Question 19
A lead–tin thermal-equilibrium diagram is shown.
The ends of the tie line give the compositions, and its arms give the percentages
Part a) and part b) read the same tie line in two different ways. Watch the ends drop to the axis first, then watch the arms balance.
Composition is where each end sits on the axis, written as both metals. Percentage is an arm over the whole tie line. The alloy sits nearer the solid end, so there is more solid.
Drag the alloy and read both answers off one tie line
This is QCAA’s 2024 diagram. Drag the orange point, or use the sliders. The readings are taken to the whole percent. At 200 °C the readings are QCAA’s own, 45% and 83% Pb. Watch the compositions change only with temperature, while the percentages change with the alloy too.
This is the question. Part a) is the two ends, solid 83% Pb and 17% Sn, liquid 45% Pb and 55% Sn. Part b) is the two arms, 65.8% solid and 34.2% liquid.
Slide the alloy along the tie line and the compositions stay put, because they belong to the temperature. Only the percentages move. That is why part a) and part b) are separate marks.
This is the β + liquid field on the tin-rich side. The solid here is β, mostly tin. The rule is the same: the solid takes the arm reaching towards the liquid.
The point is above the liquidus, so the alloy is 100% liquid with the alloy’s own composition. There is no tie line.
The point is in a single solid field, so the alloy is 100% solid with its own composition. The lever rule only works between two boundaries.
This is the swap. The near arm gives the other phase, and the swapped answers still add to 100%. The alloy sits closest to the phase you have most of, so check against the picture.
Work through the solution one mark at a time
Try each step yourself before you reveal it.
The axis counts lead, so the alloy goes at 70. Rule the vertical line at 70% Pb and the horizontal tie line at 200 °C, then drop a line from each end of the tie line to the axis.
QCAA lists what counts: “tie lines at 45% and 83% Pb”, “percentage solid and liquid”, “composition solid”, “or other suitable response consistent with a reasonable understanding.”
Marker: annotates the diagram appropriately
The solid is at the solidus end of the tie line, on the lead-rich side. Read it as both metals.
QCAA notes: “Accept 82–84% Pb inclusive and subsequent FT marks.”
Marker: determines the composition of the solid from the tie line from the line of intersection at 200 °C in the solid phase = 83% Pb and 17% Sn
The liquid is at the liquidus end. Again, both metals.
The guide accepts 44% to 46% Pb inclusive for this reading, with follow-through. The printed liquidus crosses the 200 °C grid line about halfway between 45% and 46% Pb, so read carefully and stay inside that window.
Marker: determines the composition of the liquid from the tie line from the line of intersection at 200 °C in the liquid phase = 45% Pb and 55% Sn
The tie line is $83-45=38$ long. The solid takes the arm on the far side from it, from the liquidus to the alloy.
Percentage solid at 200 °C:
$$\frac{70-45}{83-45}=\frac{25}{38}=65.8\%$$
QCAA: “Accept 63%-69% solid”.
Marker: determines the percentage solid at 200 °C
Percentage liquid at 200 °C:
$$\frac{83-70}{83-45}=\frac{13}{38}=34.2\%$$
QCAA: “Accept 31-37% liquid”. Check that $65.8+34.2=100$, and that 70 sits nearer 83 than 45, so solid is the bigger share.
Marker: determines the percentage liquid at 200 °C
Each phrase of the question gave you something
QCAA did not publish a band for this question. It reads as simple familiar because the diagram prints its key values and every mark is one reading or one division, the 5-mark lever-rule shape QCAA published as simple familiar in 2020. The 2025 syllabus asks for exactly this pair, percentages solid and liquid along with composition solid and liquid, so expect it again.
If I had to guess where you might lose marks, it would be part a). Writing 65.8% as the composition of the solid confuses the two words and loses both reading marks. The second trap is writing only “83% Pb”. The marker line names both metals, 83% Pb and 17% Sn, so write the tin as well. On the same paper the multiple choice book printed this diagram on a % Tin axis, so read the axis label every time.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording, any figures and marking-guide steps are from the 2024 QCAA Engineering external assessment, © State of Queensland (QCAA) 2024, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.
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