# Colligative properties, cont.

Remember—Colligative properties are properties which depend only on the number or concentration, not on the type, of particles.

• ### Freezing point depression

Tf = -kfm, where m = molality = moles solute/kg solvent, and kf is a constant specific to the solvent.

Which of the following solutions will have the lowest melting point: 2 m sugar (sucrose) or 0.8 m calcium chloride?

First need to look at concentration of particles.

sugar is covalent, so 2 m particles,

calcium chloride is ionic with 1 mole calcium ions and 2 moles of chloride ions for each mole of CaCl2 = (0.8m)(3mol ions/mol formula) = 2.4 m particles,

Therefore the 0.8 m calcium chloride solution will have the lower mp.

• #### What is the freezing point of the calcium chloride solution?

Freezing point = Fppure solvent Tf ; kf H2O = 1.855°C/molal

Tf = -kfm = –(1.855°C/m)(2.4m) = –4.452°C

Freezing point = 0.00°C – 4.452°C = –4.4452°C = –4°C

• ### Osmotic pressure ()

V = nRT; or, dividing both sides by V, = MRT, where M = molarity.

Example: What are the osmotic pressures of 1.00 M sugar and 1 M aluminum chloride solutions at 25°C?

sugar= MRT = (1 mol/L)(0.0821 L*atm/mol*K)(298 K) = 24.5 atm

AlCl3= MRT = (1 mol/L)(4 mol ion/mol)(0.0821 L*atm/mol*K)(298 K) = 97.9 atm.

# Liquids & Solids (Chapter 10)

### Gases vs. Liquids vs. Solids:

• Gases are either monatomic (i.e. inert gases) or covalently bonded molecules.
• Pure liquids at "comfortable" temperatures (20 - 40 °C) all consist of molecules (uncharged) or are metals (Hg, Fr, Cs, Ga, and Rb).
• At higher temperatures (around 300 - 1200 °C) ionic compounds become liquids.
• Melting points for pure metals range up to 3680 K, while the highest melting non-metal is carbon at 3820 K.
• These melting points are detemined by the types of forces involved (van der Waals, ionic, metallic, or covalent), and, to a lesser extent by the sizes of the particles.

Liquids: The particles of a liquid are in continuous motion, but the distances between collisions are very short compared to those of gases. Thus liquids are largely incompressible - need to increase pressure about a million-fold to halve volume. Diffusion though liquids is much slower than in gases (hours to days vs. seconds to minutes under standard conditions).

• Evaporation
• cooling by evaporation
• number of molecules vs. KE diagram (see Fig 10.39, p 485 of Zumdahl 9th ed)
• vapor pressure (equilibrium)
• boiling (occurs when the v.p. = atmospheric pressure)
• superheating (occurs because its hard to initiate bubbles)
• Freezing
• freezing/melting point: temperature at which solid and liquid are in equilibrium.
• supercooling (occurs because its hard to "seed" crystals - will see later when solids are discussed)
• Glasses: supercooled "solid" liquids.

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