The Question is from neet-chemistry surface-chemistry , and it was created by the author Mr. S M HUSSAIN

Question

For a zero-order reaction with a rate constant 'k', if the initial concentration of the reactant is '$[A]_0$' and the concentration at time 't' is '$[A]$', which of the following equations correctly represents the integrated rate law?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: 3
## CONCEPT FRAMEWORK
 **Primary Concept**: Integrated rate laws for zero-order reactions
 **Related Topics**: Chemical kinetics, reaction rates, order of reactions
 **Prerequisites**: Understanding of rate constants, reaction orders, and integration.
## SOLUTION PATHWAY
**Given Information**:
  * Zero-order reaction
  * Rate constant: $k$
  * Initial concentration: $[A]_0$
  * Concentration at time t: $[A]$
**Method & Steps**:
 1. **Define the rate law for a zero-order reaction:**
  Reasoning: For a zero-order reaction, the rate is independent of the reactant concentration.  The rate law is given by:  $\frac{-d[A]}{dt} = k$
  Formula/Rule: $\frac{-d[A]}{dt} = k$
 2. **Integrate the rate law:**
  Working: Integrate both sides with respect to time from $t=0$ to $t=t$ and $[A]=[A]_0$ to $[A]=[A]$:
  $\int_{[A]_0}^{[A]} -d[A] = \int_0^t k dt$
  $-[A]|_{[A]_0}^{[A]} = kt|_0^t$
  $-([A] - [A]_0) = kt$
  $[A]_0 - [A] = kt$
  $[A] = [A]_0 - kt$
  Key Point: The negative sign indicates that the concentration of reactant A decreases over time.
 3. **Identify the correct integrated rate law:**
  Result: The integrated rate law for a zero-order reaction is $[A] = [A]_0 - kt$
  Verification:  The equation shows a linear relationship between concentration and time, characteristic of zero-order kinetics.
 ## OPTION ANALYSIS
[A] :x: $[A] = [A]_0e^{-kt}$: This is the integrated rate law for a first-order reaction.
[B] :x: $ln[A] = ln[A]_0 - kt$: This is the integrated rate law for a first-order reaction.
[C] ✓: $[A] = [A]_0 - kt$: This is the correct integrated rate law for a zero-order reaction.
[D] :x: $1/[A] = 1/[A]_0 + kt$: This is the integrated rate law for a second-order reaction.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing zero-order kinetics with first-order or second-order kinetics: Carefully examine the rate law and its dependence on reactant concentration.
  2.Incorrect integration of the rate law: Pay close attention to the limits of integration and the signs.
 **Quick Tips**:
  1.Remember that for a zero-order reaction, the concentration decreases linearly with time.
  2.Visualize the integrated rate law graphically; it will be a straight line with a slope of -k.

Mr. S M HUSSAIN · Answer

$[A] = [A]_0e^{-kt}$

Mr. S M HUSSAIN · Answer

$ln[A] = ln[A]_0 - kt$

Mr. S M HUSSAIN · Answer

The correct Option is "$[A] = [A]_0 - kt$"

Mr. S M HUSSAIN · Answer

$1/[A] = 1/[A]_0 + kt$

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