Solutions — Revision Notes

⚡ 30-Second Revision

Solution: — Homogeneous mixture of solute and solvent.
Concentration Units:

- Mass %: $(\text{mass of solute} / \text{mass of solution}) \times 100$ - Volume %: $(\text{volume of solute} / \text{volume of solution}) \times 100$ - ppm: $(\text{mass of solute} / \text{mass of solution}) \times 10^6$ - **Mole Fraction ($\chi$):** $n_A / (n_A + n_B)$ - Molarity (M): $\text{moles of solute} / \text{volume of solution (L)}$ (Temperature-dependent) - Molality (m): $\text{moles of solute} / \text{mass of solvent (kg)}$ (Temperature-independent)

Henry's Law: — $P_{\text{gas}} = K_H \chi_{\text{gas}}$
Raoult's Law: — $P_A = P_A^0 \chi_A$; for non-volatile solute: $\frac{P^0 - P_s}{P^0} = \chi_{\text{solute}}$
Colligative Properties (for non-volatile solute):

- RLVP: $\frac{P^0 - P_s}{P^0} = i \chi_{\text{solute}}$ - **$\Delta T_b$ (Elevation in BP):** $\Delta T_b = i K_b m$ - **$\Delta T_f$ (Depression in FP):** $\Delta T_f = i K_f m$ - **$\Pi$ (Osmotic Pressure):** $\Pi = i CRT$

Van't Hoff Factor (i): — $i = \frac{\text{observed CP}}{\text{calculated CP}}$ or $i = 1 + (n-1)\alpha$ (dissociation) or $i = 1 + (1/n-1)\alpha$ (association).

2-Minute Revision

Solutions are homogeneous mixtures, characterized by uniform composition. Key to understanding them are concentration terms like Molarity (moles/L, temperature-dependent) and Molality (moles/kg solvent, temperature-independent), with molality being crucial for colligative properties.

Solubility of gases decreases with increasing temperature and increases with pressure (Henry's Law). Liquid solutions follow Raoult's Law, which describes vapor pressure. Ideal solutions obey Raoult's Law perfectly, while non-ideal solutions show positive (weaker A-B forces, higher vapor pressure) or negative (stronger A-B forces, lower vapor pressure) deviations, sometimes forming azeotropes.

Colligative properties—relative lowering of vapor pressure, elevation in boiling point, depression in freezing point, and osmotic pressure—depend only on the number of solute particles. For electrolytes, the Van't Hoff factor (i) modifies these properties to account for dissociation or association, leading to abnormal molar masses.

Remember to apply 'i' in all colligative property calculations for ionic compounds.

5-Minute Revision

Let's consolidate the core concepts of Solutions for NEET. A solution is a homogeneous blend of solute and solvent. Concentration is key: Molarity (M) is moles per liter of solution, varying with temperature.

Molality (m) is moles per kilogram of solvent, independent of temperature, making it ideal for colligative properties. Mole fraction ($\chi$) is the ratio of moles of a component to total moles. Solubility is influenced by 'like dissolves like', temperature (gas solubility decreases with T, solid solubility usually increases), and pressure (Henry's Law for gases: $P = K_H \chi$).

Vapor pressure behavior is governed by Raoult's Law: $P_A = P_A^0 \chi_A$. Ideal solutions follow this perfectly, with $\Delta H_{\text{mix}} = 0$ and $\Delta V_{\text{mix}} = 0$. Non-ideal solutions deviate: positive deviation (weaker A-B forces, higher vapor pressure, $\Delta H_{\text{mix}} > 0$, $\Delta V_{\text{mix}} > 0$) and negative deviation (stronger A-B forces, lower vapor pressure, $\Delta H_{\text{mix}} < 0$, $\Delta V_{\text{mix}} < 0$).

These deviations can lead to azeotropes, constant boiling mixtures.

Colligative properties are crucial: they depend on the number of solute particles, not their identity. These are:

1
Relative Lowering of Vapor Pressure (RLVP): — $\frac{P^0 - P_s}{P^0} = i \chi_{\text{solute}}$
2
Elevation in Boiling Point ($\Delta T_b$): — $\Delta T_b = i K_b m$
3
Depression in Freezing Point ($\Delta T_f$): — $\Delta T_f = i K_f m$
4
Osmotic Pressure ($\Pi$): — $\Pi = i CRT$

The Van't Hoff factor (i) is essential for electrolytes, quantifying the effective number of particles. For dissociation, $i = 1 + (n-1)\alpha$; for association, $i = 1 + (1/n-1)\alpha$. Remember to apply 'i' to all colligative property formulas for ionic or associating solutes. Practice numerical problems extensively, paying attention to units and the correct application of 'i'.

