Questions: Autocatalytic Reactions and Nonlinear Kinetics

Question 1

In an autocatalytic reaction A + B → 2B, a researcher adds extra product B at the very start of the reaction when [A] is high but [B] is very low. What effect does this have on the initial reaction rate?

• A. It decreases the rate because adding product shifts equilibrium backward
• B. It has no effect because rate only depends on reactant concentrations
• C. It increases the rate because B is the autocatalyst and rate = k[A][B]
• D. It stops the reaction entirely because the system reaches equilibrium

Answer: (C)

In autocatalysis, the product B acts as a catalyst for its own formation. The rate law is rate = k[A][B], so adding more B at the start directly increases the initial rate — the opposite of what happens in most reactions where adding product slows or reverses the reaction. This is the diagnostic feature of autocatalysis: early in the reaction, adding product accelerates it rather than opposing it. Option A confuses autocatalytic kinetics with Le Chatelier's principle, which applies to equilibrium systems, not to this kinetic phenomenon.

Question 2

Which feature of the concentration-time profile of an autocatalytic reaction (A + B → 2B) most clearly distinguishes it from a simple first-order reaction?

• A. The reaction reaches 100% conversion, whereas first-order reactions do not
• B. The concentration of A shows a sigmoidal (S-shaped) decrease: slow start, rapid acceleration, then leveling off
• C. The reaction rate is constant throughout, whereas first-order rate changes smoothly
• D. The reaction slows monotonically as A is consumed, just faster than first-order decay

Answer: (B)

A first-order reaction shows exponential decay — the rate starts highest and falls continuously as reactant is consumed. An autocatalytic reaction produces a sigmoidal profile: the rate is initially slow (because [B] is low), then accelerates rapidly as B accumulates (positive feedback), then slows as A is nearly depleted. This S-shaped curve is the kinetic signature of autocatalysis and is absent in all linear (non-autocatalytic) reaction systems.

Question 3

In autocatalytic reactions, the reaction rate is highest at the very beginning when the reactant concentration is at its maximum.

• T. True
• F. False

Answer: False

This is true for simple first-order reactions but not for autocatalytic ones. In autocatalysis, the rate depends on the product of reactant and autocatalyst concentrations (rate = k[A][B]). At the very start, [B] is near zero, so the rate is low despite [A] being high. The rate peaks somewhere in the middle of the reaction — after enough autocatalyst has accumulated but before reactant A is seriously depleted. This acceleration phase is what produces the sigmoidal concentration curve.

Question 4

Autocatalytic systems can produce chemical oscillations because positive feedback in the rate law amplifies perturbations rather than damping them back to equilibrium.

• T. True
• F. False

Answer: True

Conventional chemical systems with linear kinetics dampen perturbations and approach equilibrium monotonically. Autocatalytic reactions introduce nonlinearity and positive feedback: the product amplifies its own formation. When autocatalytic steps are embedded in networks with competing inhibitory pathways and time delays, the system can overshoot and undershoot repeatedly, producing sustained oscillations. The Belousov-Zhabotinsky reaction is the canonical example. This behavior is qualitatively impossible in any linear kinetic system.

Question 5

Why does the nonlinear rate law in autocatalytic reactions (e.g., rate = k[A][B]) produce qualitatively different behavior from the linear rate laws of conventional reactions?

Model answer: In a conventional first-order reaction, the rate depends only on reactant concentration, which falls monotonically as the reaction proceeds — the system has no memory of its own products and simply runs down to equilibrium. In autocatalysis, the rate depends on the product of reactant and product concentrations. Since the product is being created by the reaction, the system feeds back on itself: production of B accelerates the production of more B. This positive feedback means small perturbations are amplified rather than dampened, enabling behaviors — sigmoidal kinetics, bistability, oscillations, and chaos — that are impossible in systems governed by linear differential equations.

The mathematical core is that rate = k[A][B] gives a nonlinear ODE in which the solution depends on the product of two changing quantities. This nonlinearity opens the door to multiple steady states and limit cycles, which are the mathematical underpinnings of oscillatory and chaotic behavior. Linear ODEs, by contrast, have only one stable solution (equilibrium) per set of conditions.