Solutions and Colloids notes

MDCAT Chemistry

This chapter explains concentration units, vapour pressure, colligative properties, osmotic pressure, ideal solutions, and solubility equilibria. It also covers adsorption, colloids, suspensions, coagulation, protective colloids, and the factors responsible for colloidal behaviour.

Solutions and Concentration Units

A solution is a homogeneous mixture of two or more substances. The substance present in smaller amount is the solute, while the substance present in larger amount is the solvent. A solution may be solid, liquid, or gaseous.

Concentration expresses the amount of solute present in a specified amount of solution or solvent. A standard solution has accurately known concentration and is prepared in a volumetric flask because its volume is marked very accurately.

Molarity changes with temperature because solution volume changes. Molality does not change with temperature because the mass of solvent remains constant.

Molarity, M = moles of solute per litre of solution.
Molality, m = moles of solute per kilogram of solvent.
Mole fraction of a component = moles of that component divided by total moles of all components.
Mass percentage = (mass of solute ÷ mass of solution) × 100.
A saturated solution contains dissolved solute in equilibrium with undissolved solute.
An unsaturated solution can dissolve more solute at the same temperature.
A standard solution is prepared in a volumetric flask.
For 1 molal ethanol, C2H5OH, solution, 1 mole ethanol is present in 1 kg water. Its mole fraction is approximately 1 ÷ 11 = 0.091, usually taken as 0.1 at FSc level.

Vapour Pressure and Raoult’s Law

Vapour pressure is the pressure exerted by vapour in equilibrium with its liquid at a particular temperature. A non-volatile solute lowers the vapour pressure of the solvent because fewer solvent molecules escape from the surface.

Raoult’s law states that the partial vapour pressure of a volatile component is equal to its mole fraction multiplied by the vapour pressure of the pure component. For a solution containing a non-volatile solute, the vapour pressure is P = Xsolvent P°solvent.

For water with vapour pressure 23.75 torr and solvent mole fraction 0.75, P = 0.75 × 23.75 = 17.8 torr. The lowering of vapour pressure is a colligative property.

Psolution = Xsolvent P°solvent for a non-volatile solute.
Relative lowering of vapour pressure = (P° − P) ÷ P° = Xsolute for dilute solutions.
A solution containing a non-volatile solute has lower vapour pressure than the pure solvent.
At the same concentration, Al2(SO4)3 gives more dissolved particles than a non-electrolyte, so it produces the lower vapour pressure.
For an ideal solution, interactions between A-A, B-B, and A-B molecules are nearly equal.
For an ideal solution, enthalpy change of mixing is zero and volume change of mixing is zero.
Vapour pressure increases when temperature increases.

Colligative Properties

Colligative properties depend on the number of solute particles present in a solution, not on the chemical nature of those particles. They are important for dilute solutions and are affected by ionisation or association of solute particles.

The four colligative properties are relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. Electrolytes usually produce a greater effect than non-electrolytes at the same concentration because they form ions.

The van’t Hoff factor, i, represents the effective number of particles formed by one formula unit of solute. It is used in equations for electrolytes and for solutes that associate or dissociate.

Colligative properties depend on the number of solute particles, not the nature of the solute.
A non-volatile solute lowers vapour pressure.
Addition of a soluble substance lowers the freezing point of a solvent.
Addition of a soluble substance raises the boiling point of a solvent.
For dissociation, i is greater than 1.
For association, i is less than 1.
The statement that colligative properties depend on the nature of the compound is incorrect.
For complete dissociation, NaCl gives i approximately 2, while Al2(SO4)3 gives i approximately 5.

Elevation of Boiling Point and Depression of Freezing Point

The boiling point is the temperature at which vapour pressure becomes equal to external pressure. A non-volatile solute lowers the vapour pressure of a solution, so a higher temperature is needed for boiling.

The freezing point is the temperature at which the vapour pressures of the liquid solvent and solid solvent become equal. A dissolved solute lowers the freezing point of the solution.

For a dilute solution, elevation in boiling point is ΔTb = iKb m. Depression in freezing point is ΔTf = iKf m. Here, Kb and Kf are molal elevation and molal depression constants, respectively.

