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A first order reaction is 50% completed ...

A first order reaction is 50% completed in 40 minutes at 300K and in 20 minutes at 320K. Calculate the activation energy of the reaction.
(Given:`log2=0.3010," "log4=0.6021, " " R=8.314J.K^(-1)."mol"^(-1))`

Text Solution

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`k_(1)=(0.693)/(40)=0.017325" min"^(-1)`
`k_(2)=(0.693)/(20)=0.03465" min"^(-1)`
`thereforelog ((k_(2))/(k_(1)))=(E_(a))/(2.303xx8.314)xx(320-300)/(320xx300)`
or, `log .((0.03465)/(0.017325))=(E_(a))/(2.303xx8.314)xx(20)/(320xx300)`
or, `E_(a)=(log2xx2.303xx8.314xx320xx300)/(20)`
`=27666.55 " J.mol"^(-1)=27.66655"kJ.mol"^(-1)`
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