Q.5 (c) An alloy of tin and lead contain 73% tin. Find the mass of eutectic in 1kg of solid Alloy, if the eutectic contains 64% of tin.
Best answer
Given: the alloy has 73% Sn (27% Pb), and the eutectic has 64% Sn (36% Pb).
The alloy has more Sn (73%) than the eutectic (64%). On cooling, the excess Sn separates out first, and the remaining melt solidifies as eutectic. So the solid alloy is pure Sn + eutectic, and all the Pb is present in the eutectic.
Mass of Pb in 1 kg of alloy = 27% of 1000 g = 270 g.
The eutectic contains 36% Pb, so the mass of eutectic containing 270 g of Pb is:
\( \text{Mass of eutectic} = \dfrac{270 \times 100}{36} = 750\ \text{g} \)
Mass of eutectic = 750 g (0.75 kg), and the excess free Sn = 250 g.
Check: Sn in the eutectic = 0.64 × 750 = 480 g; 480 + 250 = 730 g = 73% of 1 kg. (verified)
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