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Molar mass by freezing-point depression

Record cooling curves of pure water and of a solution in an ice–salt bath, and turn the difference in freezing points into the molar mass of an unknown.

Difficulty ●●○ ≈ 25 min

Aim Determine the molar mass of an unknown non-electrolyte from its freezing-point depression (ΔTf = Kf·m), and learn to read a freezing point from a cooling curve with supercooling and a sloping plateau.
Cooling curves · ice–salt bath at −6 °C

Molar mass by freezing-point depression

0100200300400500600700Time t / s−2024Thermometer reading / °C
  • Pure water
  • Solution
Your freezing point of pure water —°C
Your freezing point of the solution —°C
Depression ΔTf
—

Record a cooling curve for the pure water and for the solution, then drag the two horizontal lines to read the freezing points.

The cooling curves are computed second by second from a lumped heat model: the tube (50.00 g of water plus about 30 J/K of glass and thermometer) loses heat to a −6 °C ice–salt bath through a conductance of 1.0 W/K. The liquid first supercools; when ice nucleates, the released heat of fusion lifts the temperature (recalescence); after that, ice grows as fast as heat leaks away and the remaining solution concentrates, so a solution’s “plateau” slopes gently downward and must be extrapolated back. The solution’s freezing point comes from the water activity (ideal for non-electrolytes). The thermometer has a fixed zero offset that differs from sample to sample — which is exactly why the pure solvent must be measured too — and reads to 0.01 °C. The depth of supercooling comes from a deterministic hash, not a random number.

Procedure

  1. Choose an unknown sample number. The tube already holds 50.00 g of distilled water; set the mass of unknown you weigh out (2–3 g works well).
  2. Press “Cool the pure water” to log its cooling curve. The temperature first dips below the freezing point (supercooling), jumps back up when ice appears, then holds a flat line.
  3. Drag the grey horizontal line onto the pure-water plateau: that is the freezing point of water as read on this thermometer.
  4. Press “Cool the solution”. Its plateau slopes — as ice separates, the remaining solution grows more concentrated. Turn on “Show extrapolation” and place the blue line where the extrapolated plateau meets the moment freezing began.
  5. Read ΔTf, compute the molality and the molar mass, then reveal the answer and your relative error.

What to notice

  • The thermometer’s zero is not exact: pure water does not read 0.00 °C. That is exactly why ΔTf must be measured twice with the same thermometer and subtracted.
  • Taking the highest point after the jump as the freezing point reads slightly low (some ice has already formed by then), which makes the molar mass come out slightly small.
  • The more solute you weigh out, the larger ΔTf and the smaller the relative reading error — but too concentrated a solution strains the dilute-solution law.
  • Try other samples: urea, glycerol, glucose, sucrose and ethylene glycol differ widely in molar mass, so the same mass can give ΔTf values more than five times apart.

In a real lab

  • Real experiments use a Beckmann thermometer or a 0.01 K digital probe and stir constantly, to limit supercooling and keep the ice crystals fine and even.
  • An air jacket around the tube slows the cooling and sharpens the plateau; keep the ice–salt bath only a few kelvin below the freezing point (6 K here).
  • An electrolyte gives an apparent molar mass about half the true one: each NaCl yields two ions (effective i ≈ 1.9).
  • An ice–salt bath can frostbite fingers: wear gloves. The solutions can go down the drain afterwards.

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