Calculate Heat Released From 1 M³ Water Gas Combustion A Step-by-Step Guide
Calculate the amount of heat released during the combustion of 1 m³ of water gas consisting of 40% carbon monoxide, 50% hydrogen, and 5% each of carbon dioxide and nitrogen, given the heat released during the combustion of 1 mole of hydrogen and carbon monoxide.
Introduction: Understanding the Heat of Combustion
In the realm of chemistry and thermodynamics, heat of combustion plays a pivotal role in understanding energy release during chemical reactions. Specifically, when dealing with gaseous fuels like water gas, calculating the heat released during combustion is crucial for various industrial and scientific applications. Water gas, a mixture primarily composed of carbon monoxide (CO) and hydrogen (H₂), along with smaller fractions of carbon dioxide (CO₂) and nitrogen (N₂), serves as an important fuel source. This article delves into the intricate process of calculating the heat released from burning 1 m³ of water gas with a defined composition, focusing on the heat evolved from the combustion of hydrogen and carbon monoxide. Understanding these principles allows for efficient energy utilization and informs safety protocols in industries relying on such fuels.
The heat of combustion is a fundamental concept in thermochemistry, representing the energy liberated as heat when a substance undergoes complete combustion with oxygen. This exothermic process is quantified in terms of energy per mole of the substance burned, often expressed in kilojoules per mole (kJ/mol). The magnitude of this value is indicative of the fuel's energy content, a critical parameter in evaluating its utility for energy generation. When considering a complex gaseous mixture like water gas, the total heat released upon combustion is the sum of the heats released by each combustible component, proportional to their respective molar fractions within the mixture. Accurate calculation necessitates a detailed understanding of both the mixture's composition and the heat of combustion values for each constituent gas. This is not only vital for predicting energy output but also for designing combustion systems that maximize efficiency and minimize emissions.
This article will meticulously walk through the steps required to calculate the total heat released during the combustion of 1 m³ of water gas, taking into account the specific volumetric composition provided: 40% carbon monoxide, 50% hydrogen, and 5% each of carbon dioxide and nitrogen. Given the heat of combustion for both hydrogen and carbon monoxide, we will apply stoichiometric principles and gas laws to determine the molar quantities of each component involved. This will lead us to a precise calculation of the total energy liberated as heat, offering valuable insights for practical applications and further research in the field of chemical thermodynamics. The heat of combustion values serve as the cornerstone of this calculation, enabling a quantitative assessment of the energy potential stored within the water gas mixture. Understanding the contribution of each component allows for informed adjustments to fuel mixtures to optimize energy output.
Problem Statement: Calculating Heat Release from Water Gas Combustion
The primary objective is to calculate the amount of heat released when 1 m³ of water gas, with a specific composition, undergoes complete combustion. The water gas in question consists of 40% carbon monoxide (CO), 50% hydrogen (H₂), and 5% each of carbon dioxide (CO₂) and nitrogen (N₂) by volume. This composition is critical as it dictates the proportion of combustible components present in the mixture. The key data provided is the heat released during the combustion of 1 mole of hydrogen and 1 mole of carbon monoxide. These values, typically expressed in kilojoules per mole (kJ/mol), represent the energy liberated when these gases react with oxygen to form water and carbon dioxide, respectively. Knowing these heats of combustion is essential for determining the total heat output from the combustion of the water gas mixture.
The problem's context is rooted in the principles of thermochemistry, where the heat released during a chemical reaction is directly proportional to the amount of reactants consumed. In this scenario, the combustion of water gas involves the oxidation of both hydrogen and carbon monoxide, each contributing to the overall heat released. The presence of carbon dioxide and nitrogen, while not combustible, affects the overall composition and the partial pressures of the reactive gases. Therefore, these components must be considered when determining the molar quantities of hydrogen and carbon monoxide within the 1 m³ volume of water gas. The calculation involves converting volumetric percentages into molar fractions, then using the given heats of combustion to find the total energy released. This process highlights the interplay between stoichiometry and thermodynamics in predicting the energy output of fuel combustion.
To accurately calculate the heat released, a step-by-step approach will be employed. First, the molar volumes of each gas component within the 1 m³ of water gas will be determined using the given percentage composition. Next, the number of moles of hydrogen and carbon monoxide will be calculated using the ideal gas law, considering standard temperature and pressure (STP) conditions. Finally, the heat released by the combustion of each gas will be calculated by multiplying the number of moles by the respective heat of combustion values, and the total heat released will be the sum of these individual contributions. This systematic approach ensures that all factors are accounted for, providing a precise estimation of the energy released from the combustion of the water gas mixture. The accurate calculation is not only important for scientific understanding but also for practical applications in energy production and industrial processes.
Methodology: Step-by-Step Calculation
The methodology for calculating the heat released during the combustion of 1 m³ of water gas involves a series of logical steps, each building upon the previous one to arrive at the final answer. The initial step is to determine the volumes of each component gas within the 1 m³ mixture. Given the composition of the water gas (40% CO, 50% H₂, 5% CO₂, and 5% N₂ by volume), we can directly calculate the volume occupied by each gas. For instance, carbon monoxide occupies 40% of the total volume, which translates to 0.4 m³ in a 1 m³ sample. Similarly, hydrogen occupies 0.5 m³, and both carbon dioxide and nitrogen occupy 0.05 m³ each. These volumes are crucial as they form the basis for subsequent molar calculations.
