Quick Revision Notes & Formula Sheet

Class: 12 Chemistry Chapter: Solutions (विलयन)

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### 1. Introduction & Types of Solutions

A solution is a homogeneous mixture of two or more chemically non-reacting substances.

• Solute (विलेय): The component present in a smaller amount.
• Solvent (विलायक): The component present in a larger amount.

Types of Solutions based on physical states:

• Gas in Liquid: Soda water, Oxygen dissolved in water.
• Liquid in Liquid: Ethanol in water.
• Solid in Liquid: Salt or Glucose in water.
• Solid in Solid: Alloys (Brass, Bronze).

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### 2. Concentration Terms (саंद्रता पद)

• Mass Percentage (w/w %): Mass % of component = (Mass of component in solution / Total mass of solution) x 100

• Volume Percentage (v/v %): Volume % = (Volume of component / Total volume of solution) x 100

• Parts per Million (ppm): ppm = (Number of parts of the component / Total number of parts of all components) x 10^6

• Molarity (M) - मोलरता: Number of moles of solute dissolved per litre of solution. M = (Moles of solute / Volume of solution in litres) M = (W_B x 1000) / (M_B x V_mL) (Where W_B = mass of solute, M_B = molar mass of solute, V = volume in mL) Note: Molarity depends on temperature because volume changes with temperature.

• Molality (m) - मोललता: Number of moles of solute dissolved per kilogram of solvent. m = (Moles of solute / Mass of solvent in kg) m = (W_B x 1000) / (M_B x W_A_g) (Where W_A = mass of solvent in grams) Note: Molality is independent of temperature.

• Mole Fraction (X) - मोल अंश: Ratio of number of moles of one component to the total number of moles of all components. For a binary solution containing components A and B: X_A = n_A / (n_A + n_B) X_B = n_B / (n_A + n_B) X_A + X_B = 1

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### 3. Solubility of Gases in Liquids (Henry's Law)

• Henry's Law: At a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of liquid or solution. P = K_H x X (Where P = Partial pressure of gas, X = Mole fraction of gas in solution, K_H = Henry's law constant)

• Key Points about K_H:

  • K_H is a function of the nature of the gas.
  • As temperature increases, K_H increases, and solubility of gases decreases (that's why aquatic species are more comfortable in cold water than warm water).

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### 4. Vapour Pressure of Liquid Solutions (Raoult's Law)

• Raoult's Law for volatile liquids: For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction. p_A = p_A^0 x X_A and p_B = p_B^0 x X_B Total pressure P_total = p_A + p_B = (p_A^0 x X_A) + (p_B^0 x X_B)

• Raoult's Law as a special case of Henry's Law: When vapour pressure p = K_H x X, here K_H becomes equal to p^0 (vapour pressure of pure component).

• Raoult's Law for Non-volatile Solutes: ((p_A^0 - p_A) / p_A^0) = X_B = (n_B) / (n_A + n_B) (Where (p_A^0 - p_A) / p_A^0 is the relative lowering of vapour pressure)

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### 5. Ideal and Non-Ideal Solutions

Property	Ideal Solutions (आदर्श विलयन)	Non-Ideal Solutions (अनादर्श विलयन)
Raoult's Law	Obey Raoult's law over entire range of concentration.	Do not obey Raoult's law.
Enthalpy of mixing ($\Delta_{mix}H$)	$\Delta_{mix}H = 0$	$\Delta_{mix}H \neq 0$
Volume of mixing ($\Delta_{mix}V$)	$\Delta_{mix}V = 0$	$\Delta_{mix}V \neq 0$
Intermolecular forces	$A-A$, $B-B$ interactions $\approx A-B$ interactions	$A-B$ interactions $\neq A-A$ or $B-B$ interactions

Non-Ideal Solutions are of two types:

1. Positive Deviation: $P_{total} > (p_A^0 X_A + p_B^0 X_B)$, $\Delta H > 0$, $\Delta V > 0$ (e.g., Ethanol + Acetone)
2. Negative Deviation: $P_{total} < (p_A^0 X_A + p_B^0 X_B)$, $\Delta H < 0$, $\Delta V < 0$ (e.g., Phenol + Aniline, $CHCl_3 + acetone$)

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### 6. Colligative Properties (अणुसंख्यक गुणधर्म)

Properties of solutions that depend upon the number of solute particles in solution irrespective of their nature are called colligative properties.

1. Relative Lowering of Vapour Pressure: ((p_1^0 - p_1) / p_1^0) = (W_B x M_A) / (M_B x W_A)

2. Elevation of Boiling Point ($\Delta T_b$ - क्वथनांक में उन्नयन): \Delta T_b = T_b - T_b^0 = K_b x m \Delta T_b = (K_b x W_B x 1000) / (M_B x W_A) (Where $K_b$ = Boiling point elevation constant / Ebullioscopic constant)

3. Depression of Freezing Point ($\Delta T_f$ - हिमांक में अवनमन): \Delta T_f = T_f^0 - T_f = K_f x m \Delta T_f = (K_f x W_B x 1000) / (M_B x W_A) (Where $K_f$ = Freezing point depression constant / Cryoscopic constant)

4. Osmotic Pressure ($\pi$ - परासरण दाब): \pi = c R T \pi = (n_B / V) R T or \pi V = (W_B / M_B) R T (Where c = Molarity, R = Gas constant, T = Temperature in Kelvin)

   • Isotonic Solutions: Solutions having the same osmotic pressure ($\pi_1 = \pi_2$).

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### 7. Abnormal Molar Mass & Van't Hoff Factor ($i$)

When solute undergoes association or dissociation in solution, the observed molar mass is different from the normal molar mass. To correct this, Van't Hoff factor ($i$) is introduced.

• Formula for $i$: i = (Normal Molar Mass) / (Abnormal Molar Mass) i = (Observed number of moles after dissociation/association) / (Initial number of moles before dissociation/association)

• Modified Colligative Property Formulas:

  • Relative lowering of vapour pressure: ((p_1^0 - p_1) / p_1^0) = i x X_B
  • Elevation of Boiling Point: \Delta T_b = i x K_b x m
  • Depression of Freezing Point: \Delta T_f = i x K_f x m
  • Osmotic Pressure: \pi = i x c R T

• Relation with Degree of Dissociation ($\alpha$) and Association ($\beta$):

  • For Dissociation ($n$ ions formed): i = 1 + (n - 1)\alpha
  • For Association ($n$ molecules associate to form 1): i = 1 + ((1/n) - 1)\beta