Solutions
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Quick Revision Notes & Formula Sheet
Class: 12 Chemistry Chapter: Solutions (विलयन)
### 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).
### 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
### 3. Solubility of Gases in Liquids (Henry's Law)
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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).
### 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_Aandp_B = p_B^0 x X_BTotal pressureP_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 top^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^0is the relative lowering of vapour pressure)
### 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:
- Positive Deviation: $P_{total} > (p_A^0 X_A + p_B^0 X_B)$, $\Delta H > 0$, $\Delta V > 0$ (e.g., Ethanol + Acetone)
- Negative Deviation: $P_{total} < (p_A^0 X_A + p_B^0 X_B)$, $\Delta H < 0$, $\Delta V < 0$ (e.g., Phenol + Aniline, $CHCl_3 + acetone$)
### 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.
-
Relative Lowering of Vapour Pressure:
((p_1^0 - p_1) / p_1^0) = (W_B x M_A) / (M_B x W_A) -
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) -
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) -
Osmotic Pressure ($\pi$ - परासरण दाब):
\pi = c R T\pi = (n_B / V) R Tor\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 ($\pi_1 = \pi_2$).
### 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
- Relative lowering of vapour pressure:
-
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
- For Dissociation ($n$ ions formed):