Two components in the ratio of x:y form an azeotropic mixture.They are...
As x:y us the ratio for being azeotropic, but we are given x:2y so 1 mol of y is more given therefore k.y moles will be evaporated i.e. more than y moles will be evaporated.
Two components in the ratio of x:y form an azeotropic mixture.They are...
Explanation:
An azeotropic mixture is a mixture of two or more liquids that have a constant boiling point and composition. This means that when the mixture is boiled, the vapors produced have the same composition as the liquid mixture. In other words, the composition of the liquid and vapor phases is the same at the boiling point.
Given that two components are in the ratio of x:y and form an azeotropic mixture, we can assume that the ratio of their moles is also x:y. Let us assume that the total number of moles in the mixture is 1 mole.
Therefore, the number of moles of component x is (x/(x+y)) and the number of moles of component y is (y/(x+y)).
When these two components are mixed in the ratio of x:2y, we can assume that the total number of moles in the mixture is (x+2y). Therefore, the number of moles of component x in the new mixture is (x/(x+2y)) and the number of moles of component y in the new mixture is (2y/(x+2y)).
To obtain the azeotropic mixture, we need to evaporate some of the component y from the new mixture until the ratio of the moles of the two components in the mixture is the same as the ratio of the moles of the two components in the azeotropic mixture.
Let us assume that we need to evaporate 'a' moles of component y from the new mixture to obtain the azeotropic mixture. Therefore, the number of moles of component y in the new mixture after evaporation is (2y-a)/(x+2y).
Now, we need to equate the ratio of the moles of the two components in the new mixture after evaporation to the ratio of the moles of the two components in the azeotropic mixture.
Therefore, we have:
(x/(x+2y)):(2y-a)/(x+2y) = x:y
Solving for 'a', we get:
a = y(x^2+y^2)/(2x^2)
Therefore, 'a' moles of component y need to be evaporated from the new mixture to obtain the azeotropic mixture.
Conclusion:
To obtain the azeotropic mixture, we need to evaporate 'a' moles of component y, where 'a' is given by:
a = y(x^2+y^2)/(2x^2)
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