The decomposition reaction of nitramide in basic environment: NH$2$NO$2($s$)->$ N$2$O$($g$)+$ H$2$O$($l$)$ is studied by collecting the gas evolved during the reaction. During a similar experiment $50\mathrm{.}0$ mg of nitramide decomposes at $15\backslash$deg C$.$ The dry gas volume released after $70$ min is equal to $6\mathrm{.}59$ cm$3$ at a pressure of $1$ bar. Calculate the rate constant and half$-$life of the above decomposition reaction