Organic Chemistry

Equilibrium

Limiting step

Often a reaction has two or more steps. One of the steps, usually the last one, is the slowest
step, and is said to berate-limiting.

Steady state approximation

Sometimes it is useful, when calculating the reaction rate, to assume that no particular step
is rate-limiting. Instead, the reaction intermediate can either proceed to the product or
return to the original reactant with an equal rate for either possibility. This is called the
steady-state approximation.

113.1.4 Example

A classical example is the hydrolysis of haloalkanes:

R-X + H 2 O→ROH + HX

This reaction can occur by two mechanisms: the SN1 and SN. The former is a unimolecular
substitution: its rate is determined only by the concentration of R-X, without regard to
the concentration of the new substituent. The latter is bimolecular: its rate is first-order in
both R-X and new substituent, for a combined rate order of 2.

113.2 Equilibrium.

Chemical equilibriumis the state when a net reaction is neither going forward nor
backward. It is adynamicequilibrium. The rate of the forward reaction equals the rate of
the reverse reaction, so the two cancel each other out, and thenetrate of change is zero.

The chemical equilibrium is dictated by theequilibrium constant(often writtenKeq),
expressed by themass-action law:

Keq=

∏

∏i∈productsCi

j∈reactantsCj

The concentrationCcan be expressed in any scale, e.g. molar franction, molarity, partial
pressure.

If the temperature and pressure are kept constant, no matter what are the initial concentra-
tions, the system will evolve until the mass-action product is equal to the Keq. In general,
systems withKeq≪ 1 are highly displaced to the reactant sides (almost no conversion at
equilibrium), whereas whenKeq≫ 1 the reaction goes to completion.

From classical thermodynamics it can be showed that the following relation holds:

Keq=exp(−∆GR/RT)

where∆GRisthetotalchangeinGibbsfreeenergywithreaction(productminusreactants).