Following the volume determination, the next critical step is to convert the volumes of the combustible gases (CO and H₂) into moles. This conversion is facilitated by the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Assuming standard temperature and pressure (STP) conditions (0°C or 273.15 K and 1 atm), we can rearrange the ideal gas law to solve for n (n = PV/RT). The ideal gas constant R has a value of 0.0821 L·atm/(mol·K). By substituting the volumes of carbon monoxide and hydrogen obtained in the previous step, along with the values for P, R, and T, we can accurately calculate the number of moles of each gas. This step bridges the gap between macroscopic volume measurements and microscopic molar quantities, essential for stoichiometric calculations.
Once the moles of carbon monoxide and hydrogen are known, the final step involves calculating the heat released by their combustion. This is achieved by multiplying the number of moles of each gas by its respective heat of combustion. The heat of combustion is the amount of heat released when one mole of a substance undergoes complete combustion. These values are specific to each gas and are typically provided in kJ/mol. By multiplying the moles of CO and H₂ by their respective heats of combustion, we obtain the heat released by each gas individually. The total heat released from the combustion of 1 m³ of water gas is then the sum of the heat released by CO and the heat released by H₂. This final calculation provides a quantitative measure of the energy produced by burning the water gas, an important parameter for assessing its fuel potential. The total heat released represents the culmination of the methodical steps taken, from initial volume determination to final energy calculation.
Calculations and Results: Quantifying the Heat Released
The calculation process begins with establishing the volumes of each component in the 1 m³ water gas mixture. Given the percentage composition, we find: Volume of CO = 40% of 1 m³ = 0.4 m³, Volume of H₂ = 50% of 1 m³ = 0.5 m³, Volume of CO₂ = 5% of 1 m³ = 0.05 m³, Volume of N₂ = 5% of 1 m³ = 0.05 m³. These volumes are the foundation for determining the molar quantities of the combustible gases, carbon monoxide and hydrogen. The accurate determination of these volumes is critical for the subsequent steps in the calculation.
Next, the volumes of CO and H₂ are converted into moles using the ideal gas law, PV = nRT, under standard temperature and pressure (STP) conditions. At STP (0°C or 273.15 K and 1 atm), 1 mole of any gas occupies approximately 22.4 liters. Therefore, we can use this molar volume to convert the volumes of CO and H₂ into moles. For CO: Moles of CO = (0.4 m³ * 1000 L/m³) / 22.4 L/mol ≈ 17.86 moles. For H₂: Moles of H₂ = (0.5 m³ * 1000 L/m³) / 22.4 L/mol ≈ 22.32 moles. These calculations provide the molar quantities of the combustible gases present in the water gas mixture, which are essential for determining the total heat released during combustion.
Finally, the heat released is calculated by multiplying the number of moles of each gas by its respective heat of combustion. Let's assume the heat of combustion for carbon monoxide (CO) is approximately 283 kJ/mol, and the heat of combustion for hydrogen (H₂) is approximately 286 kJ/mol. Heat released by CO = 17.86 moles * 283 kJ/mol ≈ 5054 kJ. Heat released by H₂ = 22.32 moles * 286 kJ/mol ≈ 6385 kJ. Therefore, the total heat released during the combustion of 1 m³ of water gas is the sum of these values: Total heat released = 5054 kJ + 6385 kJ ≈ 11439 kJ. This calculation provides a quantitative measure of the energy that can be obtained from burning 1 m³ of the given water gas mixture, highlighting the significance of combustion reactions in energy generation. The final result, approximately 11439 kJ, represents the energy potential of the water gas under the specified conditions.
Conclusion: Significance of Heat Release Calculation
The calculation of heat release from the combustion of 1 m³ of water gas is of significant importance for various practical and theoretical reasons. The result, approximately 11439 kJ, quantifies the energy potential of this specific water gas mixture, providing a valuable benchmark for assessing its fuel efficiency. Such calculations are crucial in industrial settings where water gas is used as a fuel source, as they enable engineers and operators to predict energy output, optimize combustion processes, and ensure efficient energy utilization. Understanding the energy content of fuel mixtures is essential for designing combustion systems, managing fuel supplies, and controlling emissions.
From a practical standpoint, the ability to accurately predict the heat released during combustion is vital for the design and operation of various energy-related systems. This includes power plants, heating systems, and industrial furnaces, where water gas or similar fuel mixtures are commonly used. Knowing the amount of energy that can be obtained from a given volume of fuel allows for the optimization of system parameters, such as fuel-to-air ratios, combustion temperatures, and system throughput. Moreover, understanding the heat release characteristics of different fuel mixtures can aid in the development of more efficient and environmentally friendly combustion technologies. The accurate prediction of heat output not only improves operational efficiency but also contributes to safety by preventing overpressure or other combustion-related hazards.
From a theoretical perspective, the heat release calculation exemplifies the application of fundamental thermochemical principles. It demonstrates the interplay between stoichiometry, thermodynamics, and the ideal gas law in predicting the energy changes associated with chemical reactions. The step-by-step methodology used in this calculation serves as a model for analyzing other combustion reactions and fuel mixtures. Furthermore, understanding the factors that influence heat release, such as the composition of the fuel, the heat of combustion of its components, and the conditions of combustion, is essential for advancing our knowledge of chemical energetics. This knowledge can be applied to the development of new fuels, the optimization of existing combustion processes, and the design of energy-efficient systems. In conclusion, the calculation of heat release from water gas combustion is not only a practical necessity but also a valuable exercise in applying and reinforcing fundamental scientific principles.