Liquid Solution

A solution is a uniform mixture comprising two or more substances that do not react chemically with each other and whose composition can be adjusted within specific bounds. Solutions are considered singular phases containing multiple components.

When a solution contains two components, it is termed a binary solution. The substance in a lesser quantity is the solute, while the one in a more significant amount is the solvent.

1.0Types of Solutions 

We will focus solely on binary solutions, comprising two components, which can be solid, liquid, or gaseous states and are summarized in the given table :

2.0Expressing Concentration of Solutions

Concentration, which describes the composition of a solution, can be expressed either qualitatively or quantitatively. Qualitatively, we might describe a solution as dilute or concentrated, which can lead to confusion. Therefore, a quantitative description is often preferred. This can be achieved through various methods given below:

Molarity (M): This represents the number of moles of solute per liter of solution. It is calculated using the formula:

$\text{ Molarity }(M)=\frac{\text{ moles of solute }}{\text{ volume of solution in liters }}$

Molality (m): This is the number of moles of solute per kilogram of solvent. It is calculated using the formula:

$\text{ Molality }(\mathrm{m})=\frac{\text{ moles of solute }}{\text{ mass of solvent in kilograms }}$

Mass Percent (% w/w) : This represents the mass of solute per 100 grams of solution. It is calculated using the formula:

$\text{ Mass Percent }(\%\mathrm{w}/\mathrm{w})=\frac{\text{ mass of solute }}{\text{ mass of solution }}\ast 100$

Volume Percent (% v/v): This is the volume of solute per 100 milliliters of solution. It is calculated using the formula:

Volume Percent (% v/v) = volume of solutevolume of solution*100Parts Per Million (ppm): This represents the number of units of solute per million units of solution. It is calculated using the formula:

$\text{ Volume Percent }(\%\mathrm{v}/\mathrm{v})=\frac{\text{ volume of solute }}{\text{ volume of solution }}\ast 100$

Parts Per Million (ppm): This represents the number of units of solute per million units of solution. It is calculated using the formula:

$\mathrm{ppm}=\frac{\text{ mass of solute }}{\text{ mass of solution }}\ast 10^6$

Normality (N): This measures the number of equivalents of solute per litre of solution. It is mainly used in acid-base reactions and is calculated based on the number of replaceable hydrogen or hydroxide ions in the solute.

$\text{ Mole fraction of a component }=\frac{\text{ Number of moles of the component }}{\text{ Totalnumber of moles of all the components }}$

These methods offer different perspectives on concentration, allowing for flexibility in describing solutions depending on the context and requirements of the experiment or application.

3.0Solubility 

Solubility refers to the maximum amount of solute that can dissolve in a given amount of solvent at a constant temperature. Three main factors influence it: 

• the nature of both the solute and the solvent
• temperature
• pressure.

Solubility of solid in a liquid : 

Polar solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents due to similar intermolecular forces.

When solutes dissolve in solvents, an equilibrium is established:

Solute + Solvent ⇌ Solution. This equilibrium can have a positive or negative enthalpy change (ΔH).

A saturated solution is one where no more solute can dissolve at the same temperature and pressure. An unsaturated solution can dissolve more solute. A saturated solution is in dynamic equilibrium with undissolved solute and contains the maximum amount of solute dissolved in the solvent.

• Temperature affects solubility: Endothermic dissolution (ΔH > 0) increases solubility with temperature, while exothermic dissolution (ΔH < 0) decreases it.
• Due to their incompressibility, pressure has little effect on solubility in solids and liquids.

Solubility of a Gas in a Liquid 

Certain gases, like NH₃ and HCl, are highly soluble in water, while others, such as O₂, N₂, and He, have lower solubility. Gas solubility is mainly influenced by pressure and temperature. Increasing pressure boosts solubility, especially for gases, while higher temperature decreases solubility due to the exothermic nature of gas dissolution.

• Henry's Law establishes a quantitative relationship between the pressure and solubility of a gas in a solvent, specifically for gas-liquid solutions. It states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas at a constant temperature. In simpler terms, the partial pressure of the gas in the vapor phase (p) is directly proportional to the mole fraction of the gas (x) in the solution.

