$P_{t} =P_{0}-P+2 P+P$

$=P_{0}+2 P$

Therefore,

$P =\frac{ P _{ t }+ P _{0}}{2}$

Apply the expression shown below to calculate rate constant.

$k=\frac{2.303}{t} \log \left[\frac{ P _{0}}{ P _{0}- P }\right]$

Substitute the value of $P$ in above equation.

$k=\frac{2.303}{t} \log \left[\frac{ P _{0}}{ P _{0}-\left(\frac{ P _{ t }+ P _{0}}{2}\right)}\right]$

$=\frac{2.303}{t} \log \left[\frac{2 P _{0}}{2 P _{0}- P _{ t }+ P _{0}}\right]$

$=\frac{2.303}{ t } \log \left(\frac{2 P _{0}}{3 P _{0}- P _{ t }}\right)$