Effect of temperature on rate of reation

Question

Which reaction has a minimum increase in the rate of reaction for a !!10^@!! increase in temperature?

  • Backward Reaction
  • Forward Reaction
Solution

We know:
!!k = Ae^(-E/(RT))!! where !!E!! is energy of activation.

This can be written as !!ln k = ln A - (E/(RT))!!

!!lnk_2-lnk_1=E/R(1/T_1-1/(T_1+10))!!

!!E_("forward")>E_("backward")!!

!!E_("forward")/R(1/T_1-1/(T_1+10))>E_("backward")/R(1/T_1-1/(T_1+10))!!

!!lnk_("forward 2")-lnk_("forward 1") > lnk_("backward 2")-lnk_("backward 1")!!

Thus, rate constant of backward reaction increases less than rate constant of forward reaction. Hence, answer is backward reaction.

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