Mini-Example: A 0.1 m solution of NaCl in water. Since NaCl dissociates into $Na^+$ and $Cl^-$, $n=2$. Assuming complete dissociation ($\alpha=1$), $i = 1 + (2-1) \times 1 = 2$. If $K_f$ for water is $1.86\,\text{K kg mol}^{-1}$, then $\Delta T_f = i K_f m = 2 \times 1.86 \times 0.1 = 0.372\,\text{K}$. The freezing point would be $-0.372^\circ\text{C}$.

Prelims Revision Notes

1
Solution Basics: — Homogeneous mixture (solute + solvent). Solvent is major component, determines physical state. Solute is minor component.
2
Concentration Units:

* Mass % (w/w): $(\text{mass of solute} / \text{mass of solution}) \times 100$. * Volume % (v/v): $(\text{volume of solute} / \text{volume of solution}) \times 100$. * Mass by Volume % (w/v): $(\text{mass of solute (g)} / \text{volume of solution (mL)}) \times 100$.

* ppm: $(\text{mass of solute} / \text{mass of solution}) \times 10^6$. For very dilute solutions. * **Mole Fraction ($\chi$):** $\chi_A = n_A / (n_A + n_B)$. Sum of mole fractions is 1. * Molarity (M): Moles of solute per litre of solution.

Temperature-dependent. $M = n/V_{\text{soln (L)}}$. * Molality (m): Moles of solute per kilogram of solvent. Temperature-independent. $m = n/m_{\text{solvent (kg)}}$. Preferred for colligative properties.

1
Solubility:

* Solid in Liquid: 'Like dissolves like'. Increases with T (mostly). Pressure has little effect. * Gas in Liquid: Decreases with T. Increases with P (Henry's Law: $P = K_H \chi$). $K_H$ increases with T, meaning solubility decreases.

1
Vapor Pressure:

* Raoult's Law: $P_A = P_A^0 \chi_A$. For non-volatile solute: $\frac{P^0 - P_s}{P^0} = \chi_{\text{solute}}$. * Ideal Solutions: Obey Raoult's Law. $\Delta H_{\text{mix}} = 0$, $\Delta V_{\text{mix}} = 0$.

A-B forces similar to A-A, B-B. * Non-Ideal Solutions: Deviate from Raoult's Law. * Positive Deviation: $P_{\text{obs}} > P_{\text{Raoult}}$. Weaker A-B forces. $\Delta H_{\text{mix}} > 0$, $\Delta V_{\text{mix}} > 0$.

Forms minimum boiling azeotrope. * Negative Deviation: $P_{\text{obs}} < P_{\text{Raoult}}$. Stronger A-B forces. $\Delta H_{\text{mix}} < 0$, $\Delta V_{\text{mix}} < 0$. Forms maximum boiling azeotrope.

1
Colligative Properties (depend on number of solute particles):

* Relative Lowering of Vapor Pressure (RLVP): $\frac{P^0 - P_s}{P^0} = i \frac{n_2}{n_1 + n_2} \approx i \frac{n_2}{n_1}$ (dilute). * **Elevation in Boiling Point ($\Delta T_b$):** $\Delta T_b = i K_b m$. $T_b = T_b^0 + \Delta T_b$. * **Depression in Freezing Point ($\Delta T_f$):** $\Delta T_f = i K_f m$. $T_f = T_f^0 - \Delta T_f$. * **Osmotic Pressure ($\Pi$):** $\Pi = i CRT$. C = Molarity, T = Kelvin, R = Gas constant.

1
Van't Hoff Factor (i): — Accounts for dissociation/association.

* $i = \frac{\text{observed colligative property}}{\text{calculated colligative property}}$. * $i = \frac{\text{normal molar mass}}{\text{abnormal molar mass}}$. * For dissociation: $i = 1 + (n-1)\alpha$. (n = number of ions, $\alpha$ = degree of dissociation). * For association: $i = 1 + (1/n-1)\alpha$. (n = number of molecules associating, $\alpha$ = degree of association). * For non-electrolytes, $i=1$. For strong electrolytes, $i=n$ (assuming $\alpha=1$).

Vyyuha Quick Recall

To remember the four Colligative Properties and their dependence on 'i':

Really Low Vapor Pressure Elevates Boiling Points Depresses Freezing Points Osmotic Pressure Increases

Each of these is directly proportional to the I (Van't Hoff factor) and the concentration (molality for $\Delta T_b$, $\Delta T_f$; molarity for $\Pi$; mole fraction for RLVP). So, think of 'RLVP, EBP, DFP, OPI' as a sequence, all linked by 'i'.