The Travel:

When you are traveling for an internship to a foreign university, you should always attend classes that give you insights into local customs and history. So$,$ you enroll in a course in Norwegian Naval History to learn about the shipbuilding skills of the Vikings, the ${14}^{th}$ century Cogs and their clinker or carvel frame construction, the ${17}^{th}$ century warships that remind you of the "Pirates of the Caribbean", and the modern ships of the Norwegian Cruise Line. Part of the course are stories about shipwrecks and disasters. For example, the Norwegian steamship SS Imo, a cargo liner that was built for the same company as the infamous Titanic, had sailed in late $1917$ from the Netherlands to Halifax, Nova Scotia, Canada, when it collided with the French cargo ship SS Mont$-$Blanc carrying $246$ metric tons of benzol, a coal$-$tar product consisting mainly of benzene and toluene, $250$ metric tons of TNT $(2,4,6-$trinitrotoluene$),$ and $2,367$ metric tons of picric acid $(2,4,6-$trinitrophenol$).$ The collision caused the benzol to catch fire, which ultimately ignited the largest accidental, non$-$nuclear explosions in history with over $1700$ casualties and additional $9000$ insured.

In this explosion, picric acid reacted according to

$2(O_2(N){)}_3{C}_6{H}_{2}OH(s)+\frac{1}{2}{O}_2(g)3N_2(g)+24CO(g)+6H_{2}O(g)$

$($a$)$ Calculate the maximum energy $($Helmholtz energy$)$ lost by the picric acid reaction in this accident that otherwise could have been used to do work, for example, in controlled explosions in mining enterprises. Even though it seems unrealistic for an explosion, assume that all products and reactants are provided and yielded at room temperature.

$($For picric acid, use: $H_f=-217\mathrm{.}9kJmo{l}^{-1}$;$Sm=101\mathrm{.}5Jmo{l}^{-1}{K}^{-1})$

$($b$)$ Compare the energy values for the enthalpy and the room$-$temperature entropy changes in the picric acid explosion and determine their percentage contribution to the Helmholtz energy lost in the accident.