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The order of a reaction determines how sensitive the reaction rate responds to
Changes in reactant concentrations.
For a zero order reaction is no dependence of the
The rate of concentration.
For a first order reaction
is the speed proportional to the concentration, and at a reaction
Second-order
the reaction is very sensitive.
The kinetics of the decay of NO2 was
investigated experimentally. The concentrations during the reaction increases the NO2
in the manner suggesting that the half-life was longer.
A quanitative study provided
the reaction rate law r = k (2) * [NO2] ²
r = k (2) * [NO2] ²
This is a classic second order reaction.
When the concentration drops to half,
is the speed to a quarter.
If the concentration decreases, a third speed is to
ninth back.
An example of a reaction with the total order Two
and two reactants (starting materials) is the Sn2 reaction (nucleophilic substitution second.
Order) -
for example, the reaction
between methyl bromide and hydroxide ions. If both reactant
be doubled
increases the reaction rate by a factor of four.
A frequently performed in the lab sample second order reaction is alkaline ester hydrolysis.
(Eg cleavage of ester with sodium hydroxide)
In this reaction, the course of the reaction
be followed very well by conductometric measurements.
The unit of reaction rate constant - typical for a second order reaction
Moles per liter and minute.
The rate law
is a differential equation.
For a second order reaction, the integration is simple.
We obtain the
integrated rate law
(The relationship between [A] and t): [A] = [A] ° / (1 + [A] ° * k (2) * t)
The half-life of a second order reaction
is not constant, but is
with the reaction progresses, more and more.
These relationships hold for a second order reaction, if only one reactant (the reactant) second car if you long for a
present
They also apply to a reaction with the overall order two and two reactants,
if these are reacted stoichiometrically.
If we are in such a reaction, the
Do not use stoichiometric reactants
The integrated rate law is somewhat more complicated:
We will then
k (2) * t = 1 / ([A] ° - [B] °) * ln (([A] [B] °) / ([B] [A] °))
k (2) * t = 1 / ([A] ° - [B] °) * ln (([A] [B] °) / ([B] [A] °))
The derivation of this equation
You will find in most physico-chemical textbooks -
(Integration requires a partial fractions)
(Compilation: Reactions with simple kinetics)
In the following figure, again for a reaction A-> E, the three reaction orders
Zero, one
and two
compiled:
If the plot of the concentration versus time ([A] = f (t)) is a straight line,
is a reaction
Zero order before.
If the plot of the logarithm of the concentration versus time (ln [A] = f (t)) a
Is straight,
the reaction is first order kinetics after.
And when the plot of the reciprocal of the concentration vs. time (1 / [A] = f (t)) is a straight line,
of the reaction is second order.
Indicator for zero order reactions - reaction rate constant.
- Linear integrated rate law - half life is getting shorter
- Half-life is getting shorter
Indicator for first-order reactions: - the speed is proportional to the concentration
- Speed is proportional to the concentration
- "Exponential" integrated rate law
- Half-life is constant
Indicator for second order reactions: - Speed is proportional to [A] ²
(Squared
concentration of the reactants)
- Integrated rate law of the form [A] = [A] ° / (1 + [A] ° k * (2) * t) - Half-life keeps getting longer
- Half-life keeps getting longer
Integrated rate law for reactions with the overall order two and two reactants
in non-stoichiometric driving style: k (2) * t = 1 / ([A] ° - [B] °) * ln (([A] [B] °) / ([B] [A] °))
k (2) * t = 1 / ([A] ° - [B] °) * ln (([A] [B] °) / ([B] [A] °))