Which of the following plots are correctly made for the reaction `nA hArr (A)_(n)` if it obeys first order reaction?

Options

A.
B.
C.
D.

Answer

To determine which plots are correctly made for the reaction \( nA \rightleftharpoons (A)_n \) that obeys first-order kinetics, we need to analyze the behavior of the concentration of reactants and products over time, as well as the rate of reaction.

### Step 1: Understand the Reaction and Rate Law
The reaction given is \( nA \rightleftharpoons (A)_n \). For a first-order reaction, the rate law can be expressed as:
\[ -\frac{d[A]}{dt} = k[A] \]
where \( [A] \) is the concentration of reactant A and \( k \) is the rate constant.

### Step 2: Analyze the Rate of Reaction
As the reaction proceeds, the concentration of A decreases over time. Since the rate of reaction is directly proportional to the concentration of A, as \( [A] \) decreases, the rate of reaction also decreases.

- **Conclusion for Plot A**: The plot showing the rate of reaction decreasing with time is correct.

### Step 3: Concentration of Reactant Over Time
Since A is being converted into products, the concentration of A will decrease over time.

- **Conclusion for Plot B**: The plot showing the concentration of A decreasing with time is correct.

### Step 4: Concentration of Product Over Time
As A is converted into products, the concentration of the product \( (A)_n \) will increase over time. Initially, the concentration of the product is zero, and as time approaches infinity, the concentration of A approaches zero, while the concentration of the product approaches its maximum.

- **Conclusion for Plot C**: The plot showing the concentration of the product increasing over time is correct.

### Step 5: Rate of Reaction vs. Concentration of Reactant
The rate of reaction is directly proportional to the concentration of A. Therefore, as the concentration of A decreases, the rate of reaction also decreases.

- **Conclusion for Plot D**: The plot showing the rate of reaction being directly proportional to the concentration of A is correct.

### Final Conclusion
All four plots (A, B, C, and D) are correctly made for the reaction \( nA \rightleftharpoons (A)_n \) if it obeys first-order kinetics.

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