Integrated rate equations for irreversible enzyme-catalysed first-order and second-order reactions

Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and the reaction orders are determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. A common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carried out using...

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...

The half-life of a reaction (t1/2) is the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of the remaining concentration of the reactant is consumed. For example, during the decomposition of hydrogen peroxide, during the first half-life (from 0.00 hours to 6.00 hours), the concentration of H2O2 decreases from 1.000 M to 0.500 M. During the second half-life (from 6.00 hours to 12.00 hours), the concentration decreases from 0.500 M to...

The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions describing the relationship between the rate of a chemical reaction and the concentration of its reactants.
For example, in a generic reaction aA + bB ⟶ products, where a and b are stoichiometric coefficients, the rate law can be written as:
rate = k[A]m[B]n
[A] and [B] represent the molar concentrations of reactants, and k is the rate...

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...