a First-Order Reaction:
For a first-order reaction, the rate constant is related to the time for 50% completion by:
where is the time for the reaction to reach 50% completion. From the data: - At 300 K, - At 350 K,

Step 3: Calculate the Rate Constants:
For 300 K, the rate constant is:
For 350 K, the rate constant is:

Step 4: Use the Arrhenius Equation to Find :
Now, use the Arrhenius equation in its logarithmic form to calculate the activation energy:

Final Answer:
The activation energy of the reaction is approximately .

(I) The rate-determining step is the first reaction, where hydrogen peroxide decomposes to form water and IO⁻. The rate law for the reaction will be dependent on the concentration of H₂O₂.

(II) In the second step, the intermediate IO⁻ reacts with H₂O₂ in a fast step to produce water, iodine ions, and oxygen gas. This step does not affect the rate law, as it is not rate-determining.

(1) Rate law: The rate law is determined by the slow step, so the rate law is:

Rate =

where is the rate constant.

(2) Overall order and molecularity: The overall order of the reaction is 1, as the rate law depends on the concentration of only one reactant, H₂O₂. The molecularity of the reaction is 2, as the rate-determining step involves the collision of two molecules of H₂O₂.

To solve the problem, we need to find the rates of production of and for the zero-order decomposition of on a platinum surface, given the rate constant .

1. Understanding the Reaction and Zero-Order Kinetics:
The decomposition of ammonia ( ) on a platinum surface can be represented by the balanced chemical equation:


For a zero-order reaction, the rate of reaction is independent of the concentration of the reactant and is given by:


Here, , which represents the rate of decomposition of .

2. Rate of Decomposition of :
For a zero-order reaction, the rate of reaction is:


The coefficient accounts for the stoichiometry of the reaction (2 moles of ). Thus, the rate of consumption of is:

3. Relating Rates to Stoichiometry:
From the balanced equation , the rates of production of and are related to the rate of consumption of . The stoichiometric coefficients give:


Since the rate of reaction is , we have:

4. Calculating the Rate of Production of :
Using the stoichiometric relationship:


Substitute :

Final Answer:
The rate of production of is , and the rate of production of is .

Given Data

The data for the reaction is given below:

Rate Law

The rate law for this reaction is assumed to be:

where is the order with respect to A and is the order with respect to B.

(i) Order with respect to A

Compare experiments 1 and 2 (where [B] is constant):

So,

(ii) Order with respect to B

Compare experiments 1 and 3 (where [A] is constant):

So,

Overall Order of Reaction

✅ Therefore, the reaction is first-order with respect to A and zero-order with respect to B.