Problem 29 - Chemistry and Chemical Reactivity

Question

Isooctane ( 2,2,4 -trimethylpentane), one of the many hydrocarbons that make up gasoline, burns in air to give water and carbon dioxide. $$\begin{array}{r}2 \mathrm{C}_{8} \mathrm{H}_{18}(\ell)+25 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\ell) \\\\\Delta H_{\mathrm{rsn}}^{\circ}=-10,922 \mathrm{kJ} \end{array}$$ If you burn 1.00 L of isooctane (density \(=0.69 \mathrm{g} / \mathrm{mL}\) ), what quantity of heat is evolved?

Step-by-Step Solution

Answer

The heat evolved is approximately \(-32968.44 \, \text{kJ}\).

Step 1: Calculate the Mass of Isooctane

First, find the mass of isooctane using its volume and density. The formula to find mass is: \[ \text{mass} = \text{density} \times \text{volume} \]. Given that the volume of isooctane is 1.00 L, we need to convert this to mL since density is given in g/mL. This gives us 1000 mL. Therefore, \[ \text{mass} = 0.69 \, \text{g/mL} \times 1000 \, \text{mL} = 690 \, \text{g} \].

Step 2: Calculate Moles of Isooctane

To find the number of moles of isooctane, use the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]. The molar mass of isooctane, \(\text{C}_8\text{H}_{18}\), is calculated as: \[ 8 \times 12.01 \, \text{g/mol} + 18 \times 1.008 \, \text{g/mol} = 114.224 \, \text{g/mol} \]. Thus, the moles of isooctane are \[ \frac{690 \, \text{g}}{114.224 \, \text{g/mol}} \approx 6.04 \, \text{mol} \].

Step 3: Calculate Heat Evolved

Using the balanced chemical reaction, we know that burning 2 moles of isooctane releases \(-10922\, \text{kJ}\) of heat. Thus, burning 1 mole releases \(\frac{-10922}{2} = -5461 \, \text{kJ/mol} \). Now, calculate the total heat evolved for 6.04 moles of isooctane as \[ 6.04 \, \text{mol} \times -5461 \, \text{kJ/mol} = -32968.44 \, \text{kJ} \].

Key Concepts

Chemical Reaction Stoichiometry

In chemistry, stoichiometry allows us to understand the quantities of reactants and products in a chemical reaction. This is crucial for predicting the outcomes of reactions. When gasoline, specifically isooctane, combusts in air, it transforms into water and carbon dioxide. The balanced chemical equation for this reaction is: \[2 \text{C}_8\text{H}_{18}(\ell) + 25 \text{O}_2(\text{g}) \rightarrow 16 \text{CO}_2(\text{g}) + 18 \text{H}_2\text{O}(\ell)\] With this equation, it tells us: - 2 moles of isooctane react with 25 moles of oxygen.- These reactants yield 16 moles of carbon dioxide and 18 moles of water.To use stoichiometry:

• Identify the mole ratios from the balanced equation.
• Use these ratios to convert between amounts of reactants and products.

Stoichiometry bridges the gap between the theoretical and practical aspects of a chemical reaction. It's like a recipe, but for chemical elements!

Enthalpy Change

Enthalpy change, symbolized as \(\Delta H\), measures the heat absorbed or released during a chemical reaction at constant pressure. It reflects the energy change due to bond-breaking and forming processes. In our example of burning isooctane, the enthalpy change is \(-10922\, \text{kJ}\). This negative sign indicates the reaction is exothermic, meaning it releases heat.To calculate the heat evolved per mole:1. Use the enthalpy change for the reaction.2. Since the balanced equation involves 2 moles of isooctane releasing \(-10922\, \text{kJ}\), then 1 mole releases \(-5461\, \text{kJ/mol}\).3. Once the moles are known from the stoichiometry, you can find the total heat released from the amount of isooctane combusted. Understanding \(\Delta H\) helps in determining how a reaction's energy profile behaves. It is critical for chemical engineering, environmental science, and thermochemistry disciplines.

Molar Mass Calculation

Molar mass is the total mass of one mole of a chemical substance's molecules, typically expressed in grams per mole (g/mol). Calculating the molar mass of isooctane, \(\text{C}_8\text{H}_{18}\), helps in converting mass to moles, a common step in solving chemistry problems. To determine molar mass:- Identify the atomic masses: Carbon (C) is approximately 12.01 g/mol and Hydrogen (H) is about 1.008 g/mol.- Multiply each atomic mass by the number of atoms present in the compound.- Sum these results: \[8 \times 12.01 + 18 \times 1.008 = 114.224\, \text{g/mol}\]Using the correct molar mass is essential for correct stoichiometric calculations. It acts as a conversion factor that helps us bridge the gap from the tangible mass we measure to the abstract number of atoms or molecules involved.

Combustion Reactions

Combustion reactions are chemical processes in which a substance reacts with oxygen, emitting heat and light. Commonly, hydrocarbons like isooctane combust into carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). This process is exothermic, releasing more energy than it consumes.Key characteristics of combustion are:

• Involves oxygen as a reactant.
• Rapid, producing heat and often light.

Combustion of isooctane can be represented by the balanced equation:\[ 2\text{C}_8\text{H}_{18}(\ell) + 25\text{O}_2(\text{g}) \rightarrow 16\text{CO}_2(\text{g}) + 18\text{H}_2\text{O}(\ell) \]Here, understanding combustion is pivotal for applications like engine efficiency, pollution control, and energy production. It is a fundamental concept in both applied and theoretical chemistry.