Two substances R and S decompose in solution independently, both following first order kinetics. The rate constant of R is twice of S. in an experiment, the solution initially contained 0.5 illimoles of R and 0.25 millimoles of S. The molarities of R and S will be equal just at the end of time equal to

Substance R                                                                      Substance S

            $\text{2k}$                                                                         $\text{k\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}rate\hspace{0.17em}constant}$

            ${\text{t}}_{\text{1/2}}$                                                                         ${\text{2t}}_{\text{1/2}}\text{\hspace{0.17em}Half\hspace{0.17em}life\hspace{0.17em}period}$

            ${\text{T\hspace{0.17em}=\hspace{0.17em}n\hspace{0.17em}×\hspace{0.17em}t}}_{\text{t/2}}$where n = number of half life period

            $\text{Amount\hspace{0.17em}of\hspace{0.17em}R\hspace{0.17em}left\hspace{0.17em}=\hspace{0.17em}}\frac{\text{0.5}}{{\left(\text{2}\right)}^{{\text{T/t}}_{\text{1/2}}}}\text{;}$

            $\text{Amount\hspace{0.17em}of\hspace{0.17em}S\hspace{0.17em}left\hspace{0.17em}=\hspace{0.17em}}\frac{\text{0.25}}{{\left(\text{2}\right)}^{{\text{T/2t}}_{\text{1/2}}}}$

            $\text{Equating\hspace{0.17em}both\hspace{0.17em}}\frac{\text{0.5}}{\text{0.25}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\left(\text{2}\right)}^{{\text{T/t}}_{\text{1/2}}}}{{\left(\text{2}\right)}^{{\text{T/2t}}_{\text{1/2}}}}\text{\hspace{0.17em}or\hspace{0.17em}2\hspace{0.17em}=\hspace{0.17em}}{\left(\text{2}\right)}^{{\text{T/t}}_{\text{1/2}}}$

            $\therefore {\text{\hspace{0.17em}T\hspace{0.17em}=\hspace{0.17em}2t}}_{\text{1/2}},{\text{\hspace{0.17em}2t}}_{\text{1/2}}\text{\hspace{0.17em}is\hspace{0.17em}half\hspace{0.17em}life\hspace{0.17em}of\hspace{0.17em}S\hspace{0.17em}and\hspace{0.17em}twice\hspace{0.17em}the\hspace{0.17em}half\hspace{0.17em}}-\text{\hspace{0.17em}life\hspace{0.17em}of\hspace{0.17em}R}$