Free counters!

Sunday, September 15, 2013

Stoichiometry Problem - Material Balance, 6

Category: Chemical Engineering Math, Algebra

"Published in Newark, California, USA"

A sample of coal is found to contain 63% carbon and 24% ash on weight basis. The analysis of refuse after combustion shows 7% carbon and the rest ash. Calculate the percentage of the original carbon unburnt in the refuse. 

Solution:

The given word problem is about the combustion of a coal in a furnace which involves the principles of Stoichiometry. When you add the percent compositions of a coal, it will not be equal to 100%. The rest of the composition of a coal is either water or other substances that are mostly combustible. During the combustion of a coal, the components like carbon, water, ash, and other substances are converting into flue gas and refuse. The flue gas is a mixture of carbon dioxide, carbon monoxide, water vapor, oxygen, nitrogen, and other oxide gases. The refuse is mostly ash but sometimes there are unburnt carbon or coal in the refuse. The total amount of a substance in the reactants or incoming ingredients must be equal to the total amount of a substance in the final products. In short, the Law of Conservation of Mass must be followed all the time. To illustrate the problem, it is better to draw the flow diagram as follows

Photo by Math Principles in Everyday Life

Since the amount of coal, flue gas, and refuse are not given in the problem, let's assign a basis of 100 kg of coal in the problem.

Basis: 100 kg of coal

Let x = be the amount of refuse
      y = be the amount of flue gas

Material Balance of Ash:







Therefore,