Question

For a homogeneous first order gaseous reaction
A+B+C + D, the initial pressure was P. wh
pressure after time 't' was P if (P >P
expression for the rate constant K is

Answer 1

The expression for the rate constant K is $k=\frac{2.303}{t} log\frac{2P^{0} }{3P^{0}-P }$

Explanation:

consider the initial equation:

                 A     ---->  B    +    C    +     D

Initial         P              0          0           0

At time t  P-x             x           x           x

And P  =  P-x + x + x + x=P+2x

or in this

$x=\frac{P-P^{0} }{2}$

Finally

$P_{A} =P^{0} -x=P^{0} -(\frac{P-P^{0} }{2} )$

$=\frac{3P^{0}-P }{2}$

$k=\frac{2.303}{t} log(\frac{P^{0} }{P_{A} } )$

$k=\frac{2.303}{t} log\frac{P^{0} }{\frac{3P^{0}-P }{2} }$

$k=\frac{2.303}{t} log\frac{2P^{0} }{3P^{0}-P }$

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