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

A
5.21×103 min1
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B
5.12×103 min1
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C
5.89×103 min1
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D
None of these
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Solution

The correct option is A 5.21×103 min1
N2O5(g)2NO2(g)+12O2(g)Initialpressurea00Attimetax2xx2Atcompletedissociation02aa2

2N2O5(g)4NO2(g)+O2(g)
OR
Total number of moles at time t=ax+2x+x2
=a+32x
Total number of moles at complete dissociation =2a+a2=52a
52a584.5mmHg ----- (1)
and a+32x284.5mmHg -------(2)

Solving 1 equation, we get a 233.8 mm Hg and on solving equation 2,we get x 33.8 mm Hg. Substituting the value in first order equation:

k=2.303tlogaax=2.30330minlog233.8(233.833.8)
=5.21×103min1

Hence, the correct option is A

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