Boiling point of solution = boiling point of pure solvent + ΔTb.
Freezing point of solution = freezing point of pure solvent − ΔTf.
For water, Kb = 0.52 K kg mol−1 and Kf = 1.86 K kg mol−1.
For 18.0 g glucose in 1 kg water, m = 18.0 ÷ 180 = 0.1 mol kg−1.
For this glucose solution, ΔTb = 0.52 × 0.1 = 0.052 °C, so boiling point is 100.052 °C.
Calcium chloride lowers the freezing point and raises the boiling point of water.
For equal molal solutions, a solute producing more particles gives a greater change in boiling or freezing point.

Osmotic Pressure

Osmosis is the movement of solvent molecules through a semipermeable membrane from a dilute solution or pure solvent to a concentrated solution. Osmotic pressure is the minimum pressure required to stop osmosis.

For dilute solutions, osmotic pressure follows the equation π = CRT for non-electrolytes. For electrolytes, π = iCRT. Here, C is molar concentration, R is the gas constant, and T is absolute temperature in kelvin.

At equal temperature and concentration, osmotic pressure depends on the total number of dissolved particles. Thus, equimolar solutions of BaCl2, NaCl, and sucrose have the order BaCl2 > NaCl > sucrose, assuming suitable dissociation.

Osmotic pressure of a dilute solution: π = CRT.
For an electrolyte: π = iCRT.
Temperature must be used in kelvin in the osmotic pressure equation.
At the same concentration, Al2(SO4)3 gives greater osmotic pressure than a non-electrolyte because it forms more ions.
A decimolar Al2(SO4)3 solution has high osmotic pressure when salts are equally and substantially dissociated.
Isotonic solutions have equal osmotic pressure at the same temperature.
Hypertonic solution has greater osmotic pressure than the compared solution.
Hypotonic solution has lower osmotic pressure than the compared solution.

Ionic Strength and Solubility Product

Ionic strength measures the total effect of ions in a solution. It depends on both the concentration and the square of the charge of every ion. The formula is I = 1/2 Σcz2, where c is ionic concentration and z is ionic charge.

For 0.01 M BaCl2, BaCl2 gives 0.01 M Ba2+ and 0.02 M Cl−. Therefore, I = 1/2[(0.01)(2)2 + (0.02)(1)2] = 0.03.

The solubility product, Ksp, is the equilibrium constant for the dissolution of a sparingly soluble ionic compound. It helps calculate solubility and predict precipitation.

Ionic strength formula: I = 1/2 Σcz2.
For 0.01 M BaCl2, ionic strength is 0.03 M.
For Ca(OH)2, Ksp = [Ca2+][OH−]2.
If molar solubility of Ca(OH)2 is s, then [Ca2+] = s and [OH−] = 2s.
For Ca(OH)2, Ksp = s(2s)2 = 4s3.
When Ksp = 6.5 × 10−6, s = (6.5 × 10−6 ÷ 4)1/3 = 1.17 × 10−2 mol L−1.
A precipitate forms when the ionic product is greater than Ksp.

Adsorption and Surface Phenomena

Adsorption is the accumulation of particles of one substance at the surface of another substance. The substance providing the surface is the adsorbent, and the substance held at the surface is the adsorbate. Adsorption is a surface phenomenon, while absorption occurs throughout the bulk.

Molecules at the surface of a solid have higher energy than molecules inside the solid. They attract and hold particles from the surrounding phase, which lowers their surface energy.

Physisorption is caused by weak van der Waals forces. It is generally reversible and decreases when temperature increases. Chemisorption involves chemical bond formation, is usually stronger, and may increase initially with temperature because activation energy is required.

Adsorption occurs at the surface; absorption occurs throughout the substance.
The surface molecules of a solid have higher energy than molecules inside it.
Physisorption involves weak van der Waals forces.
Chemisorption involves chemical bonding between adsorbent and adsorbate.
The rate of physisorption generally decreases when temperature increases.
An adsorption isotherm shows the variation of amount adsorbed with pressure at constant temperature.
An adsorption isostere shows the variation of pressure with temperature for a fixed amount of adsorption.
A catalyst poison completely destroys or reduces the activity of a catalyst.

Colloids, Suspensions, and Coagulation

A colloid is a heterogeneous system in which particles of one substance are dispersed in another substance. Colloidal particles are larger than ordinary solution particles but smaller than suspension particles. They remain dispersed because of Brownian motion and electrical repulsion.

A suspension contains relatively large insoluble particles that settle under gravity and can usually be separated by filtration. A true solution is homogeneous, while a colloid and a suspension are heterogeneous systems, although a colloid may appear uniform to the naked eye.

