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The gaseous mixtures with the following composition expressed in % mole are to be blended as follows:
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The three gas mixtures are to be blended in such a proportion that the final mixture should have 40% CH4, 35% C2H6, and 25% C3H8 (on mole basis). Calculate the proportion in which they should be mixed.
Solution:
The given word problem is about the mixing of gasses with different compositions which involves the principles of Stoichiometry. 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. Since all gasses have the same type and compostion, then there's no chemical reactions involved in the mixture. To illustrate the given problem, it is better to label further the flow diagram as follows
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| Photo by Math Principles in Everyday Life |
Basis: 100 kmole of Final Mixture
Let x = be the amount of Gas I
y = be the amount of Gas II
z = be the amount of Gas III
Overall Material Balance of Gas Mixer:
Material Balance of CH4:
Substitute the value of x to the first equation, we have
Material Balance of C2H6:
Substitute the value of x to the first equation, we have
Substitute the value of y to the third equation, we have
The value of y will be equal to
The value of x will be equal to
Therefore, the proportion of gas mixtures to be blended:
