Chemical Kinetics

Chemical Kinetics

Question

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be (R = 8.314 JK–1 mol–1 and log 2 = 0.301)

  • 53.6 kJ mol-1

  • 48.6 kJ mol-1

  • 58.5 kJ mol-1

  • 60.5 kJ mol-1

Answer

A.

53.6 kJ mol-1

By using Arrhenius equation,
log space straight k subscript 2 over straight k subscript 1 space equals space fraction numerator negative straight E subscript straight a over denominator 2.303 space straight R end fraction open parentheses 1 over straight T subscript 2 minus 1 over straight T subscript 1 close parentheses space.... space left parenthesis straight i right parenthesis
therefore space straight k subscript 1 over straight k subscript 2 space equals space straight r subscript 1 over straight r subscript 2
rightwards double arrow straight k subscript 1 over straight k subscript 2 space equals space fraction numerator straight r subscript 1 over denominator 2 straight r subscript 1 end fraction
straight k subscript 1 over straight k subscript 2 space equals space 1 half
straight k subscript 2 over straight k subscript 1 space equals space 2
Given, T2 = 310; T1 = 300K
On putting values in Eq (i), we get
log space 2 space equals space fraction numerator negative straight E subscript straight a over denominator 2.303 space straight x space 8.314 end fraction open parentheses 1 over 310 minus 1 over 300 close parentheses
rightwards double arrow space straight E subscript straight a space equals space 53598.6 space straight J divided by mol space equals space 53.6 space kJ divided by mol

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