Rate law for simple enzyme catalyst reaction

Enzymes are biomolecules that catalyze chemical reactions in living organisms. The rate of an enzyme-catalyzed reaction is determined by the rate at which the substrate and enzyme form an enzyme-substrate complex, and the rate at which the product is formed from the complex. The rate law for a simple enzyme-catalyzed reaction can be derived using the Michaelis-Menten equation.

Michaelis-Menten equation

The Michaelis-Menten equation relates the rate of an enzyme-catalyzed reaction to the concentration of substrate and enzyme. The equation is given as:

v = (Vmax [S])/(Km + [S])

where v is the initial rate of the reaction, [S] is the concentration of substrate, Vmax is the maximum rate of the reaction, and Km is the Michaelis constant.

Derivation of rate law

The rate law for a simple enzyme-catalyzed reaction can be derived from the Michaelis-Menten equation by assuming that the concentration of substrate is much greater than the concentration of enzyme. Under this condition, the Michaelis constant can be approximated as Km ≈ [E], where [E] is the concentration of enzyme. Substituting this approximation into the Michaelis-Menten equation gives:

v = (Vmax [S])/([E] + [S])

This equation is the rate law for a simple enzyme-catalyzed reaction. It shows that the rate of the reaction is proportional to the concentration of substrate and the maximum rate of the reaction, and inversely proportional to the sum of the concentrations of enzyme and substrate.

Conclusion

The rate law for a simple enzyme-catalyzed reaction can be derived from the Michaelis-Menten equation. The rate law shows that the rate of the reaction is proportional to the concentration of substrate and the maximum rate of the reaction, and inversely proportional to the sum of the concentrations of enzyme and substrate. The Michaelis constant is an important parameter that characterizes the behavior of enzymes and can be used to determine the efficiency of an enzyme-catalyzed reaction.