According to the phase diagram given below, the composition of the layer `a' relative to the layer `b' at point `c' is :
\(\frac{bc}{ac}\)
The stem carries a drawn phase diagram; the four options are text and are reproduced in full above.
Within a two-phase region of a phase diagram, the relative amounts of the two phases are found by the lever rule. The horizontal line joining the two phase boundaries at a given temperature is the tie line, and the overall composition point sits somewhere along it.
The rule works exactly like a mechanical lever balanced at the overall composition. Its essential and often-misremembered feature is that the amount of each phase is proportional to the length of the segment on the opposite side of the fulcrum.
So with the tie line running from a through c to b:
\(\frac{\text{amount of phase a}}{\text{amount of phase b}} = \frac{\overline{bc}}{\overline{ac}}\).
The reason is a simple mass balance. If \(n_a\) and \(n_b\) are the amounts of the two phases and \(x\) their compositions, conserving the component across the tie line gives \(n_a(x_c - x_a) = n_b(x_b - x_c)\), which rearranges directly to the ratio above.
The physical sense is easy to check: the closer the overall point c lies to boundary a, the shorter the segment \(\overline{ac}\) and the larger the ratio — that is, the more of phase a is present. An expression with \(\overline{ac}\) in the numerator would wrongly predict less of phase a as c approaches a, and the options dividing by the full length \(\overline{ab}\) give the fraction of a phase rather than the ratio of the two.
Per the official final answer key the answer is \(\frac{bc}{ac}\).
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