Chemical Kinetics

Step 1: Formula of half-life.
For a first-order reaction, the half-life is given by: Step 2: Dependence.
From the formula, we see that the half-life depends only on the rate constant , not on the initial concentration of the reactant.
Step 3: Analyze options.
(A) Incorrect, it actually depends on .
(B) Correct, it does not depend on initial concentration.
(C) Wrong, half-life is independent of initial concentration.
(D) Wrong, since only (B) is correct.
Step 4: Conclusion.
Hence, the correct answer is (B) does not depend upon initial concentration.

Step 1: Arrhenius dependence.
The rate constant varies with temperature as . Hence primarily depends on temperature.
Step 2: Eliminate others.
Mass, weight, and time do not directly determine the value of (for a given reaction and medium).
Step 3: Conclusion.
Therefore, the correct answer is (A) Temperature.

Step 1: Use stoichiometry in rate definition.
For products, rate .
Step 2: Apply to .
Rate .
Step 3: Conclusion.
All three expressions are valid (D) All of these.

Step 1: Apply the rate law.
Initial rate . If and constant, new rate
.
Step 2: Conclusion.
Rate increases by a factor of 9 nine times.

Step 1: Effect of temperature on reaction rate.
The rate of a chemical reaction generally increases with an increase in temperature. Usually, a rise of 10°C doubles or triples the rate of reaction.
Step 2: Reason.
When temperature increases, the kinetic energy of molecules also increases. This leads to more effective collisions between reactant molecules that have energy equal to or greater than the activation energy.
Step 3: Explanation using collision theory.
Only those collisions that occur with sufficient energy (≥ activation energy, ) and proper orientation result in product formation. Temperature increases the fraction of molecules possessing this minimum energy.
Step 4: Arrhenius Equation.
The temperature dependence of rate constant ( ) is expressed by Arrhenius as: where, rate constant, frequency factor, activation energy, gas constant, absolute temperature (in K).
Step 5: Logarithmic form.
Taking logarithm on both sides: This gives a straight line when is plotted against (Arrhenius plot).
Step 6: Conclusion.
Thus, the rate constant increases exponentially with temperature, leading to a faster reaction rate.

Step 1: Understanding the order of reaction.
For a second-order reaction, the rate law is given as: where is the rate constant and is the concentration of the reactant. The unit of rate is mol L sec , and the unit of concentration is mol L . To maintain the dimensional consistency, the unit of will be: Step 2: Conclusion.
The correct answer is (A) because the unit of the rate constant for a second-order reaction is mol L sec .

Step 1: Understanding the rate law.
The rate equation for the given reaction is: To determine the order of the reaction, we add the exponents of the reactant concentrations: The total order of the reaction is 1. Hence, the correct answer is (C). Step 2: Conclusion.
The order of the reaction is .

Step 1: Understanding Haber’s process.
Haber's process is used to synthesize ammonia by reacting nitrogen and hydrogen gases in the presence of a catalyst. The process requires a catalyst to increase the rate of the reaction. Step 2: Analysis of options.
(A) : Aluminum oxide is not used as a catalyst in the Haber process.
(B) : The combination of iron (Fe) with molybdenum (Mo) is used as the catalyst in the Haber process to facilitate the production of ammonia.
(C) : Copper oxide is not used in the Haber process.
(D) : Platinum is used as a catalyst in some reactions but not in the Haber process.
Step 3: Conclusion.
The correct answer is (B) because iron and molybdenum are the catalysts used in the Haber process for ammonia synthesis.

Step 1: Understanding the rate of reaction.
The rate of a chemical reaction depends on the concentration of the reacting substances, which is referred to as the active mass. The rate is proportional to the active mass of the reactants. Step 2: Analysis of options.
(A) Atomic mass: Atomic mass does not directly affect the rate of reaction.
(B) Equivalent mass: Equivalent mass is related to the amount of substance reacting, but it is not the determining factor for the reaction rate.
(C) Molecular mass: Molecular mass alone does not determine the rate of a reaction; it is the concentration (or active mass) that matters.
(D) Active mass: Correct — The rate of reaction is directly related to the active mass (or concentration) of the reactants.
Step 3: Conclusion.
The correct answer is (D) because the rate of reaction depends on the active mass, which is the concentration of reactants in the reaction.

Step 1: Analyzing the reactions.
To determine which reaction is not first order, we need to check the type of reaction for each option. A first-order reaction depends on the concentration of one reactant. Step 2: Analysis of options.
(A) The reaction is an ester hydrolysis reaction, which is typically a first-order reaction with respect to the ester.
(B) The reaction is an example of ester hydrolysis, also a first-order reaction.
(C) The reaction is the decomposition of hydrogen peroxide, which is a first-order reaction.
(D) The reaction is a second-order reaction, not a first-order reaction. This is a decomposition reaction that involves a different reaction order.
Step 3: Conclusion.
The correct answer is (D), as it is not a first-order reaction.

