For a first order reaction, more than one option are correct-

Question

For a first order reaction, more than one option are correct- (A) The degree of dissociation is equal to (1- e - K t) (B) The time taken for the completion of 75 % reaction is thrice the t1 / 2 of the reaction (C) The pre-exponential factor in the Arrhenius equation has the dimension of time, ( T -1) (D) Both (a) (c)

Tardigrade Admin · Accepted Answer

In option a, for first order reaction, if degree of dissociation is

α,

then

k = \frac{2.303}{t} lo g_{10} \frac{1}{1 - α}

or

k t = lo g_{e} \frac{1}{1 - α} = - lo g_{e} (1 - x)

e^{- k t} = 1 - α

α = 1 - e^{- k t}

in option,c according to Arrhenius equation

k = A . e^{- E_{a} / Rt}

A has

T^{(- 1)}

dimension

Q. For a first order reaction, more than one option are correct-

The degree of dissociation is equal to $(1 - e^{- K t})$

The time taken for the completion of $75%$ reaction is thrice the $t_{1/2}$ of the reaction

The pre-exponential factor in the Arrhenius equation has the dimension of time, $(T^{- 1})$

Both (a) & (c)

Q. For a first order reaction, more than one option are correct-

The degree of dissociation is equal to (1−e−Kt)

The time taken for the completion of 75% reaction is thrice the t1/2​ of the reaction

The pre-exponential factor in the Arrhenius equation has the dimension of time, (T−1)

Both (a) & (c)

In option a, for first order reaction, if degree of dissociation is α, then k=t2.303​log10​1−α1​ or kt=loge​1−α1​=−loge​(1−x) e−kt=1−α α=1−e−kt in option,c according to Arrhenius equation k=A.e−Ea​/Rt A has T(−1) dimension

The degree of dissociation is equal to $(1 - e^{- K t})$

The time taken for the completion of $75%$ reaction is thrice the $t_{1/2}$ of the reaction

The pre-exponential factor in the Arrhenius equation has the dimension of time, $(T^{- 1})$