Chemical Kinetics

To solve the problem, we need to determine the units of the rate constant for the given rate law:

Given:
Rate law:
This is a second-order reaction because the exponent on the concentration term is 2.

1. General Unit Formula for Rate Constant:
For a reaction of order , the units of the rate constant are:

2. Apply for Second-Order Reaction:
Here, :

Final Answer:
The correct units of are L mol⁻¹ s⁻¹.

Step 1: Determine the Magnetic Moment - The magnetic moment ( ) for a transition metal complex can be calculated using the formula: where is the number of unpaired electrons.

Step 2: Analyze the Complexes - : Nickel in the +2 oxidation state ( ) has 2 unpaired electrons, which gives a spin-only magnetic moment of 2.86 BM. Hence, the correct answer is .

Step 1: Using First-Order Reaction Formula
The time required for the concentration to become of its initial value in a first-order reaction is: For : Using , For : Step 2: Calculating Ratio
Thus, the correct answer is 60.

Each process is paired with its appropriate catalyst, enhancing the reaction's efficiency. For example, Ostwald's process uses to produce nitric acid from ammonia.

Step 1: Understanding Calcination
Calcination is the process of heating an ore in the absence or limited supply of air to remove volatile impurities such as water ( ), carbon dioxide ( ), or sulfur dioxide ( ). It is used primarily for carbonate and hydrated ores.

Step 2: Analyzing the Given Reactions
1. Reaction (1): Roasting Process
- This reaction involves heating a sulfide ore ( ) in the presence of oxygen ( ), leading to the formation of oxide ( ) and the release of sulfur dioxide ( ).
- This is a roasting process, not calcination.
2. Reaction (2): Dissolution Reaction
- This reaction involves aluminum oxide ( ) reacting with sodium hydroxide ( ) and water to form sodium aluminate.
- This is a leaching reaction, not calcination.
3. Reaction (3): Roasting Process
- This reaction involves heating a sulfide ore ( ) in the presence of oxygen ( ), forming copper sulfide ( ), iron sulfide ( ), and sulfur dioxide ( ).
- Since it involves oxidation of sulfides, it is also a roasting process, not calcination.
4. Reaction (4): Calcination Process
- This reaction involves heating hydrated iron oxide ( ) to remove water ( ), leaving behind anhydrous iron oxide ( ).
- This matches the definition of calcination.
Step 3: Evaluating the Given Options
- Option (1): Incorrect, as it represents roasting.
- Option (2): Incorrect, as it represents a dissolution reaction.
- Option (3): Incorrect, as it represents roasting.
- Option (4): Correct, as it represents the calcination of hydrated iron oxide.
Thus, the correct answer is

Option (4).

Step 1: Understanding the Haber Process
The Haber process is used for the industrial production of ammonia ( ) from nitrogen ( ) and hydrogen ( ) under high pressure and temperature. The reaction is:

Step 2: Identifying the Catalyst, Promoter, and Poison
- Catalyst: Iron ( ) is used as the main catalyst to increase the rate of reaction.
- Promoter: Molybdenum ( ) is added as a promoter to enhance the efficiency of iron as a catalyst.
- Poison for the Catalyst: Carbon monoxide ( ) acts as a poison for the iron catalyst by adsorbing on its active sites and deactivating it.
Step 3: Evaluating the Given Options
- Option (1): Incorrect, as tungsten ( ) is not used in the Haber process.
- Option (2): Incorrect, as cobalt ( ) is not the main catalyst.
- Option (3): Incorrect, as is not the primary catalyst poison.
- Option (4): Correct, as the correct catalyst is , the promoter is , and the poison is .
Thus, the correct answer is

Option (4).

Step 1: Understanding the First-Order Rate Equation
For a first-order reaction, the integrated rate law is: Comparing this with the equation of a straight line ( ), we see that:

Step 2: Calculating the Rate Constant
Given: Using the relation:

Step 3: Evaluating the Given Options
- Option (1): Incorrect, as is not directly equal to the slope.
- Option (2): Incorrect, as it divides by 2.303 instead of multiplying.
- Option (3): Correct, as min .
- Option (4): Incorrect, as the value is far too small.
Thus, the correct answer is

Option (3).