Problem 53 - Chemistry The Molecular Science

Question

Isooctane \((2,2,4\) -trimethylpentane), one of the many hydrocarbons that make up gasoline, burns in air to give water and carbon dioxide. $$ \begin{array}{r} 2 \mathrm{C}_{8} \mathrm{H}_{18}(\ell)+25 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{~g})+18 \mathrm{H}_{2} \mathrm{O}(\ell) \\ \Delta_{\mathrm{r}} H^{\circ}=-10,922 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Calculate the enthalpy change if you burn \(1.00 \mathrm{~L}\) isooctane (density \(=0.69 \mathrm{~g} / \mathrm{mL}\) ).

Step-by-Step Solution

Answer

Burning 1.00 L of isooctane releases -32,923.12 kJ of energy.

Step 1: Understand the Reaction

The reaction given is the combustion of isooctane (\( \mathrm{C}_8\mathrm{H}_{18} \)) in the presence of oxygen to form carbon dioxide and water. The enthalpy change for this reaction is \(-10,922 \mathrm{~kJ/mol} \) for the combustion of \(2 \mathrm{C}_{8}\mathrm{H}_{18} \), meaning \(-10,922 \mathrm{~kJ} \) is released per 2 moles of isooctane combusted.

Step 2: Calculate the Moles of Isooctane

First, find the mass of isooctane. Since the density of isooctane is \(0.69 \mathrm{~g/mL} \), and we have \(1 \mathrm{~L} \) (which is \(1000 \mathrm{~mL} \)), the mass \( m \) is:\[ m = 0.69 \mathrm{~g/mL} \times 1000 \mathrm{~mL} = 690 \mathrm{~g}\]

Step 3: Calculate the Molar Mass of Isooctane

Isooctane has the formula \( \mathrm{C}_8\mathrm{H}_{18} \). Therefore:- Carbon atomic mass: \(12.01 \mathrm{~g/mol} \)- Hydrogen atomic mass: \(1.01 \mathrm{~g/mol} \)Molar mass of \( \mathrm{C}_8\mathrm{H}_{18} \):\[ M = 8 \times 12.01 + 18 \times 1.01 = 114.23 \mathrm{~g/mol}\]

Step 4: Calculate the Number of Moles of Isooctane

The number of moles \( n \) is given by:\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{690 \mathrm{~g}}{114.23 \mathrm{~g/mol}} \approx 6.04 \text{ moles}\]

Step 5: Calculate the Enthalpy Change

The enthalpy change \( \Delta H \) for \(2\) moles of isooctane is \(-10,922 \mathrm{~kJ} \). For \(6.04 \) moles, the enthalpy change would be:\[ \Delta H = \frac{-10,922 \mathrm{~kJ}}{2} \times 6.04 = -32,923.12 \mathrm{~kJ}\]

Step 6: Compute the Result

Since the combustion reaction releases \(-32,923.12 \mathrm{~kJ} \), it means that burning \(1.00 \mathrm{~L} \) of isooctane releases approximately \(32,923.12 \mathrm{~kJ} \) of energy.

Key Concepts

Combustion Reaction

A combustion reaction is a chemical process where a substance, usually a hydrocarbon, reacts with oxygen to produce energy, water, and carbon dioxide. These reactions are highly exothermic, meaning they release heat. This is why combustion reactions are fundamental in engines, like those in cars. When isooctane—a hydrocarbon—burns, it produces water and carbon dioxide as shown in the given chemical equation.
The combustion of isooctane is a vital reaction in understanding how fuels release energy. This energy, released as heat, is what powers engines. Knowing how to calculate the energy released helps in estimating the fuel efficiency of engines.

Hydrocarbon

Hydrocarbons are organic compounds composed solely of hydrogen and carbon. Isooctane is a hydrocarbon, widely used as a fuel source. Its formula, \(\mathrm{C}_8\mathrm{H}_{18}\), indicates it contains 8 carbon atoms and 18 hydrogen atoms.
Hydrocarbons are the main constituents of fuels like gasoline. Their structure allows for significant energy storage, which is released during combustion. The efficiency of different hydrocarbons as fuels can be determined through their energy release in combustion reactions.

Molar Mass

Molar mass is a crucial concept when dealing with chemical reactions, as it allows you to translate between mass and moles of a substance. For isooctane, the molar mass is calculated using the atomic masses of carbon and hydrogen:

• Carbon: \(12.01 \mathrm{~g/mol}\)
• Hydrogen: \(1.01 \mathrm{~g/mol}\)

To find isooctane's molar mass, you multiply the number of each type of atom by its atomic mass and sum the results:
\[M = 8 \times 12.01 + 18 \times 1.01 = 114.23 \mathrm{~g/mol}\]
This molar mass is essential in the calculation of the number of moles, a key step in determining the enthalpy change in a chemical reaction.

Energy Release

Energy release during a chemical reaction like combustion is crucial for understanding how much heat is produced. In the combustion of isooctane, the energy change is denoted by \(\Delta_{\mathrm{r}} H^{\circ}\), which is measured in \(\text{kJ/mol}\).
Here, the enthalpy change of \(-10,922 \text{ kJ/mol}\) indicates the energy released when two moles of isooctane combust. Calculating total energy release involves finding how many moles you have from the mass of isooctane and applying this value to the standard enthalpy change, ensuring a realistic understanding of how much energy a certain amount of fuel can produce. This is valuable for real-world applications like optimizing fuel usage in vehicles.