The rate expression can be defined as the stoichiometric coefficients of reactants and products. An expression in which the rate of reaction is given in terms of the molar concentration of the reactants, with each term raised to some power, which may or may not is the stoichiometric coefficient of the reacting species in a balanced chemical equation.
The rate constant can be defined as the rate of the reaction when the concentration of each of the reactant is taken as unity.
Example: 2NO(g)+O2(g)--- 2NO2(g)
The rate expression for the above reaction can be written as follows:
Rate = k [NO]2 [O2] (Experimentally determined)
Now, if the concentration of NO and O2 is taken to be unity, then the rate constant is found to be equal to the rate of the reaction.
For the reaction
2NO(g) + Cl2(g) --> 2NOCl(g)
The following data were collected. All the measurements were taken at 263 K:
|
Experiment No. |
Initial [NO] (M) |
Initial [Cl2] (M) |
Initial rate of disappearance of Cl2(M/min) |
|
1 |
0.15 |
0.15 |
0.60 |
|
2 |
0.15 |
0.30 |
1.20 |
|
3 |
0.30 |
0.15 |
2.40 |
|
4 |
0.25 |
0.25 |
? |
(a) Write the expression for rate law.
(b) Calculate the value of rate constant and specify its units.
(c) What is the initial rate of disappearance of Cl2 in exp. 4?
(a) For a reaction A + B --> P, the rate law is given by,
r = k [A]1/2 [B]2.
What is the order of this reaction?
(b) A first order reaction is found to have a rate constant k = 5·5 x 10-14 s-1. Find the half-life of the reaction.
(a)
For A + B--> P
r = k [A]1/2 [B]2
The order of the reaction = 
(b) For first order reaction
k = 5.5 x 10-14 s-1
Half-life period (
) for the first order reaction
The rate constant of a first order reaction increases from 2 — 10-2 to 4 — 10-2when the temperature changes from 300 K to 310 K. Calculate the energy of activation (Ea).
(log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)
According to the Arrhenius equation.
K = Ae(-Ea/RT)
From this, we get
We are given that
initial temperature T1=300K
Final temperature T2=310 K
Rate constant at initial temperature, k 1 = 2 x 10-2
Rate constant at final temperature, k2 = 4 x 10-2
Gas constant, R = 8.314 J K-1
Substituting the value, we get
Therefore activation energy of the reaction, Ea = 
= 535985.94 J mol-
= 535.98 kJ mol-1
Nitrogen pentoxide decomposes according to equation: 2N2O5(g)---> 4NO2(g) + O2(g)
This first order reaction was allowed to proceed at 40° C and the data below were collected:
|
[N2O5] (M) |
Time (min) |
|
0.400 |
0.00 |
|
0.289 |
20.0 |
|
0.209 |
40.0 |
|
0.151 |
60.0 |
|
0.109 |
80.0 |
(a) Calculate the rate constant. Include units with your answer.
(b) What will be the concentration of N2O5 after 100 minutes?
(c) Calculate the initial rate of reaction.
|
[N2O5] (M) |
Time (min) |
log (N2O5] |
|
0.400 |
0.00 |
-0.3979 |
|
0.289 |
20.0 |
-0.5391 |
|
0.209 |
40.0 |
-0.6798 |
|
0.151 |
60.0 |
-0.8210 |
|
0.109 |
80.0 |
-0.9625 |
From the plot, log [N2O5] v/s t, we obtain by
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