Question

The time required for the complete degradation of a drug in solution is a finite value. The order of that reaction is:

• A. Zero
• B. Pseudo First
• C. Second
• D. First

Hint:

- Zero-Order: Degradation finishes at a definite, finite time ($t = \frac{C_0}{k}$). - First-Order: Approaches zero exponentially, requiring theoretical infinite time ($t \to \infty$).

Answer 1

The Correct Option is A

Understanding the Concept: Chemical kinetics describes the relationship between the rate of a reaction and the concentration of the reacting species. For an $n^{\text{th}}$-order process, the rate equation dictates how concentration decreases over time. Mathematical Proof:
• Zero-Order Kinetics: The rate of degradation is entirely independent of the remaining concentration of the reactant: \[ -\frac{dC}{dt} = k_0 \] Integrating this differential equation from time $t=0$ (initial concentration $C_0$) to time $t$: \[ C_t = C_0 - k_0 \cdot t \] To determine the time required for complete degradation, we set the final concentration $C_t = 0$: \[ 0 = C_0 - k_0 \cdot t_{\text{complete}} \quad \implies \quad t_{\text{complete}} = \frac{C_0}{k_0} \] Since $C_0$ and $k_0$ are positive real constants, $t_{\text{complete}}$ is a distinct, finite value.
• First-Order Kinetics Comparison: The rate is concentration-dependent ($C_t = C_0 \cdot e^{-k_1 \cdot t}$). For complete degradation ($C_t = 0$), $e^{-k_1 \cdot t}$ must approach $0$, which theoretically requires an infinite amount of time ($t \to \infty$). Thus, only zero-order reactions achieve total completion within a finite timeframe.