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The gaseous decomposition reaction, A(g)2B(g)+C(g) is observed to first order the excess of liquid water at 25oC. It is found that after 10 minutes the total pressure of system is 188 torr and after very long time it is 388 torr. The rate constant of the reaction (in hr1) is:
[Given: vapour pressure of H2O at 25oC is 28 torr. (ln2=0.7,ln3=1.1,ln10=2.3)]

A
0.02
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B
1.2
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C
0.2
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D
none of these
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Solution

The correct option is D 1.2
By putting values in equation k=2.303tlogP0(P0x)=2.303tlogP/3(P/3(PtP0))

We will get answer as k=1.2hr1

(A,B,C) let the initial pressure of A be Ps mm of Hg and the pressure of A decreases in 10 minute be x unit.

A(g)2B(g)+C(g)InitiallyP000At time 10 minP0x2xxAttime02P0P0
After long time interval, P=2P0+P0=3P0
After t time Pt=P0+2x
For a first order reaction, the rate constant expression would be
k=2.303tlogP0P0x

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