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Arrhenius Equation

For which of ...

Question

For which of the following reactions $k_{310} / k_{300}$ would be maximum?

A + B ⟶ C;

E_{a} = 50 k J

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X + Y ⟶ Z;

E_{a} = 40 k J

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P + Q ⟶ R;

E_{a} = 60 k J

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E + F ⟶ G;

E_{a} = 100 k J

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Solution

The correct option is C $E + F ⟶ G;$ $E_{a} = 100 k J$
$\frac{k_{310}}{k_{300}} = e^{- ⎛ ⎝ \frac{E_{a} (310 k)}{310 k_{B}} - \frac{E_{a} (300 k)}{{300 k}_{B}} ⎞ ⎠}$
Assuming $E_{a} (310 k) = E_{a} (300 k)$
$\frac{k_{310}}{k_{300}} = e^{- \frac{E_{a}}{k_{B}} (\frac{1}{310} - \frac{1}{300})}$
$∴$ for light $E_{a}$ we have highest ratio. thus $E_{a} = 100 k J$ is highest and is the answer.

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Similar questions

E a

E a

A ⟶ B

k_{1} = A_{1} e^{- {E a}_{1} / (R T)}

X ⟶ Y

k_{2} = A_{2} e^{- {E a}_{2} / (R T)}

A_{1} = 10^{8}, A_{2} = 10^{10}

{E a}_{1} = 600 c a l / m o l, {E a}_{2} = 1800 c a l / m o l

k_{1} = k_{2}

R = 2 c a l / k m o l

k_{310} / k_{300}

x = \frac{e^{a} + e^{- a}}{2 \sqrt{3}}, y = \frac{e^{a} - e^{- a}}{2}

r = ρ Z_{A B} e^{\frac{- E a}{R T}}

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