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In chemistry, a balanced chemical equation represents the conservation of mass and energy by ensuring the same quantity of each type of atom is present on both sides of the equation. For ethanol combustion, the reactants are ethanol (\( \text{C}_2\text{H}_5\text{OH} \)) and oxygen (\( \text{O}_2 \)), while the products are carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)).
To balance this equation, the goal is to have equal numbers of carbon, hydrogen, and oxygen atoms on both sides. Initially, the equation is:\[\text{C}_2\text{H}_5\text{OH} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}\]First, balance the carbon atoms by placing a coefficient of 2 before \( \text{CO}_2 \), and then balance the hydrogen by placing 3 before \( \text{H}_2\text{O} \). Finally, adjust the oxygen atoms so that both sides have an equal amount, resulting in:\[\text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O}\]This balanced equation shows that one molecule of ethanol reacts with three molecules of oxygen, producing two molecules of carbon dioxide and three molecules of water.

The concept of standard enthalpy change refers to the amount of heat absorbed or released during a chemical reaction under standard conditions, typically 1 atm pressure and 298 K temperature.
This is often denoted by \(\Delta H_{rxn}\).
For the combustion of ethanol, the standard enthalpy change can be calculated by using the standard enthalpies of formation (\(\Delta H_f^0\)) for each substance involved.
Here are the values for each relevant compound:

• \(\Delta H_f^0 (\text{C}_2\text{H}_5\text{OH}) = -277.7\, \text{kJ/mol} \)
• \(\Delta H_f^0 (\text{O}_2) = 0\, \text{kJ/mol} \)
• \(\Delta H_f^0 (\text{CO}_2) = -393.5\, \text{kJ/mol} \)
• \(\Delta H_f^0 (\text{H}_2\text{O}) = -241.8\, \text{kJ/mol} \)

The enthalpy change for the reaction is calculated as follows:\[\Delta H_{rxn} = \left[2(\Delta H_f^0 (\text{CO}_2)) + 3(\Delta H_f^0 (\text{H}_2\text{O})\right] - \left[\Delta H_f^0 (\text{C}_2\text{H}_5\text{OH}) + 3(\Delta H_f^0 (\text{O}_2))\right]\]Plug in the values:\[\Delta H_{rxn} = \left[2(-393.5) + 3(-241.8)\right] - \left[-277.7 + 3(0)\right]\]This results in a standard enthalpy change of \(-1234.4 \, \text{kJ/mol}\), indicating that the reaction is exothermic, releasing energy.

Ethanol combustion is a useful energy source due to the heat it releases. Calculating the heat produced involves understanding the relationship between the molar energy change and the number of moles reacting.
To find the energy released per liter of ethanol:

• The density of ethanol is \(0.789\, \text{g/mL}\), leading to a mass of \(789\, \text{g}\) per liter.
• The molar mass of ethanol is \(46.07\, \text{g/mol}\), so the number of moles in one liter is \(\frac{789}{46.07} = 17.13\, \text{mol}\).

Using the standard enthalpy change found previously:

• Multiply the number of moles by the enthalpy change: \(17.13\, \text{mol} \times (-1234.4\, \text{kJ/mol}) = -21133.2\, \text{kJ}\)

Thus, each liter of ethanol releases \(21133.2\, \text{kJ}\) of energy upon combustion, which makes ethanol a powerful fuel source when burned under controlled conditions.

Understanding the environmental impact of ethanol combustion involves calculating the amount of carbon dioxide produced per unit of energy.
The balanced equation indicates that each mole of ethanol combusted produces 2 moles of carbon dioxide.
For 17.13 moles of ethanol, as is found in one liter, the production of carbon dioxide can be determined:

• Twice the moles of ethanol, resulting in \(34.26\, \text{mol}\) of \(\text{CO}_2\)
• The molar mass of carbon dioxide is \(44.01\, \text{g/mol}\)
• Hence, \(34.26\, \text{mol} \times 44.01\, \text{g/mol} = 1507.05\, \text{g}\) of \(\text{CO}_2\) is produced.

Now, calculate the mass of \(\text{CO}_2\) per \(\text{kJ}\) of heat emitted:

• Using the energy per liter, \(21133.2\, \text{kJ}\)
• Divide the total CO2 mass by the energy: \(\frac{1507.05\, \text{g}}{21133.2\, \text{kJ}} = 0.0713\, \text{g/kJ}\)

This result shows that for each kilojoule of energy released from ethanol combustion, approximately \(0.0713\, \text{g}\) of carbon dioxide is emitted, highlighting the environmental impact related to air quality and greenhouse gas emissions.