Colloidal particles may carry positive or negative charges. Coagulation is the removal of charge and aggregation of colloidal particles. Electrolytes cause coagulation by neutralising the charge on colloidal particles.

A true solution has particles smaller than colloidal particles and does not show the Tyndall effect.
Colloidal particles show Brownian movement and the Tyndall effect.
Suspension particles settle on standing and can generally be filtered.
Gold sols prepared by different methods may have different colours because their colloidal particles have different sizes.
Ag and Pt colloidal sols are generally negatively charged, not positively charged.
FeCl3 helps stop bleeding because Fe3+ ions coagulate blood proteins and blood cells, helping seal the wound.
The minimum concentration of an electrolyte needed to coagulate a sol is called its coagulation value.
Hardy-Schulze rule states that the coagulating power of an ion increases with the valency of the oppositely charged ion.

Protective Colloids and Gold Number

Some lyophilic colloids protect lyophobic colloids from coagulation by forming a protective layer around their particles. The protective colloid reduces direct contact between particles and prevents aggregation.

Gold number is an index of the protective power of a colloid. It is defined as the minimum mass in milligrams of the protective colloid required to prevent the coagulation of 10 mL of a standard gold sol when 1 mL of a 10 percent sodium chloride solution is added.

A lower gold number means greater protective power. Gold number is therefore related to protection against coagulation, not to colour, particle charge, or catalytic activity.

Protective colloids prevent or delay coagulation of lyophobic sols.
Gelatin, gum, and starch can act as protective colloids.
Gold number measures the protective power of a colloid.
A smaller gold number indicates stronger protective action.
Gold number is not an index of the colour of a gold sol.
The colour of gold sol depends on the size of its colloidal particles.
Coagulation involves aggregation of colloidal particles and loss of stability.

Key terms

Solution: A homogeneous mixture of two or more substances.
Solute: The component that is dissolved in a solution.
Solvent: The component that dissolves the solute and is usually present in greater amount.
Molarity: The number of moles of solute present per litre of solution.
Molality: The number of moles of solute present per kilogram of solvent.
Mole fraction: The ratio of moles of one component to the total moles of all components.
Colligative property: A property that depends on the number of solute particles rather than their chemical nature.
Osmosis: The movement of solvent through a semipermeable membrane towards the solution with greater solute particle concentration.
Osmotic pressure: The pressure needed to stop osmosis.
Adsorption: The accumulation of particles at the surface of a substance.
Physisorption: Adsorption caused mainly by weak van der Waals forces.
Chemisorption: Adsorption involving the formation of chemical bonds.
Colloid: A heterogeneous dispersion containing particles of intermediate size between true solution particles and suspension particles.
Suspension: A heterogeneous mixture containing large insoluble particles that settle on standing.
Coagulation: The aggregation and settling of colloidal particles after loss of stability.
Gold number: The minimum mass of protective colloid needed to prevent coagulation of a standard gold sol.
Ionic strength: A measure calculated from the concentration and square of charge of ions in a solution.
Solubility product: The equilibrium constant for the dissolution of a sparingly soluble ionic compound.

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Chemistry shortcuts

Finding the limiting reactant and percentage composition

Convert every given mass or volume into moles first. The reactant that produces the least amount of the required product is the limiting reactant.

Write the balanced equation and calculate moles using n = mass/Mr.
Use the mole ratio to calculate the product. For percentage composition, use percentage = mass of element in one mole of compound divided by molar mass, multiplied by 100.
Example: Percentage of nitrogen in KNO3 = 14/101 × 100 = 13.86%.
Answer: 13.86% nitrogen.

Use gas volume at molar volume only when the gas conditions are stated or are standard conditions.

Using gas volume, pressure and temperature relations

At the same temperature and pressure, gas volume is directly proportional to the number of molecules. For changing conditions, use P1V1/T1 = P2V2/T2.

At constant temperature and pressure, divide or multiply the volume in the same ratio as the number of molecules.
Example: 10 mL H2 contains 2 × 10^3 molecules. Oxygen in 200 mL contains 20 × 2 × 10^3 = 4 × 10^4 molecules.
Answer: 4 × 10^4 molecules.
For a rigid container, increasing temperature increases molecular speed and mean free path if the gas remains in the same phase.

The direct volume to molecule ratio does not apply when temperature or pressure changes.

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