For the reaction xA(g) → yB(g), which of the following statements are correct?
Answer
🔬 Reaction Kinetics: Zero-Order Analysis
🧪 Problem Overview
A reaction is monitored by plotting concentration vs. time. Based on the plot and provided data, we determine:
- The order of the reaction
- The rate constant
- The truth of several statements about the reaction
📈 Step 1: Graph Interpretation
The graph of [A] vs. time is a straight line with a negative slope. This indicates a zero-order reaction, where:
[A]t = [A]0 − kt
🧪 Step 2: Rate Law and Constant
Rate = −d[A]/dt = k[A]n
For zero-order (n = 0):
−d[A]/dt = k = constant
📏 Step 3: Rate Constant from Slope
- [A]0 = 0.2 M, [A]t = 0.0 M
- t = 10 s
k = (0.2 − 0) / 10 = 0.02 mol·L⁻¹·s⁻¹
✅ Step 4: Statement Evaluation
| Statement | Analysis | Result |
|---|---|---|
| The reaction is zero order. | Confirmed by linear [A] vs. time plot. | True ✔️ |
| The rate constant units are incorrect. | Units should be mol·L⁻¹·s⁻¹ for zero order. | True ✔️ |
| Changing [A] changes k but not the rate. | k is constant and not dependent on [A]. | False ❌ |
| The reaction is complex. | Zero-order reactions often involve surface or saturation phenomena. | True ✔️ |
🧠 Summary
- The reaction follows zero-order kinetics.
- The rate is constant and does not depend on concentration.
- The calculated rate constant is 0.02 mol·L⁻¹·s⁻¹.
- Only statements 1, 2, and 4 are correct.