Question

# 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 5.21×10−3 min−1N2O5(g)→2NO2(g)+12O2(g)Initialpressurea00Attimeta−x2xx2Atcompletedissociation02aa22N2O5(g)→4NO2(g)+O2(g)ORTotal number of moles at time t=a−x+2x+x2=a+32xTotal number of moles at complete dissociation =2a+a2=52a∴52a∝584.5mmHg ----- (1)and a+32x∝284.5mmHg -------(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=2.303tlogaa−x=2.30330minlog233.8(233.8−33.8)=5.21×10−3min−1Hence, the correct option is A

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