Question

The given graph is a representation of kinetics of a reaction.
The y and x axes for zero and first order reactions, respectively are

• A. zero order (y = concentration and x = time), first order (\(y = t\frac{1}{2}\), and x = concentration)
• B. zero order (y = concentration and x = time), first order (y = rate constant and x = concentration)
• C. zero order (y = rate and x = concentration), first order (\(y = t\frac{1}{2}\) and x = concentration)
• D. zero order (y = rate and x = concentration), first order (y = rate and \(x = t\frac{1}{2}\))

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The graph shows a horizontal straight line parallel to the $x$-axis.
This implies that the value of $y$ is constant and independent of the value of $x$.
Key Formula or Approach:
Zero order rate law: $\text{Rate} = k[A]^{0} = k$ (Rate is constant).
First order half-life: $t_{1/2} = \frac{0.693}{k}$ (Half-life is constant).
Step 2: Detailed Explanation:
For a zero-order reaction, the rate does not change as the concentration changes.
Thus, a plot of Rate ($y$) vs Concentration ($x$) will be a horizontal line.
For a first-order reaction, the half-life ($t_{1/2}$) is independent of the initial concentration.
Thus, a plot of $t_{1/2}$ ($y$) vs Concentration ($x$) will be a horizontal line.
Step 3: Final Answer:
The description in option (3) fits the horizontal line graph for both orders.