How many moles of isooctane must be burned to produce 100 kJ of heat under standard state conditions?

The amount of heat given out when one mole of a substance is burnt in the presence of excess oxygen, the amount of heat generated is called heat of combustion. The combustion reaction of isooctane is:

\[{{\bf{C}}_{\bf{8}}}{{\bf{H}}_{{\bf{18}}}}{\bf{(l) + }}\frac{{{\bf{25}}}}{{\bf{2}}}{{\bf{O}}_{\bf{2}}}{\bf{(g) }} \to {\bf{ 8C}}{{\bf{O}}_{\bf{2}}}{\bf{(g) + 9}}{{\bf{H}}_{\bf{2}}}{\bf{O(l)}}\]

Observing the above reaction, we can say,

The amount of oxygen needed to burn one mole of isooctane is 25/2 mole.

From Table 5.2,

For the above combustion reaction of isooctane, the enthalpy of combustion is:\[{\rm{\Delta H}}_{\rm{C}}^{\rm{^\circ }}{\rm{ = - 5461 kJmo}}{{\rm{l}}^{{\rm{ - 1}}}}\][Negative sign implies, energy is released]

It means, on burning one mole of isooctane, the amount of energy released is 5461 kJ.

We have to calculate the no of moles of isooctane to produce 100 kJ of heat.

\[\begin{aligned}{\rm{ 5461kJ}}\;{\rm{amount}}\;{\rm{of}}\;{\rm{energy}}\;{\rm{is}}\;{\rm{released}}\;{\rm{on burning 1 mole of isooctane}}\\{\rm{So,}}\;{\rm{100}}\;{\rm{kJ}}\;{\rm{amount}}\;{\rm{of}}\;{\rm{energy}}\;{\rm{is}}\;{\rm{released}}\;{\rm{on}}\;{\rm{burning}}\;\frac{{{\rm{1 mol \times 100 kJ}}}}{{{\rm{5461 kJ}}}}\;{\rm{of }}\;{\rm{ isooctane}}\\{\rm{ = 0}}{\rm{.0183 }}\;{\rm{mol}}\;{\rm{ of }}\;{\rm{isooctane}}\end{aligned}\]

Hence, the amount of moles of Isooctane needed will be 0.0183 moles.