Question

For a reaction the energy of activation is zero. What is the value of rate constant at $300K$ , if $k = 1.6 \times {10^6}{s^{ - 1}}$ at $298K$ ? $\left[ {R = 8.31J{K^{ - 1}}mo{l^{ - 1}}} \right]$ .

Answer 1

Hint: We have to know that, the rate steady, or the particular rate consistent, is the proportionality constant in the condition that communicates the connection between the pace of a synthetic response and the convergences of the responding substances.

Complete answer:
We need to know that in actual science, the Arrhenius condition is an equation for the temperature reliance of response rates. The condition was proposed by Svante Arrhenius, in the view crafted by Dutch physicist Jacobus Henricus van't Hoff who had noted, that the van 't Hoff condition for the temperature reliance of harmony constants recommends such a recipe for the paces of both forward and switch responses. This condition has a huge and significant application in deciding pace of substance responses and for computation of energy of initiation. Arrhenius gave actual support and understanding for the formula. Currently, it is best seen as an experimental relationship. It can be utilized to display the temperature variety of dissemination coefficients, populace of precious stone opening, creep rates, and numerous other thermally-incited measures.
In the given data,
${T_1} = 298K$ , ${T_2} = 300K$, ${k_1} = 1.6 \times {10^6}{s^{ - 1}}$ , ${k_2} = ?$ , ${E_a} = 0$ ,
By using Arrhenius equation,
$\log \dfrac{{{k_1}}}{{{k_2}}} = \dfrac{{{E_a}}}{{2.303R}}\left[ {\dfrac{{{T_2} - {T_1}}}{{{T_2}{T_1}}}} \right]$
Where,
${E_a} = 0$
Therefore,
$\log \dfrac{{{k_1}}}{{{k_2}}} = 0$
Then,
$\dfrac{{{k_1}}}{{{k_2}}} = 1$ (or) ${k_1} = {k_2}$
Therefore, the rate constant at $300K$ is $1.6 \times {10^6}{s^{ - 1}}$ .

Note:
We need to remember that Arrhenius contended that for reactants to change into items, they should initially gain a base measure of energy, called the actuation energy. At an outright temperature T, the small amount of particles that have an active energy more noteworthy than activation energy can be determined from measurable mechanics.