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:
— delta T-b equals K-b times b. is the rise in boiling point in °C, is the solution's molality in mol/kg, and is the solvent's ebullioscopic constant, 0.512 °C·kg/mol for water. Its twin is , where is the drop in freezing point and 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: 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 ; freezing point becomes . An answer of “1.02 °C” to a boiling-point question is a half-finished answer.
Third: osmotic pressure, — 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. is the molar concentration in mol/L, is absolute temperature in kelvin, and is the same 8.314. Look at its shape: it is with renamed . 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.