CUET: Solutions - Physical Chemistry

• This CUET (Common University Entrance Test) lecture comprehensively addresses the Solutions chapter and provides a revision of board exam basics.
• NCERT concepts related to physical chemistry are covered.
• The approach to study prioritizes frequently asked question types.
• Students with a weaker background in 11th-grade should still be able to grasp the fundamental concepts.
• The lecture covers solutions, concentration metrics, Henry’s Law, Raoult’s Law, colligative properties, the Van’t Hoff factor, and abnormal molecular mass.
• Understanding solution concepts is related to real-world applications like scuba diving, high-altitude breathing, and using salt in ice cream production.

Solutions

• A solution is a homogeneous mixture of multiple components.
• Matter is either a pure substance (element or compound) or a mixture.
• Mixtures can be classified as homogeneous (uniform) or heterogeneous (non-uniform).
• Homogeneous mixtures are referred to as a "True Solution".
• True solutions feature extremely small particles that are not visible to the naked eye.
• True solutions do not exhibit the Tyndall effect.
• Solutions consist of a solute and a solvent.
• Solute: The component present in the smaller amount in solutions.
• Solvent: The component present in the larger amount, which determines the solution's physical state.

Types of Solutions

• Binary solutions contain two components.
• Ternary solutions contain three components.
• Quaternary solutions contain four components.
• Regardless of the solution type, there is only one solvent, even if there are multiple solutes.
• The physical state of the SOLVENT (gas, liquid, or solid) determines the solution type.
• Gaseous Solutions: Examples include camphor in nitrogen gas (solid in gas), chloroform in nitrogen gas (liquid in gas), and oxygen and nitrogen mixed (gas in gas).
• Liquid Solutions: Examples include glucose in water (solid in liquid), ethanol in water (liquid in liquid), and oxygen in water (gas in liquid).
• Solid Solutions: Examples include copper in gold (solid in solid), mercury in sodium (liquid in solid), and hydrogen in palladium (gas in solid).

Concentration Terms

• Concentration indicates the amount of solute present in a given amount of solvent or solution.
• Concentration is calculated as the amount of solute divided by the amount of the solution.
• Examples include weight by weight (w/w) percentage and volume by volume (v/v) percentage.

Mass Percentage (w/w)

• Formula: (Mass of solute / Mass of solution) x 100.
• Useful when both solute and solvent are solids.
• For example, a solution with 11g of oxalic acid in 500ml with a density of 1.1 g/mL would require using the density to find the mass of the solution, resulting in approximately 2% w/w.
• 5% w/w NaCl means 5g of NaCl in 100g of solution.

Volume Percentage (v/v)

• Formula: (Volume of solute / Volume of solution) x 100
• Useful when both solute and solvent are liquids.
• A 10% v/v ethanol solution contains 10 mL of ethanol in 100 mL of solution with the solvent volume at 90mL.
• Converting v/v to w/w requires using density to find mass and applying the w/w formula.

Weight by Volume Percentage (w/v)

• Formula: (Mass of solute / Volume of solution) x 100
• Useful for a solid solute in a liquid solution.
• A 10% w/v glucose solution contains 10g of glucose in 100 mL of solution.

Parts Per Million (PPM)

• PPM is similar to percentage but is calculated per million units.
• PPM formulas are as such for each: m/m, v/v, and m/v.
• Used for very dilute solutions, such as measuring pollutants in air or water.
• For example,10 ppm SO2 gas in solution means 10mL of SO2 gas in 10^6 mL of solution.

Moles

• A mole is a number, approximately 6.022 x 10^23.
• Molar mass is the mass of one mole of a substance.
• It is the molecular mass plus the atomic mass of the elements in the molecule.
• Use the formula as no. of moles = Given mass / molar mass.
• One can also use the formula (for gas at Standard Temperature and Pressure) as Given volume / 22.4

Mole Fraction

• Formula: (Moles of component / Total moles in solution).
• The symbol for 'Mole Fraction' is x.
• For a binary solution of A and B, the 'Mole Fraction of A' is (Moles of A) divided by ((Moles of A) + (Moles of B)).
• The sum of all mole fractions in a solution equals 1.
• If the mole fraction of A is known, the 'Mole Fraction of B' = 1 - (Mole Fraction of A).
• A 10% w/w glucose solution contains 10g of glucose in 100g of solution.
• To calculate the mole fraction, calculate the moles of water: (90g H2O) / (18g/mol) = 5 moles.

Molarity

• Indicates the total no. of moles of solute present in 1 L solution.
• Formula: Molarity = (Moles of solute)/(Volume of solution in liters).
• For volume in mL: Molarity = (Moles of solute / Volume of solution in mL) times a 1000.
• Moles can be calculated as Molarity * Volume.
• Milli moles = Molarity * Volume in mL.
• A 2 Molar aqueous NaCl solution contains 2 moles of NaCl per 1 L solution.

Molarity on Dilution

• Formula upon dilution: M1V1 = M2V2, where M is molarity, and V is volume.

Molarity of Mixture

• Formula for Molarity = (M1V1 + M2V2) / (V1 + V2).

Molality

• Indicates the total no. of moles of solute present in 1kg of Solvent.
• Represented as lowercase m.
• Formula: m = (Moles of solute) / (Weight of solvent in kg).
• If the weight is in grams, use: m = (Moles of solute / Weight of solvent in grams) times a 1000
• Molality is preferred over molarity because temperature does not affect molality.

