Melting point of 40% Sn and 60% Pb

From first principles? Or, did you just want a value for the Sn-Pb eutectic?

 

Sn-Pb is NOT an ideal mixture; go to http://www.tpub.com/steelworker1/57.htm for a phase diagram and brief description of the system behavior --- or to http://www.turbobraze.co.uk/alloysssa.htm for a list of compositions and m.p. ranges.

Bottom line? The eutectic temperature is 175-180 C, 60-40 has a m.p. range that starts at only a slightly higher temperature --- your daddy is looking for hot grease all over the kitchen. Brazing or silver-soldering is going to make for much happier results. (Plumbing shops should be able to steer you to decently priced Ag solders --- stronger, nicer to work with, more corrosion resistant, and easier cleaning in the kitchen.) The Pb toxicity issue isn't that big a deal unless he's planning on frying things with lots of acids or salt that might leave residues in the grease, corrode the Pb, then soak soluble lead into the next batch being cooked.

 

"Why" do positive and negative azeotropes exhibit b.p.s higher/lower than those of the pure components? Same situation, different phases --- solid-liquid solution equilibrium rather than vapor-liquid.

Melting points of even ideal mixtures aren't going to be a composition weighted average --- and, definitely not a mass/weight weighted average. The colligative properties of the components are going to control ideal mixture m.p.s, and interspecific interactions have to be taken into account for real mixtures.

I'll be picky and correct you here --- the eutectic is the specific composition at the lowest T on the phase diagram --- it can be considered the m.p. of a compound, Sn4Pb, and the compositions of both the liquid and solid phases are identical; the melting "range" for other compositions is the range of temperature over which the solid phase(s) melt to yield a liquid phase the composition of which varies as T changes.

 

Colligative properties are those properties depending only upon concentrations of solutes in a solution --- clumsy wording --- for instance, you've run into osmometric determinations of molecular weights of quite a few biological molecules; dissolve a known weight of substance in some suitable solvent, determine the reduction in the solvent vapor pressure as a result of the solution process, and from knowledge of the solvent's colligative properties (determined from enthalpies of phase changes at particular temperatures plus a little van't Hoff magic) out pops the number of moles of solute in the solution. You've got the weight, now you know how many moles, and voila! a molecular weight. Same game for freezing point depression, osmotic pressure, and whatever else that's slipped my mind at the moment.

By interspecific interactions, I mean the various molecular interactions, in the solder case, tin with lead, and the intraspecific interactions tin-tin and lead-lead; these are non-zero, and yield some very interesting behaviors in mixed or multi-component systems.

Melting point is a measured property. Given a homologous series, say odd numbered (or even) straight chain saturated hydrocarbons, the melting points (and other physical properties) of missing (data-wise) members of the series can be interpolated from known data for higher and lower MW members. There are similar correlations for invariant structures subject to modifications of functional groups from limited sets --- the DNA vs. base pair game you mention. These are NOT based on any rigorous analysis of intermolecular potential functions. In principle, calculations of melting points and vapor pressures are possible; in practice, no one has the foggiest idea what an intermolecular potential function looks like, let alone how to handle it mathematically.

The DNA correlation depends upon probably hundreds to thousands of measurements; these have since been correlated to three independent variables, and since most DNA does not depart significantly from the ranges of base fractions for the original correlation, it works. I'd be very surprised if the correlation did NOT fail for "synthetic" DNAs of repeated short sequences, or the single base cases (except, a single base DNA can't be made to pair with itself in the helix), so make that single "base-pair" cases.

 

Now, I learned something --- they've played with short string syntheses for physical property measurements; in any case, application of the algorithm outside the ranges of base compositions, or chain lengths is getting into "iffy" territory.

The question came up in context other than PF regarding enthalpies, entropies, and free energies of formation of nucleic acids --- anybody got any decent measurements on these?