Question

Which of the following is correct with respect to the graph given?
[R] = Conntration at time 't' 
[R]$_0$ = Initial conntration 

• A. I, III represent first order and II represents zero order reaction
• B. I, II represent zero order and III represents first order reaction
• C. I, II, III all represent zero order reactions
• D. I, II, III all represent first order reaction

Hint:

Order of Reactions and Graphs.

• Zero order: $[\textR]$ vs $t$ is linear.
• First order: $\log [\textR]$ vs $t$ is linear.
• Rate vs $[\textR]$:
  • Constant line: Zero order
  • Linear through origin: First order

Answer 1

The Correct Option is B

Let’s analyze the three graphs:

• Graph I: Rate vs Concentration. It shows constant rate, independent of concentration — indicative of a zero-order reaction.
• Graph II: [R] vs time — linear decrease, indicating constant rate — again zero-order reaction.
• Graph III: $\log [R]$ vs time is linear with negative slope. This is characteristic of first-order kinetics.

Hence: \[ \text{Graph I: Zero order}, \quad \text{Graph II: Zero order}, \quad \text{Graph III: First order} \]

Answer 2

Step 1: Analyzing Graph I (Rate vs Concentration)
Graph I shows the rate of reaction plotted against the concentration of the reactant. The rate remains constant regardless of changes in concentration, indicating that the reaction rate does not depend on the concentration of reactant. This behavior is characteristic of a zero-order reaction.

Step 2: Analyzing Graph II (Concentration [R] vs Time)
Graph II depicts the concentration of reactant decreasing linearly with time. A linear decrease in concentration with time means the rate of reaction is constant, which again confirms a zero-order reaction where the rate is independent of reactant concentration.

Step 3: Analyzing Graph III (log [R] vs Time)
Graph III shows a plot of the logarithm of concentration of reactant versus time. The graph is a straight line with a negative slope, which is a signature of first-order kinetics. For first-order reactions, the plot of log [R] against time is linear, reflecting exponential decay of concentration.

Step 4: Summary and Conclusion
From the analysis:
- Graph I corresponds to a zero-order reaction.
- Graph II also corresponds to a zero-order reaction.
- Graph III corresponds to a first-order reaction.