Problem : 1
In gaseous reactions important for understanding of the upper atmosphere H2O and O react bimolecularly to form two OH radicals. DH for this reaction is 72kJ/mol at 500 K and Ea = 77 kJ/mol, then Ea for two bimolecular recombination of 2OH radicals to form H2O & O is
(A) 3 kJ mol-1
(B) 4 kJ mol-1
(C) 5 kJ mol-1
(D) 7 kJ mol-1
Sol. As ΔH is positive, therefore reaction is endothermic
This is the energy profile diagram for an endothermic reaction.
Now when the products is converted back to reactant the energy of activation is x as shown in fig.
Evidently x = Ea - ΔH
= (77 - 72) = 5 kJ mol-1 Therefore, (C)
Problem : 2
In a certain reaction 10% of the reactant decomposes in the first hour, 20% is second hour, 30% in third hour and so on. What are the dimensions of rate constant.
(B) mol lit-1 sec-1
(C) lit mol-1 sec-1
(D) mol sec-1
Sol. If the amount of products formed which is 10%, 20% and 30% is plotted against time i.e., 1 hr, 2 hr and 3 hr respectively, it is a straight line passing through the origin.
Therefore, it is a zero order reaction where x = kt ⇒ = k
Therefore, dimensions of k = moles lit-1 sec-1
Problem : 3
Two substances A(t½ = 5 mins) and B(t½ = 15 mins) are taken is such a way that initially [A] = 4[B]. The time after which the conentration of both will be equal is
(A) 5 min
(B) 15 min
(C) 20 min
(D) concentration can never be equal
Sol. t½ of A is 5 min
Therefore, in 15 mins it will become 1/8 of initial and t½ of B is 15 mins
Therefore, in 15 mins it will become ½ of initial
Therefore, ratio of [A] : [B] after 15 min is 4 : 1
But given [A] = 4[B]
Therefore, [A] = [B] after 15 min
Problem : 4
The reaction A(g) 2B(g) → C(g) D(g) is an elementary process. In an experiment, the initial partial pressure of A & B are PA = 0.60 and PB = 0.80 atm. When Pc = 0.2 atm the rate of reaction relative to the initial rate is
(Rate)i = k[A] [B]2 = k[0.6][0.8]2
(Rate)t = k[0.4] [0.4]2
= Therefore, [D]
Problem : 5
For a hypothetical reaction A B → C D, the rate = k[A]-1/2[B]3/2. On doubling the concentration of A and B the rate will be
(A) 4 times
(B) 2 times
(C) 3 times
(D) none of these
Sol. k = k-1/2 3/2 = k3/2-1/2 = k = 1 = 2k
Problem : 6
An organic compound A decomposes by following two parallel first order mechanisms :
; , k1 = 0.693 hr -1
Select the correct statement(s)
(A) If three moles of A are completely decomposed then 2 moles of B and 1 mole of C will be formed.
(B) If three moles of A are completely decomposed then 1 moles of B and 2 mole of C will be formed.
(C) half life for the decomposition of A is 20 min
(D) half life for the decomposition of B is 0.33 min
Problem : 7
For any Ist order gaseous reaction A → 2B Pressure devoloped after 20 min is 16.4 atm and after very long time is 20 atm. What is the total pressure developed after 10 min.
t = 0 PO -
t = 10 PO - P 2P
t = 20 PO - P' 2P'
2PO = 20 PO = 10
16.4 = PO - P' 2P'
16.4 = 10 P'
P' = 6.4
for first order reaction at equal time conc/pr is in G. P.
3.6 × 10 = (10 - P)2
10 - P = 6
P = 4
P10 min = PO P = 10 4 = 14 atm
Problem : 8
For any reaction, 2A → B, rate constant of reaction is 0.231 min-1. Time (in sec) when 25% of A will remain unreacted.
= 3 mm
= 180 sec
Problem : 9
For any reaction A(g) → B(g), rate constant k = 8.21 × 10-2 atm/min at 300 K. If initial concentration of A is 2M then what is the half life (in hr.)?
Rate = k =
t1/2 = = 300 min
= 5 hr.
Problem : 10
2A B C
The mechanism of the above reaction given as
2A X 2B (fast)
X B C (slow)
E1 = Activation energy for K1
E2 = Activation energy for K2
E3 = Activation energy for K3
(given : E1 = 10 kJ, E3 = 5 kJ, E2 = 12 kJ)
rate = K3 [x][B]
, [X] =
rate = k3 . , = k3 . .
Keff = , Etotal = E1 E3 - E2