Chemistry in Calculus!

A reaction flask of capacity 1 liter, contains 4 moles of $\text{P}_{4}$ , 7 moles of $\text{NaOH}$ and 9 moles of $\text{H}_{2}\text{O}$ at $t=0$ . The reaction is governed by the following 3rd order chemical equation (unbalanced):

$\text{P}_{4}(s)+\text{NaOH}(l)+\text{H}_{2}\text{O}(l) \rightarrow \text{PH}_{3}(g)+\text{NaH}_{2}\text{PO}_{2}(aq)$

If the time taken for the formation of $3$ moles of $\text{PH}_{3}$ is $\frac{a}{b}\ln\left(\frac{c}{d}\right),$ what is the value of $a+b+c+d?$

Details and Assumptions:

$\bullet$ The rate constant is $k= 1.5\text{ L}^{2}\text{mol}^{-2}\text{s}^{-1}.$

$\bullet$ If you think the reaction will terminate before the formation of the required amount of product, enter your answer as $0$ .

$\bullet$ $a$ and $b$ , $c$ and $d$ are pairs of co-prime integers.