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N2O5 decomposes according to the equation, N2O5(g)2NO2(g)+12O2(g)
This is a first order reaction. A closed container has N2O5 and Ne gases at a total pressure of 333.8 mm of Hg. Thirty minutes after N2O5 starts decomposing, the total pressure is found to be 384.5 mm Hg. On complete decomposition of N2O5, the total pressure is 684.5 mm Hg. What is rate constant of decomposition of N2O5?
(Take ln(1.169) = 0.156)

A
2.6×101 s1
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B
0.312 s1
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C
5.2×103 s1
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D
8.67×105 s1
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Solution

The correct option is C 5.2×103 s1
N2O5(g)2NO2(g)+12O2(g)

000initial pressurep0p2p12pat 30 min02p0p02at long time

Let p1 be the pressure of Ne gas.
Then, p0+p1=333.8 mm of Hg .....(1)
p0+32p+p1=384.5 mm of Hg .....(2) and
2p0+12p0+p1=684.5 mm of Hg (3)
Solving equation (1), (2) and (3)
p0=233.8 mm of Hg and p=33.8 mm of Hg
So, k=130lnp0p0p=130ln233.8200 =130ln1.169=0.15630=5.2×103 min1
=8.67×105s1

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