The value of rate constant of a pseudo first order reaction

Options

A. depends on the concentration of reactants present in small amount
B. depends on the concentrations of reactants present in excess
C. is independent of the concentration of reactants
D. depends only on temperature

Explanation

To determine the value of the rate constant of a pseudo first-order reaction, we need to understand the characteristics of such reactions. Here’s a step-by-step solution:

### Step 1: Understanding Pseudo First-Order Reactions
A pseudo first-order reaction occurs when one reactant is in excess compared to the other reactant. This means that the concentration of the excess reactant does not change significantly during the reaction, allowing us to simplify the rate law.

**Hint:** Identify the reactants and their concentrations to determine which one is in excess.

### Step 2: Writing the Rate Law
For a reaction involving two reactants A and B, the rate law can be expressed as:
\[ \text{Rate} = k[A][B] \]
In a pseudo first-order scenario, if B is in excess, we can treat its concentration as constant. Thus, we can express the rate as:
\[ \text{Rate} = k'[A] \]
where \( k' = k[B] \) (a new constant that incorporates the concentration of B).

**Hint:** Recognize that the rate constant \( k' \) is derived from the original rate constant \( k \) and the concentration of the excess reactant.

### Step 3: Analyzing the Options
Now, let's analyze the options given in the question:
1. **Depends on the concentration of reactant present in small amount** - This is true because the rate constant \( k' \) is directly related to the concentration of A.
2. **Depends on the concentration of reactants present in excess** - This is false as the rate constant does not depend on the concentration of B.
3. **Is independent of the concentration of reactant** - This is false because it does depend on the concentration of A.
4. **Depends only on the temperature** - This is partially true; while the rate constant does depend on temperature, it also depends on the concentration of the reactant in small amounts.

**Hint:** Evaluate each option based on the derived rate law and the definition of pseudo first-order reactions.

### Step 4: Conclusion
From the analysis, the correct answer is:
- The value of the rate constant of a pseudo first-order reaction **depends on the concentration of the reactant present in small amount**.

**Final Answer:** The correct option is that the value of the rate constant of a pseudo first-order reaction depends on the concentration of the reactant present in small amount.