Calculating the combustion of ethane involves understanding both the stoichiometry (the quantitative relationships between reactants and products) and the thermodynamics (the energy released or absorbed) of the reaction. This process is essential for applications ranging from industrial energy production to environmental impact assessments.
Understanding the Combustion of Ethane
Combustion is a high-temperature exothermic redox chemical reaction between a fuel (like ethane, C₂H₆) and an oxidant (usually atmospheric oxygen, O₂), producing oxidized, often gaseous products, in a mixture termed smoke. For complete combustion of hydrocarbons, the products are carbon dioxide (CO₂) and water (H₂O).
The balanced chemical equation for the complete combustion of ethane is:
2C₂H₆(g) + 7O₂(g) → 4CO₂(g) + 6H₂O(g)
This equation is fundamental to all calculations, as it dictates the molar ratios between all reactants and products.
1. Stoichiometric Calculations
Stoichiometry allows you to determine the amounts of reactants consumed and products formed during a chemical reaction.
Key Steps for Stoichiometric Calculations:
- Balance the Chemical Equation: As provided, the balanced equation is:
2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O. This shows that 2 moles of ethane react with 7 moles of oxygen to produce 4 moles of carbon dioxide and 6 moles of water. - Convert Given Quantities to Moles: If you are given mass, volume (for gases at STP), or number of particles, convert these to moles using molar mass, molar volume, or Avogadro's number, respectively.
- Molar Mass: The mass of one mole of a substance (e.g., C₂H₆ ≈ 30.07 g/mol, O₂ ≈ 32.00 g/mol, CO₂ ≈ 44.01 g/mol, H₂O ≈ 18.02 g/mol).
- Use Mole Ratios from the Balanced Equation: Apply the coefficients from the balanced equation to find the moles of any other reactant or product.
- Convert Calculated Moles to Desired Units: Convert moles back to mass, volume, or number of particles as required by the question.
Example: Calculating CO₂ Produced from Ethane
Let's say you want to calculate the mass of carbon dioxide (CO₂) produced from the complete combustion of 150 grams of ethane (C₂H₆).
- Balanced Equation:
2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O - Molar Masses:
- C₂H₆: (2 × 12.01) + (6 × 1.008) = 30.07 g/mol
- CO₂: 12.01 + (2 × 16.00) = 44.01 g/mol
- Convert Ethane Mass to Moles:
- Moles of C₂H₆ = 150 g / 30.07 g/mol ≈ 4.988 moles
- Use Mole Ratio to Find Moles of CO₂: From the balanced equation, 2 moles of C₂H₆ produce 4 moles of CO₂.
- Moles of CO₂ = (4.988 moles C₂H₆) × (4 moles CO₂ / 2 moles C₂H₆) = 9.976 moles CO₂
- Convert Moles of CO₂ to Mass:
- Mass of CO₂ = 9.976 moles × 44.01 g/mol ≈ 439.06 grams
Thus, 150 grams of ethane would produce approximately 439.06 grams of carbon dioxide.
Limiting Reactant
In many real-world scenarios, reactants are not present in perfect stoichiometric ratios. The limiting reactant is the reactant that is completely consumed first, thereby limiting the amount of product that can be formed. Identifying the limiting reactant is crucial for maximizing product yield or minimizing waste. You can determine the limiting reactant by calculating the amount of product each reactant would produce if it were entirely consumed, and the reactant yielding the least product is the limiting one.
2. Energy Calculations (Heat of Combustion)
Combustion reactions are exothermic, meaning they release energy, typically as heat. The heat of combustion ($\Delta H_c$) quantifies this energy release.
Key Concepts for Energy Calculations:
- Enthalpy of Combustion ($\Delta H_c$): The change in enthalpy when one mole of a substance undergoes complete combustion with oxygen under standard conditions. It is usually expressed in kJ/mol. For exothermic reactions, $\Delta H_c$ is negative.
- Standard Enthalpies of Formation ($\Delta H_f^\circ$): The enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. These values are typically tabulated.
How to Calculate Heat of Combustion:
The total enthalpy change for a reaction can be calculated using the standard enthalpies of formation of the reactants and products:
$\Delta H_{reaction}^\circ = \sum n \Delta H_f^\circ(products) - \sum m \Delta H_f^\circ(reactants)$
Where:
- $n$ and $m$ are the stoichiometric coefficients from the balanced equation.
- $\Delta H_f^\circ$ for elements in their standard state (like O₂) is 0.
Example: Calculating $\Delta H_c^\circ$ for Ethane Combustion
Using the balanced equation: 2C₂H₆(g) + 7O₂(g) → 4CO₂(g) + 6H₂O(g)
And typical standard enthalpy of formation values (approximated for illustration; precise values should come from a reliable source like NIST Chemistry WebBook):
| Substance | $\Delta H_f^\circ$ (kJ/mol) |
|---|---|
| C₂H₆(g) | -84.7 |
| O₂(g) | 0 |
| CO₂(g) | -393.5 |
| H₂O(g) | -241.8 |
Now, apply the formula:
$\Delta H_{reaction}^\circ = [4 \times \Delta H_f^\circ(\text{CO}_2) + 6 \times \Delta H_f^\circ(\text{H}_2\text{O})] - [2 \times \Delta H_f^\circ(\text{C}_2\text{H}_6) + 7 \times \Delta H_f^\circ(\text{O}_2)]$
$\Delta H_{reaction}^\circ = [4 \times (-393.5 \text{ kJ/mol}) + 6 \times (-241.8 \text{ kJ/mol})] - [2 \times (-84.7 \text{ kJ/mol}) + 7 \times (0 \text{ kJ/mol})]$
$\Delta H_{reaction}^\circ = [-1574 \text{ kJ} - 1450.8 \text{ kJ}] - [-169.4 \text{ kJ} + 0 \text{ kJ}]$
$\Delta H_{reaction}^\circ = [-3024.8 \text{ kJ}] - [-169.4 \text{ kJ}]$
$\Delta H_{reaction}^\circ = -3024.8 \text{ kJ} + 169.4 \text{ kJ}$
$\Delta H_{reaction}^\circ = -2855.4 \text{ kJ}$
This value represents the heat released for the combustion of 2 moles of ethane. To find the heat of combustion per mole of ethane, you would divide this by 2.
- $\Delta H_c^\circ$ per mole of C₂H₆ = -2855.4 kJ / 2 moles = -1427.7 kJ/mol
The negative sign indicates that the reaction is exothermic, releasing approximately 1427.7 kJ of energy per mole of ethane combusted under standard conditions.
Practical Insights and Applications
- Energy Production: Ethane is a significant component of natural gas and is widely used as a fuel for electricity generation, industrial furnaces, and heating. Calculating its combustion properties is crucial for designing efficient power plants and optimizing fuel consumption.
- Industrial Processes: Ethane is also a feedstock for producing ethylene, a vital chemical building block. Understanding its combustion is important for safety and process control in chemical plants.
- Environmental Impact: The combustion of ethane, like other fossil fuels, produces carbon dioxide, a greenhouse gas. Accurate calculation helps in assessing emissions and developing strategies for carbon capture and reduction. For more on environmental regulations, you can refer to resources from organizations like the EPA.
- Safety: Knowing the combustion properties, including flammability limits and heat release, is critical for safe handling, storage, and transport of ethane and other hydrocarbons.
By mastering both stoichiometric and thermochemical calculations, you gain a complete understanding of how ethane combustion proceeds and its implications.