Normality

• Represented as “ N “.
• The total number of gram equivalents present in 1 L of solution.
• Formula: Normality = Molarity * n-factor.
• The “ n “ factor depends on different cases, be it acid or base or salt.
• For acids, this depends on the total no. of ionisable H positive ions.
• For bases, this depends on the total no. of Hydroxide ions.
• For salt, the total of absolute value of the positive value.
• For 1 M of H2SO4 with its 2 moles of H+, the n-factor is 2.

Solubility

• Indicates how well a solute dissolves in a solvent.
• For solid solutes, solubility increases with temperature.
• Depends on whether the process is exothermic or endothermic.
• In exothermic processes, solubility decreases when temperature increases.
• In endothermic processes, solubility decreases when temperature decreases.
• Pressure application does not affect solids and liquids.
• Temperature and pressure affect the solubility of gas in liquid.

Henry's Law

• The solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
• Henry's law is expressed as S = Kp or P = KH times by S.
• P = KH times mole fraction.
• At constant temperature, the mole fraction is fixed.
• KH is the Henry constant.
• KH depends on the nature of the gas and, mostly, on temperature.
• The unit of KH is pressure.
• Applications of Henry's Law include:
• Lower oxygen solubility in warm water reduces death of water animals in cold water.
• Sodas are packed at high pressure to increase CO2 solubility.
• Breathing problems underwater are due to differences in air pressure.
• In deep water, bloods gets nitrogen dissolved, once the diver ascends the Nitrogen comes out as bubble, so helium gas is used, since it is less soluble.

Vapour Pressure

• The pressure at which evaporation reaches equilibrium with condensation.
• Vapour pressure is affected by temperature, the nature of the liquid, and InterMolecular Forces (IMF).
• Vapour pressure is not affected by the shape, size, or surface area of a liquid.
• Boiling occurs when the vapour pressure equals atmospheric pressure.

Raoult's Law and Dalton's Law

• Raoult's Law: For solutions of volatile liquids, each component's partial pressure is proportional to its mole fraction.
• For liquid A, P1 directly proportional to x1.
• P1 = P (0)times X1 .
• P (total) = PA + PB = P (0) + P (0) 1-X2.
• Dalton's Law of Partial Pressure: In a mixture, the mole fractions have a similar relationship. There is a strong connection between Dalton's and Raoult's Laws.

Ideal and Non - Ideal solution

• Ideal solutions obey Raoult’s law.
• Non-ideal solutions do not obey the law.
• In ideal solutions, all intermolecular forces are balanced and equal.
• In non-ideal solutions, this is not true.
• Delta Volume is zero during mixing for ideal solutions, indicating volume is conserved.
• Delta H = 0 for ideal solutions, and delta S >0 for both.
• Benzene and toluene follow ideal solution behavior.
• Acetone and ethanol do not follow these rules.

Azeotropic mixtures ( or constant boiling mixtures).

• Mixtures with constant composition and boiling points that cannot be easily separated by distillation.
• They mostly form from non-ideal solutions.
• Two forms of azeotropic solutions are:
• Minimum boiling azeotropes, which boil easily by reducing external temperature.
• Maximum boiling azeotropes show a negative relation in components, requiring high temperatures for boiling.

Colligative Properties

“Colligative properties depend on the number of particles, not their nature."

• A colligative property depends on the number of particles and not what they are.
• The four colligative properties are:
• Relative lowering of vapour pressure.
• Elevation in boiling.
• Decreasing in freezing.
• Osmotic pressure.”
• 1. Relative lowering of the vapor pressure:.
• It depends on the number of particles added.
• Pure solvents have higher vapour pressure, and non-volatile solutes decrease that pressure.
• P1 - Ps /p (0)s = not equal to small n upon (N +n).
• 2. Elevation at boiling point:
• The higher the amount of solute, the lower the volume pressure with more number of particles.
• For a given vapour pressure, the boiling point increases with more particles. delta T b is directly proportional to molality m.
• 3. Freezing point Depression
• The freezing point of such material will drop.
• "NOTE the air pressure inside a car tyre that is in good condition never be out till there is puncture.”
• 4. Osmotic pressure / Osmosis / RO Reverse Osmosis:
• Osmosis is when the solute moves towards the high concentration material from the low concentration solution.
• Applying pressure can prevent this flow.
• Osmotic pressure is directly proportional to molarity.
• The formula of osmotic pressure is Pi = CRT, where C is the concentration of solute. Pi * V = NRT -"Reverse Osmosis occurs, because the molecule or matter flow from high concentrations directly to the low concentrations"

Van’t Hoff Factor.

• "For non-electrolytes, values are correct, but ionic solutions are harder to predict."

• The Van't Hoff Factor is I = Normal molar mass / Abnormal molar mass "

• I= Real Colligative properties / calculated colligative properties.

• I= no of moles after association divided by no of moles before

• 1)In case NaCl dissociates into Na+ and Cl-, I will always be 2 because it breaks apart

• 2. Acetic acid dimerizes, I is less than 1 because it is in combine version.

Formula List:

• I = 1 - alpha + alpha * X + alpha * Y

• I = 1+(N-1) * alpha, where N is the number of product items when broken apart

• Alpha = I-1/ N-1 also equals the degree of dissociation

• IN ASSOCIATION WHEN ACETIC ACID

• It combines to form a dimer A2, so alpha becomes alpha by 2 and

• I = 1 - alpha+ alpha/2

• For A2, alpha = 1-I/(1-1/n)

• The number of moles divided by volume in liters equals molarity.

• M1 * V1 = M2 * V2 upon dilution, the number of moles remain the same.

• Molality does not change with temperature.