1 \({{\text{k}}_2} = {\text{4}}{{\text{k}}_{\text{1}}}\)
2 \({{\text{k}}_{\text{2}}} = 0.25{{\text{k}}_{\text{1}}}\)
3 \({{\text{k}}_{\text{2}}} = 2{{\text{k}}_{\text{1}}}\)
4 \({{\text{k}}_{\text{2}}} = 0.5{{\text{k}}_{\text{1}}}\)
Explanation:
For every \(10^{\circ} \mathrm{C}\) rise, rate constant gets doubled. Hence, for every \(20^{\circ} \mathrm{C}\) rise, rate constant will be 4 times. Therefore, according to the given statement,
Temperature\(\quad 280\;{\text{K}}\quad 300\;{\text{K}}\)
\(Rateconstant{\rm{ }}\,\,{{\rm{k}}_{\rm{2}}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {{\rm{k}}_{\rm{1}}}\left( {{\rm{4}}{{\rm{k}}_{\rm{2}}}} \right)\)
\({\rm{Thus,}}{\mkern 1mu} \,\,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} {\mkern 1mu} {{\rm{k}}_{\rm{1}}} = 4{{\rm{k}}_{\rm{2}}} \Rightarrow {{\rm{k}}_2} = 0.25{{\rm{k}}_{\rm{1}}}\)