Sucrose concentration C₀ decreases with time and with rate constant k as

Concept:

1. First-Order Kinetics:- The rate of decomposition of a substance is often described by first-order kinetics, where the rate of change of concentration is proportional to the concentration.
2. Rate Law for First-Order Reactions:- The mathematical form of the first-order reaction is given by: Integrating this differential equation leads to an exponential decay function.

Explanation:

The integrated form of the rate law for a first-order reaction is:

The left side integrates to ln C) and the right side integrates to (-kt):

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Exponentiate both sides to solve for ( C ):

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To determine the constant, consider the initial condition when ( t = 0 ), ( C = C₀ ):

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Therefore, the constant is (ln C₀) and we can write:

• C = C₀ e^{-kt}

This equation indicates that the concentration of sucrose C decreases exponentially with time t and the rate constant k .

Conclusion:

The correct answer is C = C₀e^-kt