Ethane Combustion: CO2 Production Calculation

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When ethane (C₂H₆) undergoes combustion, it reacts with oxygen to produce carbon dioxide (CO₂) and water (H₂O). This is a fundamental reaction in chemistry, and understanding the stoichiometry is crucial for calculating the amounts of reactants and products involved. The balanced chemical equation for the combustion of ethane is: 2 C₂H₆(g) + 7 O₂(g) → 4 CO₂(g) + 6 H₂O(l). This equation tells us that for every 2 moles of ethane that react, 4 moles of carbon dioxide are produced. We can use this ratio, along with the ideal gas law, to determine the volume of carbon dioxide produced when a specific volume of ethane is burned.

Understanding the Stoichiometry of Ethane Combustion

Stoichiometry is the part of chemistry that deals with the relative quantities of reactants and products in chemical reactions. The balanced chemical equation provides the mole ratios needed for these calculations. In the case of ethane combustion, the coefficients in front of each compound in the balanced equation (2, 7, 4, and 6) tell us the number of moles of each substance involved in the reaction. For instance, the coefficient '2' in front of C₂H₆ means that 2 moles of ethane are consumed for every reaction. Similarly, the coefficient '4' in front of CO₂ indicates that 4 moles of carbon dioxide are produced. These mole ratios are the core of our calculations.

To translate these mole ratios into volumes, especially for gases, we can use the ideal gas law (PV = nRT). However, when dealing with gases under the same conditions of temperature and pressure, we can use Avogadro's Law. Avogadro's Law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This means the volume ratio is the same as the mole ratio. Therefore, we can directly relate the volume of ethane to the volume of carbon dioxide produced.

The balanced equation shows us that 2 moles of ethane produce 4 moles of carbon dioxide. Since the volume of a gas is directly proportional to the number of moles (at constant temperature and pressure), we can state that 2 volumes of ethane produce 4 volumes of carbon dioxide. This simplifies the calculation significantly.

This principle is extremely important in industrial chemistry, where combustion reactions are common. For example, in power plants that use natural gas (primarily methane and ethane) as fuel, understanding the amount of COâ‚‚ produced is crucial for both efficiency and environmental impact. Calculating the volumes of gases involved, and their ratios, helps in the design of combustion chambers and the implementation of emission control technologies.

Furthermore, the stoichiometry helps in the calculation of theoretical yields of the products of combustion, which helps determine the effectiveness of the process. In addition, the calculations assist in understanding and managing chemical reactions in various applications, from simple laboratory experiments to the complex processes involved in large-scale industrial operations.

Step-by-Step Calculation of COâ‚‚ Production

Let's break down the calculation to determine the volume of carbon dioxide (CO₂) produced when 89.5 L of ethane (C₂H₆) is burned. We'll utilize the volume ratios derived from the balanced chemical equation.

  1. Identify the Mole Ratio: From the balanced equation 2 C₂H₆(g) + 7 O₂(g) → 4 CO₂(g) + 6 H₂O(l), we know that 2 moles of C₂H₆ produce 4 moles of CO₂. Since we are working with gases at the same temperature and pressure, we can directly use the volume ratio: 2 volumes of ethane produce 4 volumes of carbon dioxide.

  2. Set up the Proportion: We know the initial volume of ethane (89.5 L) and want to find the volume of COâ‚‚ produced (let's call it x L). Using the volume ratio, we can set up a proportion:

2 volumes C₂H₆ / 4 volumes CO₂ = 89.5 L C₂H₆ / x L CO₂

  1. Solve for x: Cross-multiply and solve for x:

2 * x = 4 * 89.5

2x = 358

x = 358 / 2

x = 179 L

Therefore, when 89.5 L of ethane are burned, 179 L of carbon dioxide are produced. This calculation assumes that the reaction goes to completion and that the temperature and pressure remain constant throughout the process. In a real-world scenario, factors like incomplete combustion, temperature fluctuations, and pressure variations can influence the actual volumes produced.

The Role of Ideal Gas Law

While we solved the problem using the volume ratios directly derived from the balanced equation, a deeper understanding can be achieved using the Ideal Gas Law. The Ideal Gas Law is a fundamental concept in chemistry and physics, expressed as: PV = nRT, where:

  • P is the pressure of the gas (in atmospheres, atm).
  • V is the volume of the gas (in liters, L).
  • n is the number of moles of the gas.
  • R is the ideal gas constant (0.0821 L·atm/mol·K).
  • T is the absolute temperature of the gas (in Kelvin, K).

This law describes the behavior of an ideal gas, which assumes that gas particles have no volume and do not interact with each other. While no gas is perfectly ideal, this law provides a good approximation under many conditions.

To see how the Ideal Gas Law applies to our combustion problem, we could convert the volumes to moles, perform the stoichiometric calculation, and then convert the moles of COâ‚‚ back to volume, assuming constant temperature and pressure. The volume ratio method simplifies the process because the temperature and pressure are assumed constant, allowing us to directly use the relationship between the volumes of ethane and carbon dioxide.

In essence, both the volume ratio and the Ideal Gas Law approaches are based on the same underlying principles of stoichiometry. The volume ratio method is a shortcut, but it is accurate if the conditions of temperature and pressure are the same for the reactants and products. The Ideal Gas Law provides a more general and versatile approach, especially when conditions change.

For example, if the temperature or pressure changed during the combustion process, we would need to use the Ideal Gas Law to accurately calculate the volume of COâ‚‚ produced. This demonstrates the versatility of the Ideal Gas Law, allowing for more complex and accurate calculations.

Practical Implications and Applications

The ability to calculate the volume of carbon dioxide produced from ethane combustion has many practical implications. It's not just a theoretical exercise; these calculations are essential in various fields.

  • Industrial Processes: In industries that use hydrocarbons as fuel, knowing the amount of COâ‚‚ produced is crucial for designing efficient combustion systems and for complying with environmental regulations. This includes the energy sector, chemical manufacturing, and other industries where combustion processes are common.
  • Environmental Monitoring: The knowledge of COâ‚‚ production is fundamental to understanding climate change. It helps quantify the contribution of different fuels to greenhouse gas emissions and is used in the development of strategies to reduce these emissions.
  • Research and Development: Researchers use these calculations to study combustion processes and to develop more efficient and environmentally friendly fuels. This includes studying the reaction kinetics, thermodynamics, and the influence of different parameters like temperature, pressure, and the presence of catalysts.
  • Education: Understanding these calculations is fundamental for anyone studying chemistry, chemical engineering, or related fields. It provides a basis for understanding chemical reactions and their impact on the environment.

Furthermore, by understanding the stoichiometry of the combustion reaction, professionals can optimize the fuel-to-air ratio, maximizing efficiency and minimizing the production of pollutants, such as carbon monoxide (CO) and unburnt hydrocarbons.

In essence, the skills gained from these calculations are vital for professionals working on energy production, environmental protection, and scientific research. They bridge theoretical knowledge with practical applications, creating a base for innovation and improvement.

Conclusion

In conclusion, calculating the volume of carbon dioxide produced from the combustion of ethane is a straightforward application of stoichiometry and the principles of gas behavior. By using the balanced chemical equation to determine the mole/volume ratios and applying this to the initial volume of ethane, we can accurately predict the volume of COâ‚‚ produced. This understanding is crucial for a variety of applications, from industrial processes to environmental monitoring, and underscores the importance of chemical knowledge in real-world scenarios. Remember the key steps: write the balanced chemical equation, determine the mole/volume ratios, and then use these ratios to calculate the unknown quantity. This method applies not only to ethane but to any combustion or chemical reaction where the amounts of reactants and products are important.

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