Step 1: Understanding rate of reaction.
The rate of a reaction is defined as the change in concentration of reactants or products per unit time. In other words, it measures how fast a reaction occurs. The rate of a reaction can be represented by the formula: where and are the changes in concentration of products and reactants over a time interval .
Step 2: Factors affecting the rate of reaction.
Several factors influence the rate of a chemical reaction:
1. Concentration of reactants:
The rate of reaction generally increases with an increase in the concentration of reactants, as there are more molecules or ions available to collide and react.
2. Temperature:
Higher temperature generally increases the rate of reaction. This is because an increase in temperature results in a higher kinetic energy, which leads to more frequent and energetic collisions between reacting molecules.
3. Catalysts:
Catalysts are substances that increase the rate of a reaction without being consumed in the process. They lower the activation energy required for the reaction to proceed.
4. Surface area of reactants:
A larger surface area of reactants increases the rate of reaction, as more particles are exposed to collisions.
5. Nature of reactants:
Some substances react more readily than others due to their chemical properties. For example, ionic compounds generally react faster than covalent compounds.
Step 3: Conclusion.
The rate of a reaction depends on the concentration of reactants, temperature, catalysts, surface area, and the nature of the reactants. By understanding and manipulating these factors, the rate of a reaction can be controlled.

Step 1: Understand the Arrhenius Equation.
The Arrhenius equation describes the relationship between the rate of a chemical reaction and the temperature. It is given by the equation: Where: - is the rate constant of the reaction. - is the pre-exponential factor (frequency factor), which represents the number of collisions that result in a reaction. - is the activation energy of the reaction. - is the universal gas constant (8.314 J/mol·K). - is the temperature in Kelvin.
Step 2: Explanation.
This equation shows that the rate constant increases with temperature, as the exponential factor becomes larger as increases. Thus, higher temperatures result in more frequent and energetic collisions, which speeds up the reaction.
Final Answer: The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy, given by:
Final Answer:

Step 1: Understand the temperature coefficient.
The temperature coefficient of a reaction indicates how much the rate of the reaction increases with a 10°C increase in temperature. For most reactions, this coefficient lies between 1 and 3.
Step 2: Analyze the options.
- 1 and 3 (Option A) is the correct range for most reactions. - 2 and 3 (Option B) would suggest a higher rate of reaction, which is uncommon for most reactions. - 1 and 4 (Option C) suggests an unusually high temperature dependence. - 2 and 4 (Option D) is also not typical for most reactions.
Step 3: Apply to the options.
The correct answer is (A) 1 and 3.
Final Answer:

Step 1: Understand the rate expression.
The rate expression is given as , where is the rate constant, and are the concentrations of reactants, and is the order with respect to reactant B.
Step 2: Analyze the options.
- 1 (Option A) suggests the reaction is first order, which is not always true in this case. - n (Option B) indicates that the reaction order depends on the concentration of , which is true for a specific rate expression, but we are considering the combined order of reaction. - n + 1 (Option C) is the correct choice, as the total order of the reaction is the sum of the orders with respect to each reactant. - None of these (Option D) is incorrect as we do have a correct option.
Step 3: Apply to the options.
The correct answer is (C) .
Final Answer:

Step 1: Understand the rate constant.
For a first order reaction, the rate constant (k) does not depend on the concentration of reactants or products but on the time for the reaction to occur.
Step 2: Analyze the options.
- Concentration of reactants (Option A) affects the rate of reaction but not the rate constant. - Concentration of products (Option B) is similarly related to reaction rate, not the rate constant. - Time (Option C) is the correct factor that the rate constant of a first order reaction depends on, since the rate constant remains constant over time. - Temperature (Option D) does affect the rate of reaction but not the rate constant for a given reaction.
Step 3: Apply to the options.
The correct answer is (C) time.
Final Answer:

Step 1: Understand the reaction.
The hydrolysis of ethyl acetate with dilute NaOH is a simple ester hydrolysis reaction. This reaction follows a first-order rate law with respect to both the ester and NaOH.
Step 2: Analyze the options.
- 1st order (Option A) is correct as ester hydrolysis with dilute NaOH is a first-order reaction. - 2nd order (Option B) would imply a second-order dependence, which is not the case for this reaction. - 3rd order (Option C) is not typical for ester hydrolysis. - Zero order (Option D) would indicate that the reaction rate does not depend on concentration, which is not true for this reaction.
Step 3: Apply to the options.
The correct answer is (A) 1.
Final Answer: