The mass fraction and the apparent molecular weight of the products and the mass of air required per unit mass of fuel burned.

Answer to Problem 38P
The mass fraction of carbon dioxide is
Explanation of Solution
Express the total mass of the coal when the ash is substituted.
Here, mass of ash is
Express the mass fraction of carbon.
Here, mass of carbon is
Express the mass fraction of hydrogen.
Here, mass of hydrogen is
Express the mass fraction of oxygen.
Here, mass of oxygen is
Express the mass fraction of nitrogen.
Here, mass of nitrogen is
Express the mass fraction of sulphur.
Here, mass of sulphur is
Express the number of moles of carbon.
Here, molar mass of carbon is
Express the number of moles of hydrogen.
Here, molar mass of hydrogen is
Express the number of moles of oxygen.
Here, molar mass of oxygen is
Express the number of moles of nitrogen.
Here, molar mass of nitrogen is
Express the number of moles of sulphur.
Here, molar mass of sulphur is
Express the total number of moles.
Express the mole fraction of carbon.
Express the mole fraction of hydrogen.
Express the mole fraction of oxygen.
Express the mole fraction of nitrogen.
Express the mole fraction of sulphur.
Express the total molar mass of the products.
Here, number of moles of carbon dioxide, carbon monoxide, water, sulphur dioxide, and nitrogen is
Express the mole fraction of carbon dioxide.
Here, molar mass of carbon dioxide is
Express the mole fraction of carbon monoxide.
Here, molar mass of carbon monoxide is
Express the mole fraction of water.
Here, molar mass of water is
Express the mole fraction of sulphur dioxide.
Here, molar mass of sulphur dioxide is
Express the mole fraction of nitrogen.
Here, molar mass of nitrogen is
Express the total number of moles of product.
Express the apparent molecular weight of the product gas.
Express the air-fuel mass ratio.
Conclusion:
Refer Table A-1, “molar mass, gas constant, and the critical point properties”, and write the molar masses.
Here, molar mass of air is
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Express the combustion equation.
Perform the species balancing:
Carbon balance:
Hydrogen balance:
Sulphur balance:
Oxygen balance:
Nitrogen balance:
Substitute
Refer Equation (XXVIII), and write the number of moles of products.
Refer Table A-1, “molar mass, gas constant, and the critical point properties”, and write the molar masses.
Substitute
Substitute
Hence, the mass fraction of carbon dioxide is
Substitute
Hence, the mass fraction of carbon monoxide is
Substitute
Hence, the mass fraction of water is
Substitute
Hence, the mass fraction of sulphur dioxide is
Substitute
Hence, the mass fraction of nitrogen is
Substitute
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Hence, the apparent molecular weight of the products is
Since each
Refer Equation (XXVIII), and write the number of moles of reactants.
Substitute
Hence, the mass of air required per unit mass of fuel burned is
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Chapter 15 Solutions
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