1. The document discusses slow reactions, their rates, and various methods to measure reaction rates including observing changes in partial pressure, concentration, color, spectrophotometry, conductance, and calorimetry. 2. It also covers molecularity and order of reactions, chain reactions involving initiation, propagation, termination and retardation steps, and using the steady state approximation to derive rate laws. 3. An example is given for determining the rate of the chain reaction between H2 and Br2 and the thermal decomposition of acetaldehyde is discussed as a specific example of a three-halves order reaction.

1. • Slow reaction and its rate determination
• Molecularity of reactions
• Chain reaction and mechanism

2. Slow reaction: These are the reactions which proceed slowly and their
rates can be measured by conventional methods. An example is the
inversion of cane sugar in aqueous solution.
C12H22O11O → C6H12O6 + C6H12O
cane sugar Glucose Fructose
In slow reaction a large number of bonds have to be broken in reactant
molecules and a large number of new bonds have to be form in the
product molecules.

3. Measurement of Rate of Slow Reaction
There are several techniques, in general, to measure the rate of slow reactions. They are:
1. By Observing The Partial Pressure Change:
Reactions that occur in gaseous phase proceed by changing the partial pressures of the
reactant species. So, by observing how the partial pressure changes, rate of the reaction
can be observed.
.Conversation of CH3NC to CH3CN

4. 2. By observing the change of concentration:
When the density measurements are restricted to dilute solutions, the change in
concentration of the sample is a function of the percentage completion of the
reaction.

5. 3. By Colorimetric Method:
Colorimetry may be adopted to the study of reactions in which the disappearance
of a colored reactant results in the formation of a differently colored product. By
observing the change of color with time, the reaction rate can be calculated.

6. 4.By Spectrophotometric method:
Every chemical species has an identical spectrum in UV-Vis or even IR
spectra. By observing the spectra of the whole chemical reaction, the
change of reactants’ absorption spectra with time the rate of the whole
chemical process can be calculated.

7. 5.By observing the conductance change:
Reactions that correspond with the formation of various ions, the rate of such reactions
can be observed by measuring the change of conductance with time. Not all the ions
contribute same in the conductance and hence, conduction changes as the reaction
proceeds.
The equation regarding this: Ct =
1
𝐴 0
𝑘
𝐶0
−𝐶𝑡
𝑡
+ 𝐶∞

8. 6.Calorimetry method:
• Calorimetry is a unique among the methods used to determine
kinetics of slow reaction .
• Calorimetry directly measures the rate of heat generation which is
proportional to the rate of the process.
• The equation regarding this:
Rmd =
∅
∆𝐻
Here,
Rmd is the minimum detectable rate of the slow reaction
Ø is the minimum detectable heat rate of the calorimeter.
∆H is the enthalpy change for the reaction .

9. A plot of Ø×∆H versus kt to determine rate of slow reaction.

10. Molecularity of a Reaction
Molecularity of a reaction:
• The molecularity of a reaction is defined as the number of reactant
molecules which take part in an elementary reaction or rate determining
step.
• The reaction are said to be unimolecular , bimolecular or tri molecular
depending upon whether one ,two or three molecules are involved in a
chemical reaction.
For example, H2 + I2 →2HI
The molecularity and order of the reaction is two.
C12H22O11 + H2O → C6H12O6 + C6H12O6
Sucrose GLUCOSE FRUCTOSE
The molecularity of the reaction is two but order is one.

13. Order of a reaction:
• The order of a reaction is defined as the sum of powers of the concentration
terms in the rate equation.
• The molecularity and order of a reaction are generally different. But
sometimes they may be same.
Types of reaction with respect to their Order
First-Order Reaction Zero-Order Reaction
Pseudo-Order
Reaction
Second-Order
Reaction

16. The Steady-State Approximation
• The steady-state approximation is a method used to derive a rate law.
• The method is based on the assumption that one intermediate in the
reaction mechanism is consumed as quickly as it is generated.
• Intermediate’s concentration remains the same in a duration of the
reaction.

17. Chain Reaction
Chain reaction: A chain reaction is a sequence of reactions where a
reactive product or by-product causes additional reactions to take place.
Steps of Chain Reaction
Initiation Propagation
Termination Retardation
Chain reaction: A chain reaction is a sequence of reactions where the
formation of free radicals initiate the reactions and the reactions proceed
until the free radicals terminate.

18. The main types of steps in chain reaction are of the following types:
• Initiation: In which a reactive intermediate, which may be an atom,
anion, or a neutral molecular fragment is formed, usually through the
action of an agent such as light, heat or a catalyst. Formation of active
particles or chain carriers.
• Propagation: Whereby the intermediate reacts with the original
reactants, producing stable an another intermediate, whether of the same
or different kind; the new intermediate reacts as before, so a repetitive
cycle begins. In effect the active particle serves as a catalyst for the overall
reaction of the propagation cycle. Particular cases are:
• Termination: It is an elementary step in which the active particle loses its
activity; e. g. by recombination of two free radicals.

19. Mechanism of Formation of HBr
1. Initiation:
Br2 → 2Br• (thermal) or Br2 + hv → 2Br• (photochemical)
Each ‘Br’ atom is a free radical, indicated by the symbol ‘•’ representing an
unpaired electron.
2. Propagation:
Br• + H2 → HBr + H•
H• + Br2 → HBr + Br•
The sum of these two steps corresponds to the overall reaction H2 + Br2 →
2 HBr, with catalysis by Br• which participates in the first step and is
regenerated in the second step.

