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Chemical Kinetics

Question
CBSEENCH12011115

What is the activation energy for a reaction if its rate doubles when the temperature is raised from 200C to 350C ?(R=8.314 J mol-1 K-1).

  • 342 kJ mol-1

  • 269 kJ mol-1

  • 34.7 kJ mol-1

  • 15.1 kJ mol-1

Solution

C.

34.7 kJ mol-1

Given, initial temperature,
T1 = 20+273 =293 K
Final temperature
T2 =35+273 = 308 K
R= 8.314 J mol-1 K-1 
Since, rate becomes double on raising temperature,
therefore,
r2 =2r1 or r2/r1 = 2
As space rate space constant comma space straight k space straight alpha space straight r
therefore space straight k subscript 2 over straight k subscript 1 space equals space 2
From space Arrnhenius space equation comma we space know space that
log straight k subscript 2 over straight k subscript 1 space equals negative fraction numerator straight E subscript straight a over denominator 2.303 straight R end fraction open square brackets fraction numerator straight T subscript 1 minus straight T subscript 2 over denominator straight T subscript 1 straight T subscript 2 end fraction close square brackets
log space 2 space equals negative fraction numerator straight E subscript straight a over denominator 2.303 space straight x 8.314 end fraction open square brackets fraction numerator 293 minus 308 over denominator 293 space straight x 308 end fraction close square brackets

0.3010 equals negative fraction numerator straight E subscript straight a over denominator 2.303 space straight x 8.314 end fraction open square brackets fraction numerator negative 15 over denominator 293 space straight x 308 end fraction close square brackets

therefore comma
straight E subscript straight a space equals space fraction numerator 0.3010 space straight x 2.303 space straight x 8.314 space straight x 293 space straight x 308 over denominator 15 end fraction
equals space 34673.48 space straight J space mol to the power of negative 1 end exponent space equals space 34.7 space kJ space mol to the power of negative 1 end exponent