Solutions

Binary Solution Components

Solvent: Largest quantity; determines physical state.
Solute: Lesser quantity; dissolved in solvent.

9 Types by Physical State

• Gaseous: Solute (Gas, Liq, or Sol) + Gas Solvent (e.g. Air, Humidity)
• Liquid: Solute (Gas, Liq, or Sol) + Liquid Solvent (e.g. Soda water, Ethanol in water)
• Solid: Solute (Gas, Liq, or Sol) + Solid Solvent (e.g. Alloys like Brass, Amalgams)

• Mass % (w/w): (Mass of solute / Total mass) $\times 100$
• ppm: (Mass of component / Total mass) $\times 10^6$
• Mole Fraction ($x_A$): $n_A / (n_A + n_B)$

Molarity vs Molality

Molarity ($M$): Moles of solute per Litre of solution.
Molality ($m$): Moles of solute per kg of solvent.

Temperature Effect: Molarity changes with temp (volume dependent). Molality and Mole Fraction are independent of temp (mass dependent).

Interconversion

$$ m = \frac{1000 \times M}{(1000 \times d) - (M \times M_2)} $$

Solid in Liquid

"Like dissolves like." Temp effect depends on Le Chatelier's principle: solubility increases if endothermic, decreases if exothermic.

Henry's Law (Gas in Liquid)

Partial pressure of gas in vapour phase is directly proportional to its mole fraction in solution.

$$ p = K_H \cdot x $$

• Higher $K_H$ means lower solubility.
• $K_H$ increases with Temp $\implies$ Solubility decreases with Temp.

Applications

• Soda bottles sealed at high pressure.
• Scuba divers use He-diluted air to avoid "The Bends".
• Low $O_2$ pressure at high altitudes causes Anoxia.

For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction.

$$ p_1 = p_1^0 x_1 \quad \text{and} \quad p_2 = p_2^0 x_2 $$ $$ P_{total} = p_1 + p_2 = p_1^0 x_1 + p_2^0 x_2 $$

Raoult's vs Henry's Law

Raoult's law is a special case of Henry's law where $K_H$ becomes strictly equal to $p_i^0$.

Non-Volatile Solute

Adding a non-volatile solute (e.g., salt) to a volatile solvent lowers the vapour pressure of the solution.

Ideal Solutions

Obey Raoult's law perfectly. A-B interactions = A-A and B-B interactions.
$\Delta H_{mix} = 0$, $\Delta V_{mix} = 0$. (e.g. n-hexane + n-heptane)

Non-Ideal: Positive Deviation

A-B interactions weaker than pure. Vapour pressure is higher.
$\Delta H_{mix} > 0$, $\Delta V_{mix} > 0$. Forms Minimum Boiling Azeotrope.
(e.g. Ethanol + Acetone)

Non-Ideal: Negative Deviation

A-B interactions stronger than pure. Vapour pressure is lower.
$\Delta H_{mix} < 0$, $\Delta V_{mix} < 0$. Forms Maximum Boiling Azeotrope.
(e.g. Chloroform + Acetone)

Properties that depend only on the number of solute particles, not their nature.

1. RLVP

Relative Lowering of Vapour Pressure is equal to the mole fraction of the solute.

$$ \frac{p_1^0 - p_1}{p_1^0} = x_2 = \frac{n_2}{n_1 + n_2} $$

2. Elevation of Boiling Point

Adding non-volatile solute lowers VP, so solution must be heated more to boil.

$$ \Delta T_b = K_b \cdot m $$

$K_b$ = Ebullioscopic constant. $m$ = molality.

3. Depression of Freezing Point

Solution's lower VP curve intersects solid solvent curve at a lower temperature.

$$ \Delta T_f = K_f \cdot m $$

$K_f$ = Cryoscopic constant.

4. Osmotic Pressure ($\pi$)

Excess pressure applied to solution side to stop osmosis (flow of solvent via SPM).

$$ \pi = C R T = \frac{n_2}{V} R T $$

Best for Polymers

Osmotic pressure is ideal for proteins/polymers because it is measured at room temp (prevents denaturation) and uses Molarity.

If solute undergoes dissociation or association, colligative property values deviate from expected.

van't Hoff Factor ($i$)

$$ i = \frac{\text{Observed Colligative Property}}{\text{Calculated Colligative Property}} $$ $$ i = \frac{\text{Normal Molar Mass}}{\text{Abnormal Molar Mass}} $$

• $i > 1$: Dissociation (e.g., NaCl $\to$ $Na^+$ + $Cl^-$)
• $i < 1$: Association (e.g., Acetic acid dimerizing)
• $i = 1$: No association/dissociation

Degree of Dissociation / Association

• Dissociation ($\alpha$): $\alpha = \frac{i - 1}{n - 1}$
• Association ($\alpha$): $\alpha = \frac{1 - i}{1 - 1/n}$