To solve this question we will use the integrated rate late law for first order reaction:
[tex]\begin{gathered} ln[A]=-kt+ln[A]_0 \\ [A]:concentration\text{ }of\text{ }A\text{ }at\text{ }certain\text{ }time=1.89mg \\ k:rate\text{ }constant=x \\ t:time=474\text{ }mins \\ [A]_0:initial\text{ }concentration=2.56mg \end{gathered}[/tex]By substituting the values we have to determine the unknown we get:
[tex]\begin{gathered} ln1.89=-k\times474min+ln2.56 \\ \frac{0.637-0.940}{-474min}=k \\ k=6.392\times10^{-4}\text{ }min^{-1} \end{gathered}[/tex]Answer: Rate constant k is 6.392x10^-4 per min.
