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Arrhenius Equation

If for two re...

Question

If for two reactions, $E_{a_{1}} > E_{a_{2}}$ and $T C_{1}$ and $T C_{2}$ are temperature coefficient respectively, then which alternative is correct?

A

T C_{1} > T C_{2}

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B

T C_{1} < T C_{2}

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C

T C_{1} = T C_{2}

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D

none of the above

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Solution

The correct option is C $T C_{1} < T C_{2}$
As we know,
$\frac{K_{1}}{K_{2}} = e x p [- \frac{E_{a}}{2.303 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]]$
$T C_{1} = e x p [- \frac{E_{a_{1}}}{2.303 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]]$
$T C_{2} = e x p [- \frac{E_{a_{2}}}{2.303 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]]$
$∴ \frac{T C_{1}}{T C_{2}} = e x p [- \frac{(E_{a_{1}} - E_{a_{2}}) (T_{2} - T_{1})}{2.303 R T_{1} T_{2}}]$
If $E_{a_{1}} > E_{a_{2}}$ , then $T C_{1} < T C_{2}$ .

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Similar questions

Q. If for two reactions

E_{a_{1}} > E_{a_{2}}

T C_{1}

T C_{2}

are temperature coefficient respectively, then which alternative is correct?

Q. For two reactions, activation energies are

E_{a_{1}}

E_{a_{2}}

; rate constants are

k_{1}

k_{2}

at the same temperature. If

k_{1} > k_{2}

Q. Tangents to the parabola at the extremities of a common chord

A B

x^{2} + y^{2} = 5

and the parabola

y^{2} = 4 x

intersect at the point

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A B C D

is constructed on this chord lying inside the parabola, then

\frac{{[{(T C)}^{2} + {(T D)}^{2}]}^{2}}{1600}

Q. For reaction;

A \to B

, the rate of constant

k_{1} = A_{1} e^{- E a_{1} / R T}

and for the reaction;

P \to Q

, the rate constant

k_{2} = A_{2} e^{- E a_{2} / R T}

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

E a_{1} = 600, E a_{2} = 1200

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Q. For a reaction

A ⟶ B

, the rate constant

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and for the reaction

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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

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