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Which reactions are more temperature sensitive: the ones with higher $E_\mathrm{a}$ or the ones with lower $E_\mathrm{a}$? And why?

I wasn't able to find much useful content on googling it, however on doing the math I came to a conclusion that the ones with higher $E_\mathrm{a}$ are more sensitive to increase in temperature. But why is it so? I mean math proves it, but why exactly does it happen?

Here are my calculations:

enter image description here

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    $\begingroup$ hint: see Maxwell velocity or kinetic energy distribution $\endgroup$
    – Mrigank
    Commented Apr 20, 2016 at 21:10

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The reaction with the lower activation energy can proceed smoothly without the increase in temperature whereas the the reaction with the higher activation energy cannot. When you increase the temperature, it won't make much difference to the reaction with a lower activation energy since it was already fine with a lower temperature. On the contrary, the reaction with higher activation energy will now gain sufficient energy making the molecules more likely to react and thus, the temperature change affects this reaction much more.

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enter image description here

Plotting a graph between lnK vs 1/T shows that reaction having high activation energy are more temperature sensitive. Since the slope of high Ea is more steeper than the one having low Ea. This shows that rate constant hence rate of reaction will be high for large Ea

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    $\begingroup$ Hi Amit Ujjwal, welcome to Chem.SE! Take the tour to get familiar with our site. Regular text can be formatted with Markdown, and mathematical expressions and chemical equations can be formatted using Latex syntax. That said, can you please properly photoscan your image, currently it's a little difficult to interpret. Thanks! $\endgroup$
    – Gaurang Tandon
    Commented Apr 4, 2018 at 14:27

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