Chemca Formula Sheet - Solutions

CHEMCA

EXAM MASTER FORMULA SHEET

Solutions & Colligative Properties

Optimized for JEE Main, Advanced & NEET

1. Henry's Law (Solubility of Gases)

Describes the solubility of a gas in a liquid at a constant temperature. The partial pressure of the gas in vapor phase ($P$) is proportional to the mole fraction of the gas ($\chi$) in the solution.

Mathematical Form:

\[ P = K_H \cdot \chi \]

$P$ = Partial pressure of gas

$K_H$ = Henry's Law constant

Crucial Dependencies:

• • $K_H$ is a function of the nature of the gas.
• • Higher the value of $K_H$ at a given pressure, the lower is the solubility of the gas in the liquid.
• • $K_H$ increases with temperature ($T$). Therefore, solubility of gases decreases with an increase in temperature (aquatic life is more comfortable in cold water).

2. Liquid-Liquid Solutions (Raoult's Law)

Raoult's Law (Volatile Components)

\[ P_{\text{total}} = P_A^\circ \chi_A + P_B^\circ \chi_B \]

\[ P_{\text{total}} = P_A^\circ + (P_B^\circ - P_A^\circ)\chi_B \]

$P_A^\circ, P_B^\circ$ = Vapour pressures of pure components A and B.

Vapor Phase Composition

To find mole fraction in vapor phase ($Y_A, Y_B$), use Dalton's Law:

\[ Y_A = \frac{P_A}{P_{\text{total}}} = \frac{P_A^\circ \chi_A}{P_{\text{total}}} \]

Property	Ideal Solution	Positive Deviation (+ve)	Negative Deviation (-ve)
Forces of Attraction	$A-B = A-A = B-B$	$A-B < A-A$ or $B-B$	$A-B > A-A$ or $B-B$
Vapor Pressure	$P_T = P_A^\circ \chi_A + P_B^\circ \chi_B$	$P_T > P_A^\circ \chi_A + P_B^\circ \chi_B$	$P_T < P_A^\circ \chi_A + P_B^\circ \chi_B$
Enthalpy ($\Delta H_{mix}$)	0	$> 0$ (Endothermic)	$< 0$ (Exothermic)
Volume ($\Delta V_{mix}$)	0	$> 0$ (Expansion)	$< 0$ (Contraction)
Azeotrope Formed	None	Minimum Boiling	Maximum Boiling
Classic Examples	Benzene + Toluene n-Hexane + n-Heptane	Ethanol + Water Ethanol + Acetone	Phenol + Aniline Chloroform + Acetone

3. Colligative Properties

Properties of dilute solutions that depend only on the number of solute particles in solution, irrespective of their nature.

1. Relative Lowering of V.P. (RLVP)

\[ \frac{P^\circ - P_s}{P^\circ} = i \cdot \chi_{\text{solute}} = i \left( \frac{n}{n+N} \right) \]

Calculation Shortcut:

\[ \frac{P^\circ - P_s}{P_s} = i \frac{n}{N} = i \frac{w M}{m W} \]

2. Elevation in Boiling Point

\[ \Delta T_b = T_b - T_b^\circ = i \cdot K_b \cdot m \]

Where $m$ = molality. $K_b$ is the Ebullioscopic constant (depends ONLY on the solvent).

3. Depression in Freezing Point

\[ \Delta T_f = T_f^\circ - T_f = i \cdot K_f \cdot m \]

Where $m$ = molality. $K_f$ is the Cryoscopic constant (depends ONLY on the solvent).

4. Osmotic Pressure ($\pi$)

\[ \pi = i \cdot C R T \]

$C$ = Molarity of solution. $R$ = Universal Gas Constant ($0.0821$ L·atm/K·mol).

Isotonic Solutions: $\pi_1 = \pi_2 \implies C_1 = C_2$

4. van 't Hoff Factor ($i$)

Accounts for the extent of dissociation or association of solute particles.

\[ i = \frac{\text{Observed Colligative Property}}{\text{Calculated Colligative Property}} = \frac{\text{Calculated Molar Mass}}{\text{Observed Molar Mass}} \]

For Dissociation ($i > 1$):

Let $\alpha$ be the degree of dissociation.

\[ i = 1 + (n - 1)\alpha \]

$n$ = number of ions produced per molecule. E.g., for $\ce{CaCl2}$, $n=3$.

If strong electrolyte ($\alpha = 1$), then $i = n$.

For Association ($i < 1$):

Let $\alpha$ be the degree of association.

\[ i = 1 + \left(\frac{1}{n} - 1\right)\alpha \]

$n$ = number of molecules associating. E.g., for Dimerization (Acetic acid in benzene), $n=2$.

If 100% associated ($\alpha = 1$), then $i = 1/n$.

5. Thermodynamic Derivations of Constants

These formulas show that $K_b$ and $K_f$ depend only on the nature of the solvent.

Cryoscopic Constant ($K_f$)

\[ K_f = \frac{R \cdot M_1 \cdot (T_f^\circ)^2}{1000 \cdot \Delta H_{fus}} \]

$M_1$ = Molar mass of solvent (g/mol)

Ebullioscopic Constant ($K_b$)

\[ K_b = \frac{R \cdot M_1 \cdot (T_b^\circ)^2}{1000 \cdot \Delta H_{vap}} \]

$\Delta H$ must be in Joules if $R=8.314$ J/(K·mol)

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