20. 3) Retardation (inhibition):
H• + HBr → H2 + Br•
this step is specific to this example, and corresponds to the first propagation
step in reverse.
4) Termination:
2 Br• → Br2
recombination of two radicals, corresponding in this example to initiation in
reverse.

21. Let consider a reaction,
H2 + Br2
𝑘
2HBr
Normally the reaction rate for the reaction is,
Ѵt =
𝑘[𝐻2][𝐵𝑟2]
3
2
1+
[𝐻𝐵𝑟]
𝑚[𝐵𝑟2]
Where k and m are constants; the value of m is about 10 and is
practically independent of temperature.
But the accepted mechanism for the reaction of Br2 and H2 is chain mechanism
.The mechanism have the following steps.
Determination of rate of a chain reaction

22. Initiation :
Br2 + M
𝑘 𝑖
2Br▪ + M
Chain propagation:
Br▪ + H2
𝑘 𝑝
HBr + H▪
Br2 + H▪
𝑘 𝑝
′
HBr + Br▪
Retardation:
H▪ + HBr
𝑘 𝑟
H2 + Br▪
Termination:
Br▪ + Br▪ + M
𝑘 𝑡
Br2 + M
The steady state hypothesis must be applied to the two intermediates
Br▪ and H▪, both of which are present at very low concentrations. The
steady state equation for H is
𝑑[𝐻▪]
𝑑𝑡
= kp[Br▪][H2] – 𝑘 𝑝
′
[H▪][Br2] - kr[H▪][HBr] = 0 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙(1)
And for Br▪ is
𝑑[𝐵𝑟▪]
𝑑𝑡
=2ki[Br2][M] – kp[Br▪][H2] + 𝑘 𝑝
′
[H▪][Br2] + kr[H▪][HBr] – 2kt[Br▪]2[M]
= 0 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙(2)
So, [Br▪] = (
𝑘 𝑡
𝑘 𝑡
)
1
2 . [Br2]
1
2 [H▪] ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙(3)
Substitution the value of [H▪] in equation (3),

23. [H▪] =
𝑘 𝑝 (
𝑘 𝑖
𝑘 𝑡
)
1
2 [𝐻2][𝐵 𝑟2]
1
2
𝑘 𝑝
′ 𝐵𝑟2 + 𝑘 𝑟 [𝐻𝐵𝑟 ]
So the rate of formation of [HBr] is ,
𝑑[𝐻𝐵𝑟 ]
𝑑𝑡
= kp[Br▪][H2] + 𝑘 𝑝
′
[H▪][Br2] – kr[H▪][HBr]
Now substitution the value of [H▪] and [Br▪] we get,
𝑑[𝐻𝐵𝑟 ]
𝑑𝑡
=
2𝑘 𝑝 (
𝑘 𝑖
𝑘 𝑡
)
1
2[𝐻2][𝐵𝑟2]
3
2
1+ (
𝑘 𝑝
𝑘 𝑝
′ )
[𝐻𝐵𝑟]
[𝐵𝑟2]
=
𝑘 𝐻2 [𝐵𝑟2]
3
2
1 +
[𝐻𝐵𝑟]
𝑚[𝐵𝑟2]
Where ,
K = 2𝑘 𝑝 (
𝑘𝑖
𝑘 𝑡
)
1
2 and
1
𝑚
=
𝑘 𝑝
𝑘 𝑝
′

24. Determination the rate of thermal decomposition of acetaldehyde
To obtain three-halves – order kinetics, there can still be first order
initiation , but now the termination step must be combination of two
identical chain carriers. Moreover , they must be those carries that are
involved in a second order propagation reaction. A good example is the
mechanism originally proposed by Rice and Herzfeld for the thermal
decomposition of acetaldehyde:
It has involved the following steps:
Initiation:
CH3CHO
𝑘 𝑖
▪𝐶𝐻3 + ▪CHO
Chain propagation:
CH3CHO + ▪CH3
𝐾 𝑃
𝐶𝐻4 + ▪CH3CO
▪CH3CHO
𝐾 𝑃
′
▪CH3 + CO
Chain termination:
▪CH3 + ▪CH3
𝐾 𝑡
𝐶𝐻3—CH3

25. The radical ▪CHO undergoes further reactions , but for simplicity they
are ignored here. For this reason the Rice and Herzfeld scheme is close
to the truth.
The steady state equation for the methyl radicals ,
𝑑[▪𝐶𝐻3]
𝑑𝑡
=Ki[CH3CHO] – kp[CH3CHO][▪CH3] + 𝑘 𝑝
′
[▪CH3CO] –
2kt[▪CH3]2
= 0 ……………(1)
And for the ▪CH3CO radicals ,
𝑑[▪CH3CO ]
𝑑𝑡
= kp[CH3CHO][▪CH3] - 𝑘 𝑝
′
[▪CH3CO] = 0
………………………(2)

26. From the equation 1 and 2 , we get
Ki[CH3CHO] - 2kt[▪CH3]2
= 0
So, [▪CH3] = (
𝑘𝑖
2𝑘 𝑡
)
1
2[CH3CHO]
1
2
Now the rate of formation of CH4 is ,
𝑑[𝐶𝐻4]
𝑑𝑡
=[▪CH3] [CH3CHO]
= kp [CH3CHO] (
𝑘𝑖
2𝑘 𝑡
)
1
2[CH3CHO]
1
2
= 𝑘 𝑝 (
𝑘𝑖
2𝑘 𝑡
)
1
2[CH3CHO]
3
2
= k [CH3CHO]
3
2 [where, k = 𝑘 𝑝 (
𝑘𝑖
2𝑘 𝑡
)
1
2