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Question

The decomposition of N2O5 according to equation: 2N2O5(g)4NO2(g)+O2(g), is a first-order reaction. After 30 minutes from the start of the decomposition in a closed vessel, the total pressure developed is found to be 284.5 mm of Hg and on complete decomposition, the total pressure is 584.5 mm of Hg.

The rate constant of a reaction is:

A
5.206×103min1
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B
4.261×103min1
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C
3.316×104min1
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D
None of these
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Solution

The correct option is A 5.206×103min1
For the given reaction:

2N2O5(g)4NO2(g)+O2(g)
a 0 0 -------- initial time (t=0)
aX 2X X/2 ------- after time (t=30 min)
0 2a a/2 ----- after complete reaction

No. of mole at any time pressure developed at that time
aP0 at t=0 ------- 1

a+(3X/2)284.5 at t=30 ------ 2

(5a/2)584.5 at t=completely reacted ------ 3

From 1 and 3 equation, we get
a233.8 ----------------------- 4

Substituting 4 in 2 equation we get
X33.8 --------------------------------- 5

Now,

K=2.303tloga(aX)

K=2.30330log233.8200

=5.206×103min1
Option A is correct.

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