Rate equation and order of reaction by xiuliliaofz

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```									   Rate equation and order of
reaction
7S Chan Po Hang ( 3 )
Ng Lai Man ( 24 )

2001/1                      1
Rate equation
For a general reaction:
2A + B + 3C  D
The rate law for the above reaction can be expressed as

Rate of reaction = k Ax By Cz

where k = rate constant for the reaction at temperature
[A], [B] and [C] = concentrations
x, y and z = order of reaction

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Rate constant

The rate constant k, is temperature
dependent.
At a fixed temperature,it is a constant
for a reaction.
k

The unit of k depends on the overall
order of the reaction.
rate of reaction
E.g.    k
A B C
x    y   z

unit of k = M   1-(x+y+z) s-1

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Order of Reaction

The overall order of reaction is the sum of
powers of the concentration of individual
reactants.
The order of reaction can only be determined
experimentally.

(a) For a zeroth order reaction,
the rates of reaction are independent of the
concentration of reaction.

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(b) For a first order reaction,
the rate is directly proportional to the
concentration of the reactant.

(c) For a second order reaction,
the rate of the reaction is directly
proportional to the square of the
concentration of the reagent.

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For a simple reaction: A  products

Order of reaction      Rate law        Unit of k

d
(a)   Zeroth order                   A         Mol dm-3 s-1
dt
d
(b)   First order                 A  k A         s-1
dt
d
(c)   Second order                A  k A2   Mol-1 dm3 s-1
dt
d
(d)   N th order                  A  k An   Mol-2 dm6 s-1
dt

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Simple rate equations determined
from experimental results

(1) Initial rate method
Example:
In the kinetic study of the reaction,
CO(g) + NO2(g)  CO2(g) + NO(g)

Experiment   Initial concentration Initial concentration Initial
of CO                 of NO2                rate M/s
1            0.1 M                0.1 M                 0.015
2            0.2 M                0.1 M                 0.030
3            0.1 M                0.2 M                 0.030
4            0.4 M                0.1 M                 0.060
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Establish the rate equation for the reaction.

Solution
0.015 = k (0.1)m (0.1)n ----------(1)
0.030 = k (0.2)m (0.1)n ----------(2)
0.030 = k (0.1)m (0.2)n ----------(3)
: 0.5  0.5 
(1)                     (1)
: 0.5  (0.5) n
m

(2)                     (2)
m=1                n=1
0.060=k(0.4)(0.1)  k=1.5
Rate =k[CO][NO2]

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(2) Rate-concentration graph
Example:
Tabulated below are the initial rate of decomposition of
hydrogen peroxide at different concentrations. Plot a
graph of initial rate against concentration.

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Solution:

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(3) Log(rate)-log(concentration)
graph
log(rate)= n log[A]+log k
Slope = order

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(4) Integrated Rate equation

Order          Equation

Zeroth       [A]=-k0 + [A]0

A0    k1t
First        In
A
Second         K2t + 1/[A]0

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