Ascorbic acid degradation in sweet potatoes at a water...

Ascorbic acid degradation in sweet potatoes at a water activity of 0.11 is first order with a rate constant of $0.001500 \mathrm{~h}^{-1}$ at $25^{\circ} \mathrm{C}$. If the $\mathrm{Q}_{10}$ for this reaction is 1.8 , calculate the amount of ascorbic acid remaining in dried sweet potato stored at $30^{\circ} \mathrm{C}$ after 3 months in storage if the initial ascorbic acid content was $33 \mathrm{mg} / 100 \mathrm{~g}$.

Key Concepts

First-Order Kinetics

In first-order kinetics, the rate of a reaction is directly proportional to the concentration of the reactant. This means that the decrease in the concentration of a substance over time follows an exponential decay pattern, which can be mathematically described using an integrated rate law formula. This concept is widely used in chemical and biochemical processes to predict how a substance degrades over time.

Rate Constant

The rate constant is a specific numerical value that quantifies the speed of a chemical reaction under given conditions. In the context of first-order kinetics, the rate constant directly influences how quickly the reactant concentration decreases, and its units typically reflect inverse time (such as h?¹). It is a central parameter used in calculating the extent of reaction progress over time.

Temperature Coefficient (Q10)

The Q10 factor is a useful concept in chemical kinetics that indicates how the rate of a reaction changes with a 10°C increase in temperature. Essentially, it provides a ratio that can be applied to adjust the rate constant when the temperature deviates from a reference value. This factor is instrumental in modeling and predicting reaction behavior under different temperature conditions.

Temperature Dependence of Reaction Rates

Temperature has a significant impact on reaction rates, primarily because it influences the kinetic energy of molecules and the frequency of effective collisions leading to reaction. This dependency is often embedded in Arrhenius-type relationships or represented by factors like Q10, which allow for the estimation of reaction rate changes as the temperature varies, an essential consideration in both laboratory and industrial processes.

Time Conversion in Reaction Kinetics

Accurate time conversion is important in kinetics problems, especially when storage or reaction durations are given over different time units such as months, days, or hours. Converting these time scales into a consistent unit is crucial for correctly applying the first-order kinetic equations and accurately predicting the extent of reaction or degradation over the intended period.

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