Problem: Reaction A and reaction B have identical frequency factors. However, reaction B has a higher activation energy than reaction A.Which reaction has a greater rate constant at room temperature?

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The temperature dependence of a chemical reaction is represented by the Arrhenius equation:


<math xmlns="http://www.w3.org/1998/Math/MathML"><menclose mathcolor="#0000FF" notation="box"><mi>k</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>A</mi><mo>&#xB7;</mo><msup><mi>e</mi><mrow><mo>-</mo><mfrac><msub><mi>E</mi><mi>a</mi></msub><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></mrow></msup></menclose><mspace linebreak="newline"></mspace><mi>w</mi><mi>h</mi><mi>e</mi><mi>r</mi><mi>e</mi><mo>,</mo><mspace linebreak="newline"></mspace><mi mathvariant="normal">k</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>rate</mi><mo>&#xA0;</mo><mi>constant</mi><mspace linebreak="newline"></mspace><mi mathvariant="normal">A</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>frequency</mi><mo>&#xA0;</mo><mi>factor</mi><mspace linebreak="newline"></mspace><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>activation</mi><mo>&#xA0;</mo><mi>energy</mi><mspace linebreak="newline"></mspace><mi mathvariant="normal">R</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>gas</mi><mo>&#xA0;</mo><mi>constant</mi><mspace linebreak="newline"></mspace><mi mathvariant="normal">T</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>temperature</mi></math>


We have to determine whether reaction A or reaction B has a greater rate constant at room temperature while we are given that the activation energy for reaction B is higher.


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Problem Details

Reaction A and reaction B have identical frequency factors. However, reaction B has a higher activation energy than reaction A.

Which reaction has a greater rate constant at room temperature?

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