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The first order rate constant for the de...

The first order rate constant for the decompoistion of `C_(2)H_(5)I` by the reaction.
`C_(2)H_(5)I(g)rarrC_(2)H_(4)(g)+HI(g)`
at `600 K is 1.60xx10^(-5)s^(-1)`. Its energy of activation is `209 kJ mol^(-1)`. Calculate the rate constant at `700 K`

Text Solution

Verified by Experts

Here, `T_(1)=600" K",k_(1)=1.60xx10^(-5)s^(-1)`
`T_(2)=700" K",k_(2)=?,E_(a)=209" kJ mol"^(-1)`
Applying Arrhenius equation, `log""(k_(2))/(k_(1))=(E_(a))/(2.303R)((1)/(T_(1))-(1)/(T_(2)))`
or `logk_(2)=logk_(1)+(E_(a))/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2)))=log(1.60xx10^(-5))+(209000" J mol"^(-1))/(2.303xx8.314"JK"^(-1)mol^(-1))((700-600)/(600xx700))`
`=(-5+0.2041)+2.5989=-2.197=3.8030`
`k_(2)=" Antilog"bar(3).8030=6.353xx10^(-3)s^(-1)`
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