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Simple Interest

Which is the ...

Question

Which is the correct expression for relating rate constant of a reaction at two different temperature?

A

l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} (\frac{T_{1} - T_{2}}{T_{1} . T_{2}})

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B

l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} (\frac{T_{2} - T_{1}}{T_{1} . T_{2}})

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C

l n \frac{k_{1}}{k_{2}} = \frac{E_{a}}{R} (\frac{T_{2} - T_{1}}{T_{1} . T_{2}})

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D

l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} (\frac{T_{2} - T_{1}}{T_{1} . T_{2}})

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Solution

The correct option is B $l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} (\frac{T_{2} - T_{1}}{T_{1} . T_{2}})$
Arrhenius equation:
$k = A e^{\frac{- E_{a}}{R T}}$

Taking natural log on both side,
$l n k = l n (A e^{\frac{- E_{a}}{R T}})$
$l n k = l n A - \frac{E_{a}}{R T}$
Let us consider, for a particular reaction $k_{1}$ and $k_{2}$ are the rate constant at temperature $T_{1}$ and $T_{2}$ .
$∴$
$l n k_{1} = l n A - \frac{E_{a}}{R T_{1}} . . . . . e q n (1)$

$l n k_{2} = l n A - \frac{E_{a}}{R T_{2}} . . . . . e q n (2)$

Subtracting equation (1) from (2) we get,
$l n k_{2} - l n k_{1} = - \frac{E_{a}}{R T_{2}} + \frac{E_{a}}{R T_{1}}$

$l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R T_{1}} - \frac{E_{a}}{R T_{2}}$

$l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$

$l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} (\frac{T_{2} - T_{1}}{T_{1} T_{2}})$

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Similar questions

k_{1} =

rate constant at temperature

T_{1}

k_{2} =

rate constant at temperature

T_{2}

for a first-order reaction, then which of the following relations is correct?
[

E_{a} =

activation Energy]

Q. Activation energy

(E_{a})

and rate constants (

k_{1}

k_{2}

) of a chemical reaction at two different temperature (

T_{1}

T_{2}

) are related by:

Q. Two different first order reactions have rate constants

k_{1}

k_{2}

T_{1} (k_{1} > k_{2})

. If temperature is increased from

T_{1}

T_{2}

, then new constants become

k_{3}

k_{4}

respectively. Which among the following relations is correct?

Q. Activation energy

(E_{a})

and rate constant

(k_{1}

k_{2})

of a chemical reaction at two different temperatures

(T_{1}

T_{2})

are related by:

Q. For decomposition of

N_{2} O_{5}

, rate constant were determined at two different temperature. At

27^{\circ} C,

rate constant was

2 \times 10^{- 4} {sec}^{- 1}

47^{\circ} C

the rate constant is

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Then identify the correct statement(s).
(Given

l n 3 = 1.1

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