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Question

Decomposition of 3A(g)2B(g)+2C(g) follows first order kinetics. Initially only A is present in the container. Pressure developed after 20 min. and infinite time are 3.5 and 4 atm respectively. Which of the following is/are true?

A
t50=20min
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B
t75=40min
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C
t99=64/3min
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D
t87.5=60min
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Solution

The correct options are
A t75=40min
B t50=20min
D t87.5=60min
The decomposition reaction is 3A(g)2B(g)+2C(g)

Initially, let P0 be the pressure of A.

After 20 minutes, the pressures of A, B and C are P0x,2x3and2x3 respectively.

After very large time, the pressures of A, B and C are 0,2P03and2P03 respectively.

4P03=4

Thus the initial pressure of A is P0=3atm

P0+x3=3.5

x=1.5
Thus 20 minutes is the half life period. t50=20

The time for 75% completion will be t75=2×20=40min.

The time for 87.5% completion will be t87.5=3×t50=3×20=60min

The time for 99% completion will be t99=23×t99.9=23×10×t50=4003.

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