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The reflux ratio effects the positioning of the rectifying section operating line ( Xd/(Rmin+1) this equation gives the point at which the rectifying operating line intersects the y-axis ). therefore an infinte value for the reflux ratio will give the very minimum number of stages required. SO basically the relationship is, the higher the reflux ratio, the less stages needed. hope this answers your question.

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Q: What is the relationship between Reflux Ratio and the number of contact stages?
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