Physic Labs

Physical chemistry

Catalysis

A catalyst provides an alternative lower-barrier pathway, helping a system reach equilibrium faster without net consumption or shifting equilibrium.

A homogeneous catalyst shares the reactants’ phase; a heterogeneous catalyst is in another phase and often acts through surface adsorption. Enzymes are highly selective biological catalysts.

Model and quantities

Read the relation together with assumptions about state, experimental conditions, and sign conventions. Keep units consistent and check dimensions before interpreting a result.

v=Vmax[S]KM+[S]v=\frac{V_{max}[S]}{K_M+[S]}

Definition: Michaelis–Menten kinetics

A simple enzyme model gives v=Vmax[S]/(KM+[S])v=V_{max}[S]/(K_M+[S]), where [S] is substrate concentration. At [S]=K_M, the rate is half Vmax. This saturation model is not universal for every enzyme.

Quantities in the relation are defined for the reaction or system at hand. In particular, distinguish standard-state quantities from actual conditions and do not infer a mechanism from a general expression alone.

Example: Worked example

An enzyme has Vmax=12 μmol/min and KM=3 mM. Find the initial rate at [S]=3 mM.

Solution

Since [S]=KM, v=Vmax/2=6v=Vmax/2=6 μmol/min. At much higher substrate, the rate approaches but does not exceed Vmax in this model.

Concept summary
ConceptDescriptionUnit / note
Key relationUse under stated conditionsCheck units and sign convention
Measured quantityRelates a state or processCompare data with model
ScopeModel specific conditionsCheck assumptions first

Enzymes often show substrate saturation and may be inhibited; KM and Vmax depend on conditions. Heterogeneous catalysis distinguishes adsorption, surface reaction, and desorption.

In the worked example, which result follows from the given data?

Which statement is consistent with this lesson?

References

  1. Peter Atkins, Julio de Paula (2014). Physical Chemistry