Question

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

Short answer

The enthalpy change is approximately \(-32,983 \text{ kJ}\).

Step-by-step solution

Calculate the Mass of Isooctane

Given that the density of isooctane is 0.69 g/mL, we need to determine the mass of 1.00 L of isooctane. First, convert 1.00 L to mL: \[ 1.00 \text{ L} = 1000 \text{ mL} \] Then use the density to find the mass:\[ \text{mass} = \text{volume} \times \text{density} = 1000 \text{ mL} \times 0.69 \text{ g/mL} = 690 \text{ g} \]

Convert the Mass to Moles

Now, convert the mass of isooctane into moles. First, calculate the molar mass of isooctane \(\mathrm{C}_8\mathrm{H}_{18}\):- Carbon (C): 12.01 g/mol \(\times 8 = 96.08 \text{ g/mol} \)- Hydrogen (H): 1.01 g/mol \(\times 18 = 18.18 \text{ g/mol} \)Thus, the molar mass of \(\mathrm{C}_8\mathrm{H}_{18}\) is:\[ 96.08 + 18.18 = 114.26 \text{ g/mol} \]Now, calculate the number of moles:\[ \text{moles} = \frac{690 \text{ g}}{114.26 \text{ g/mol}} \approx 6.04 \text{ mol} \]

Compute the Enthalpy Change

The enthalpy change for the reaction given is \(-10,922 \text{ kJ/mol-rxn}\). This value corresponds to the combustion of 2 moles of isooctane. Thus, the enthalpy change per mole of isooctane is:\[ \text{Enthalpy change per mole} = \frac{-10,922 \text{ kJ}}{2} = -5461 \text{ kJ/mol} \]Now, multiply the moles calculated by the enthalpy change per mole:\[ \text{Total enthalpy change} = 6.04 \text{ moles} \times (-5461 \text{ kJ/mol}) \approx -32,983 \text{ kJ} \]

Conclusion

The total enthalpy change upon burning 1.00 L of isooctane is approximately \(-32,983 \text{ kJ}\). This indicates a highly exothermic reaction.

Key concepts

Combustion Reaction

When substances burn in the presence of oxygen, a combustion reaction occurs. These reactions are typically exothermic, meaning they release energy in the form of heat.
For hydrocarbons like isooctane, burning in air generally yields carbon dioxide and water as the primary products.
The general form of a combustion equation is:

• Hydrocarbon + Oxygen (O₂) → Carbon Dioxide (CO₂) + Water (H₂O)

For isooctane, the reaction involves breaking bonds in the fuel and oxygen molecules and forming new bonds in CO₂ and H₂O. This process releases considerable energy, as indicated by the negative enthalpy change. This energy release is why fuels are used for energy production on a massive scale.

Isooctane

Isooctane, also known as 2,2,4-trimethylpentane, is a compound composed of 8 carbon and 18 hydrogen atoms. It is known for its use in gasoline to enhance performance by providing higher energy upon combustion.
Isooctane is measured against a standard scale in the octane rating system.
It is considered as having a high octane number, which means it resists knocking in engines by burning smoothly.
Understanding the chemical structure of isooctane helps in grasping how hydrocarbons function as fuel. Its formula is C₈H₁₈, which reflects its composition and relates directly to calculating parameters such as molar mass and energy release when burned.

Molar Mass Calculation

Calculating the molar mass of a compound involves summing up the atomic masses of all atoms in its molecular formula. For isooctane ( C₈H₁₈), this includes:

• Carbon (C): 12.01 g/mol, and 8 carbon atoms → 12.01 g/mol × 8 = 96.08 g/mol
• Hydrogen (H): 1.01 g/mol, and 18 hydrogen atoms → 1.01 g/mol × 18 = 18.18 g/mol

Adding these gives us the total molar mass of isooctane, which is 114.26 g/mol.
This value is crucial when converting the mass of a substance into moles, a step necessary for linking the consumed amount of fuel to the enthalpy change.

Density and Volume Conversion

Density is a physical property defined as mass per unit volume, often expressed in g/mL or g/cm³ for liquids like isooctane. Knowing the density allows us to calculate the mass from a given volume:

• Here, isooctane has a density of 0.69 g/mL.
• To find the mass of 1.00 L of isooctane, convert the volume: 1.00 L = 1000 mL.
• Then, multiply the volume by the density to find mass: 1000 mL × 0.69 g/mL = 690 g.

Volume to mass conversion is essential when dealing with liquids because most volume measurements in the lab start in liters or milliliters, while stoichiometric calculations require mass in grams.