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For the reaction of H(2) with I(2), the ...

For the reaction of `H_(2)` with `I_(2)`, the constant is `2.5 xx 10^(-4) dm^(3) mol^(-1)s^(-1)` at `327^(@)C` and `1.0 dm^(3) mol^(-1) s^(-1)` at `527^(@)C`. The activation energy for the reaction is `1.65 xx 10x J//"mole"`. The numerical value of x is __________. `(R = 8314JK^(-1) mol^(-1))`

A

150

B

72

C

166

D

59

Text Solution

Verified by Experts

The correct Answer is:
C
`k_(1) =2.5xx10^(-4)" dm"^(3)" mol"^(-1) s^(-1) T_(1) =327^(@)C rArr 600 K`
`k_(2)=1.0" dm"^(3)" mol"^(-1)s^(-1) T_(2) =527^(@)C rArr 800 K`
`E_(A) rArr" in kJ/mole"`
Given R=8.314 J/k mole
From `log""(k_(2))/(k_(1))=(E_(a))/(2.303 R) ((1)/(T_(1))-(1)/(T_(2)))`
`log""(1)/(2.5xx10^(-4)) =(Ea)/(2.303 R) ((1)/(T_(1))-(1)/(T_(2))) rArr" log "(1)/(2.5xx10^(-4))=(Ea)/(2.303xx8.314) ((1)/(600)-(10)/(800))`
`E_(a) =165.54 kJ`
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