nx mole of substance x was dissolved in ny mole of substance y. A. The total…

Concept: The mole fraction of a component i in a solution is defined as χi = (moles of i) / (total moles of all components in the solution). For a solution made of exactly two components, the mole fractions of the two components always add up to 1, since each is a share of the same total.

Application: Here the solution has only two components, x and y, so total moles = nx + ny. Check each statement against the definition:

1. Statement A: χx + χy = nx/(nx+ny) + ny/(nx+ny) = 1 — this is exactly the two-component identity above, so A holds.

2. Statement B: χx = (moles of x)/(moles of solution) = nx/(nx+ny) — this is the definition itself, so B holds.

3. Statement C: χy = ny/(nx+ny) — again the definition applied to y, so C holds.

4. Statement D: claims χx = nx/(ny+ny) = nx/(2ny). The denominator here is 2ny, which equals the true total (nx+ny) only in the special case nx=ny, not in general — so D is not a valid identity.

Cross-check: Take nx=2, ny=3 (total = 5). Then χx = 2/5 and χy = 3/5, and 2/5 + 3/5 = 1, confirming A, B and C. D's expression instead gives 2/(3+3) = 2/6 = 1/3, which does not match the true value 2/5, confirming D fails.

So statements A, B and C are correct and D is not.