Autocatalytic reactions show sigmoidal rate-time profiles

Steps:

• Recall that autocatalysis involves a product accelerating the reaction, starting slow due to low initial catalyst.
• As product accumulates, rate increases rapidly, forming an inflection point.
• Eventually, reactant depletion causes the rate to level off or decline.
• Plot rate vs. time yields a sigmoidal (S-shaped) curve matching option C.

Why C is correct:

• The sigmoidal shape reflects the rate law for autocatalysis, where rate = k [reactant][product], leading to exponential product growth initially then saturation.

Why the others are wrong:

• A: Linear curve implies constant rate, typical of zero-order kinetics, not autocatalysis.
• B: Decreasing curve suggests inhibition or depletion without acceleration, opposite of autocatalysis.
• D: Exponential rise without plateau ignores reactant limits, unrealistic for finite systems.

Final answer: C