Rate constant of a reaction depends upon

For reaction $A o B,$ the rate constant ${k_1} = {A_1}{e^{ - E{a_1}/RT}}$ and for the reaction $X o Y,$ the rate constant${k_2} = {A_2}{e^{ - E{a_2}/RT}}.$ If ${A_1} = {10^8},{A_2} = {10^{10}}$ and $E{a_1} = 600\;{\rm{cal}}/{\rm{mol}},\;E{a_2} = 1800\;{\rm{cal}}/{\rm{mol}},$ then the temperature at which ${k_1} = {k_2}\;is\;\left( {R = 2\;{\rm{cal}}/{\rm{k }}\;{\rm{mol}}} \right)$

Temperature coefficient of a reaction is 2. When temperature is increased from $30^\circ C\;to\;100^\circ C$, rate of the reaction increases by

In a reaction $2A o products$; the concentration of A decreases from $0.5\;{\rm{mol}}\;{\rm{litr}}{{\rm{e}}^{ - 1}}\;to\;0.4\;{\rm{mol}}\;{\rm{litr}}{{\rm{e}}^{ - 1}}$ in 10 minute. The rate of reaction during this interval is:

The order of reaction, with respect to one of the reacting component $Y$, is zero. In implies that

The rate constant of a first order reaction is $3 imes {10^{ - 6}}$ per second and initial concentration is $0.10\;{\rm{ }}M.$ Then the initial rate of reaction is

Arrhenius equation is

Consider following two reaction,A o product - \frac{{d\left[ A \right]}}{{dt}} = {k_1}{\left[ A \right]^0}$$B o product - \frac{{d\left[ B \right]}}{{dt}} = {k_2}{\left[ B \right]^0}$${k_1}\;and\;{k_2} are expressed in term of molarity $\left( {mol\;{L^{ - 1}}} \right)$) and time ${s^{ - 1}}$ as

For the reaction, ${{\rm{N}}_2}{{\rm{O}}_5} o 2{\rm{N}}{{\rm{O}}_2} + \frac{1}{2}{{\rm{O}}_2}$

Given, $- \frac{{d\left[ {{{\rm{N}}_2}{{\rm{O}}_5}} \right]}}{{dt}} = {K_1}\left[ {{{\rm{N}}_2}{{\rm{O}}_5}} \right]$

$\frac{{d\left[ {{\rm{N}}{{\rm{O}}_2}} \right]}}{{dt}} = {K_2}\left[ {{{\rm{N}}_2}{{\rm{O}}_5}} \right]$

${\rm{and}}\;\;\frac{{d\left[ {{{\rm{O}}_2}} \right]}}{{dt}} = {K_3}\left[ {{{\rm{N}}_2}{{\rm{O}}_5}} \right]$

The relation in between ${K_1},{K_2}\;and\;{K_3}$ is:

According to Arrhenius equation, the rate constant $\left( k \right)$ is related to temperature $\left( T \right)$ as

For a reaction $\frac{1}{2}A o 2B$, rate of disappearance of ‘A’ is related to the rate of appearance of B by the expression