For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth?

Related Formula

Core Logic

Since r = k[A]$r = k[A]$, the reaction follows first-order kinetics. The half-life (50%$50\%$ decomposition) is t1/2 = 120 minutes$t_{1/2} = 120\text{ minutes}$.

Step 1: Calculating for 90% decomposition

For 90%$90\%$ completion of the reaction, [A]₀ = 100$[A]_0 = 100$ and [A]ₜ = 100 - 90 = 10$[A]_t = 100 - 90 = 10$.

Rounding off to the nearest integer, we get 399 minutes$399\text{ minutes}$.

Pattern Recognition

For a first order reaction, t90% ≈ 3.32 × t50%$t_{90\%} \approx 3.32 \times t_{50\%}$. 120 × 3.32 = 398.4$120 \times 3.32 = 398.4$, so roughly 399$399$.

Chapter Mix

Class 12 Chemistry: Chemical Kinetics

Core Logic

Consider a general gas phase reaction: A arrow B + C$A \rightarrow B + C$

Initial (t=0$t=0$): Pᵢ 0 0$\quad P_i \quad\quad 0 \quad\quad 0$ At time t$t$: Pᵢ - x x x$\quad P_i - x \quad\quad x \quad\quad x$

Total pressure at time t$t$:

x = Pₜ - Pᵢ$x = P_t - P_i$

Partial pressure of A at time t$t$ (PA$P_A$): PA = Pᵢ - x$P_A = P_i - x$

For a first-order reaction:

Here, P₀ = Pᵢ$P_0 = P_i$ and the pressure of the reactant at time t$t$ is PA$P_A$.

Chapter Mix

Class 12 Chemistry: Chemical Kinetics