# Chemistry in Calculus!

Chemistry Level pending

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.

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