                               p = K_HX ; where K_H = Henry's Constant

Henry's law is observed under certain conditions:

• The gas should not dissociate.
• The pressure should not be excessively high.
• The gas should not be highly soluble in the solvent.
• The temperature should not be excessively low.
• The gas should ideally be inert.

Additionally, regardless of pressure changes at a specific temperature, the volume of the dissolved gas remains constant.

Applications of Henry's Law:

• Sealing soft drink bottles at high pressure increases CO₂  solubility, maintaining carbonation.
• When divers descend underwater, body tissues absorb more gases due to increased pressure. 
• Oxygen is vital for cellular respiration, but nitrogen absorption can lead to nitrogen narcosis, posing a threat. 
• As depth increases, pressure rises, causing more nitrogen absorption. To mitigate risks, scuba divers use air with helium, nitrogen, and oxygen. 
• Low oxygen levels in blood and tissues at high altitudes cause weakness and impaired cognition, known as anoxia.

4.0Vapour Pressure of Liquid Solutions

Vapor pressure represents the pressure exerted by a vapor in balance with its condensed phases (either solid or liquid) within a sealed system at a given temperature. The vapor pressure of a liquid is determined by both its inherent characteristics and the prevailing temperature.

• According to Raoult's Law, in a solution with a nonvolatile solute, the vapor pressure of the solution is directly proportional to the mole fraction of the solvent at a specific temperature.

Each component's partial vapour pressure is directly proportional to its mole fraction at a specific temperature for a solution containing two miscible and volatile liquids.

Mathematically, this relationship can be expressed as:

$P_A=P_0{}^A\cdot X_A$

$P_B=P_0{}^B\cdot X_B$

Where:  P_A and P_B ​are the partial vapour pressure of components A and B respectively.

P₀^A and  P₀^B​  are the vapour pressures of pure components A and B respectively.

In the solution, X_A ​and X_B ​ are the mole fractions of components A and B, respectively.

The solution's total vapour pressure (P_total​​) is the sum of the partial pressures:  

P_total​ = P_A + P_B​

• Raoult’s Law as a special case of Henry’s Law

In both Henry’s Law and Raoult’s Law s, the partial pressure of volatile component is directly proportional to its mole-fraction in solution. Only the proportionality constant K_H differs from P⁰. Hence, Raoult's law becomes a special case of Henry's law in which K_H becomes P⁰. 

5.0Ideal and Non Ideal Solutions

 Ideal solution

• An ideal solution adheres to Raoult's Law under all temperature and concentration conditions and where no change in enthalpy and volume occurs during the mixing of components.

Non ideal Solutions

• Non-ideal solutions may deviate from Raoult's Law, showing positive or negative deviation. These deviations are standard in non-ideal solutions where solute-solvent interactions differ from solvent-solvent interaction.

Comparison between Ideal and Non-ideal solutions

6.0Colligative Properties and Determination of Molar Mass

Colligative properties depend exclusively  on the number of solute particles in a solution, regardless of the solute's identity.

• Relative Lowering of Vapor Pressure: The addition of a nonvolatile solute lowers the vapour pressure of a solvent, with the relative lowering being equal to the mole fraction of the solute.
• Elevation in Boiling Point:The addition of a nonvolatile solute to a solvent leads to an increase in the boiling point of the solution compared to that of the pure solvent.
• Depression in Freezing Point: Adding a nonvolatile solute to a solvent decreases the freezing point of the solution compared to the pure solvent.
• Osmosis and Osmotic Pressure: Osmosis is the process by which solvent molecules move from an area of low solute concentration to an area of higher solute concentration through a semipermeable membrane. The resulting hydrostatic pressure is termed osmotic pressure.
• Abnormal Molecular Mass: When a substance exhibits a molecular mass determined by colligative properties that differ from its expected value.
• Van't Hoff Factor: The ratio of the experimental colligative property value to the calculated value, providing insight into the degree of dissociation or association of solute particles in solution.

7.0Abnormal Molar Masses

Abnormal molar masses refer to situations where the calculated molar mass of a substance, determined through colligative properties, deviates from its expected value. This discrepancy typically arises due to factors such as the association or dissociation of solute particles in solution or other non-ideal behaviour.