Question

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

Short answer

The number of moles of isooctane must be burned equal to 0.0183 moles.

Step-by-step solution

Combustion reaction

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.

Enthalpy of combustion

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.

Number of moles

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.