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Question

For a first-order homogeneous gaseous reaction, A2B+C.
If the total pressure after time t was Pt and after long time (t) was P then k in terms of Pt,P and t is :

A
k=2.303tlog(2PPPt)
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B
k=2.303tlog(2P2(PPt))
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C
k=2.303tlog(2P3(PPt))
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D
none of these
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Solution

The correct option is C k=2.303tlog(2P3(PPt))
A2B+C
t=0 Pi 0 0
t Ptx 2x x
t 0 2Pi Pi

P=3Pi or Pi=P3;Pi+2x=Pt
x=PtPi2
As we know k=2.303tlog(PiPix)

so k=2.303tlog(2P3(PPt))
Hence optoin (C) is correct.

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