Problem 55 - Chemistry The Molecular Science

Question

"Gasohol," a mixture of gasoline and ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) is used as automobile fuel. The alcohol releases energy in a combustion reaction with \(\mathrm{O}_{2}\). $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ If \(0.115 \mathrm{~g}\) ethanol evolves \(3.62 \mathrm{~kJ}\) when burned at constant pressure, calculate the combustion enthalpy for ethanol.

Step-by-Step Solution

Answer

The combustion enthalpy for ethanol is \(-1448\) kJ/mol.

Step 1: Calculate the moles of ethanol

First, we need to find the number of moles in 0.115 g of ethanol. The molar mass of ethanol, \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \), is calculated as follows: \(2\times 12.01 + 6\times 1.01 + 16.00 = 46.08\) g/mol. Thus, the number of moles \( n \) of ethanol is given by the formula:\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{0.115 \text{ g}}{46.08 \text{ g/mol}} = 0.00249 \text{ mol} \approx 0.0025 \text{ mol}\]

Step 2: Determine the enthalpy change per mole

The problem states that when 0.115 g of ethanol is burned, it evolves 3.62 kJ of energy. Therefore, we can calculate the energy released per mole of ethanol:\[ \Delta H = \frac{3.62 \text{ kJ}}{0.0025 \text{ mol}} = 1448 \text{ kJ/mol} \]

Step 3: Assign the sign for combustion enthalpy

Combustion reactions are exothermic, meaning they release heat. Therefore, the combustion enthalpy should be negative, indicating the release of energy:\[ \Delta H_{combustion} = -1448 \text{ kJ/mol} \]

Key Concepts

Ethanol Combustion

Ethanol, a type of alcohol, serves as an alternative fuel source due to its ability to combust with oxygen. When ethanol burns, it reacts with oxygen (O_{2}) to form carbon dioxide (CO_{2}) and water (H_{2}O). This reaction is significant because it converts chemical energy within the ethanol into heat energy. The balanced chemical equation for ethanol combustion is:\[\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g})\longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}\mathrm{O}(\ell)\]This reaction is important in various applications, such as powering engines. Ethanol combustion releases energy, making it a useful fuel. The energy evolved from ethanol when it combusts can be measured in terms of enthalpy, a concept we will explore further.

Exothermic Reaction

Combustion reactions, like ethanol burning, fall into the category of exothermic reactions. These reactions are characterized by the release of heat or energy into the surroundings.

• In the case of ethanol combustion, energy is released in the form of heat, which can be felt as warmth.
• This characteristic of releasing energy is what makes exothermic reactions crucial for various practical applications like heating and energy generation.

The enthalpy change (\Delta H) for exothermic reactions is negative, which indicates energy is released. For ethanol combustion in our example, the enthalpy is \(-1448 \text{ kJ/mol}\), indicating a release of 1448 kJ of energy per mole of ethanol combusted. Understanding that the process is exothermic helps explain why ethanol is such an appealing fuel source.

Molar Mass Calculation

To accurately determine the enthalpy of combustion, knowing the molar mass of ethanol is essential. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (\text{g/mol}). It helps in converting grams of a substance to moles, a vital step in many chemical calculations.

• For ethanol, \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH},\) calculate its molar mass by adding up the atomic masses:
• 2 carbon atoms: 2 \times 12.01 = 24.02 \,\text{g/mol}
• 6 hydrogen atoms: 6 \times 1.01 = 6.06 \,\text{g/mol}
• 1 oxygen atom: 16.00 \,\text{g/mol}
• Sum: 24.02 + 6.06 + 16.00 = 46.08 \,\text{g/mol}This value is used to convert the given mass of ethanol to moles, which in turn helps determine how much energy is released per mole when ethanol is combusted. Keeping the concept of molar mass in mind aids in effective chemical calculations and understanding stoichiometry.