# Chemistry in Calculus!

**Chemistry**Level pending

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

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.