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Lesson 41 · Colligative counting
Properties that only count
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Properties that only count

A colligative property depends on HOW MANY solute particles are dissolved and not at all on what they are — the word shares a root with “collect”. Sugar and urea at the same molality shift water's boiling point by exactly the same amount. Three of them earn marks:

ΔTb=Kb b\Delta T_b = K_b\,b — delta T-b equals K-b times b. ΔTb\Delta T_b is the rise in boiling point in C°, bb is the solution's molality in mol/kg, and KbK_b is the solvent's ebullioscopic constant, 0.512 °C·kg/mol for water. Its twin is ΔTf=Kf b\Delta T_f = K_f\,b, where ΔTf\Delta T_f is the drop in freezing point and KfK_f is the cryoscopic constant, 1.86 °C·kg/mol for water — more than three times the boiling one, which is why salt on a driveway earns its keep and salt in a pot barely does. Both constants belong to the SOLVENT, never to the solute.

The trap worth tattooing: ΔT\Delta T is a change, not a temperature. The formula hands you the size of the shift; you still have to apply it to where the pure solvent started. Boiling point becomes 100+ΔTb100 + \Delta T_b; freezing point becomes 0−ΔTf0 - \Delta T_f. An answer of “1.02 C°” to a boiling-point question is a half-finished answer.

Third: osmotic pressure, Π=MRT\Pi = MRT: Π\Pi is the capital Greek letter pi, and it is the pressure in kPa you would have to push back with to stop solvent crossing a membrane into the solution. MM is the molar concentration in mol/L, TT is absolute temperature in kelvin, and RR is the same 8.314. Look at its shape: it is PV=nRTPV = nRT with n/Vn/V renamed MM. These forms are the non-electrolyte ones — a salt that splits into ions counts each ion separately, and that correction is a later chapter's business.

ΔTbKbb

ΔTb=Kb b\Delta T_b = K_b \, b

  • ΔTb\Delta T_b= Boiling-point elevation (temperature difference)
  • KbK_b= Ebullioscopic constant (molal constant)
  • bb= Molality of solution (molality)
Boiling-Point Elevation solver →
ΔTfKfb

ΔTf=Kf b\Delta T_f = K_f \, b

  • ΔTf\Delta T_f= Freezing-point depression (temperature difference)
  • KfK_f= Cryoscopic constant (molal constant)
  • bb= Molality of solution (molality)
Freezing-Point Depression solver →
ΠMT

Π=MRT\Pi = M R T

  • Π\Pi= Osmotic pressure (pressure)
  • MM= Molar concentration (molar concentration)
  • TT= Absolute temperature (temperature)
Osmotic Pressure (Π = MRT) solver →