Solutions Class 12 Chemistry Chapter 1 Notes

Solution

Solutions are homogeneous mixtures composed of two or more components.
A homogeneous mixture means that the composition and properties are consistent throughout the mixture.
The component present in the largest quantity is known as the solvent.
The solvent determines the physical state in which the solution exists.
The components in the solution, other than the solvent, are called solutes.
In this unit, we focus on binary solutions, which consist of two components.
Here are the types of binary solutions:

1. Gaseous Solutions:

Solute: Gas
Solvent: Gas
Common Example: Mixture of oxygen and nitrogen gases

2. Liquid-Gas Solutions:

Solute: Gas
Solvent: Liquid
Common Example: Chloroform mixed with nitrogen gas

3. Solid-Gas Solutions:

Solute: Gas
Solvent: Solid
Common Example: Camphor in nitrogen gas

4. Liquid-Liquid Solutions:

Solute: Liquid
Solvent: Liquid
Common Example: Ethanol dissolved in water

5. Solid-Liquid Solutions:

Solute: Solid
Solvent: Liquid
Common Example: Glucose dissolved in water

6. Solid-Solutions:

Solute: Gas
Solvent: Solid
Common Example: Solution of hydrogen in palladium

7. Liquid-Solid Solutions:

Solute: Liquid
Solvent: Solid
Common Example: Amalgam of mercury with sodium

8. Solid-Solid Solutions:

Solute: Solid
Solvent: Solid
Common Example: Copper dissolved in gold

Solution Concentration:

The composition of a solution is often described by its concentration.
Concentration can be expressed either qualitatively or quantitatively.
Qualitatively, we can describe a solution as:
- Dilute: When there is a relatively small quantity of solute compared to the solvent.
- Concentrated: When there is a relatively large quantity of solute compared to the solvent.
However, qualitative descriptions like “dilute” and “concentrated” can be ambiguous and lead to confusion.
Therefore, there is a need for quantitative descriptions of solutions to provide precise information about their composition.

1. Mass Percentage (w/w) as a Quantitative Description:

Mass percentage (w/w) is a quantitative measure used to express the concentration of a component in a solution.
The formula for calculating the mass percentage (w/w) of a component in a solution is as follows:
Mass % of a component = (Mass of the component in the solution / Total mass of the solution) x 100 (Equation 1.1)
For example, if a solution is described as “10% glucose in water by mass,” it means that:
- 10 grams of glucose is dissolved in 90 grams of water, resulting in a total mass of 100 grams for the solution.
- Using Equation 1.1, we can calculate the mass percentage of glucose in the solution as (10 g / 100 g) x 100 = 10%.
Mass percentage (w/w) is commonly used in industrial chemical applications to specify the concentration of components in solutions.
A practical example is commercial bleaching solution, which may contain 3.62 mass percentage of sodium hypochlorite in water. This means that for every 100 grams of the bleaching solution, 3.62 grams are sodium hypochlorite.

Mass percentage (w/w) is a straightforward and widely used method for expressing the concentration of components in various industrial and chemical processes.

2. Volume Percentage (V/V) as a Quantitative Description:

Volume percentage (V/V) is another quantitative measure used to express the concentration of a component in a solution.
The formula for calculating the volume percentage (V/V) of a component in a solution is as follows:
Volume % of a component = (Volume of the component / Total volume of the solution) x 100
For example, if a solution is described as “10% ethanol solution in water,” it means that:
- 10 mL of ethanol is dissolved in water in such a way that the total volume of the solution is 100 mL.
- Using the formula, we can calculate the volume percentage of ethanol in the solution as (10 mL / 100 mL) x 100 = 10%.
Volume percentage (V/V) is commonly used for solutions that contain liquids as their components.
An example is a 35% (v/v) solution of ethylene glycol, which is used as an antifreeze in cars to cool the engine. This means that for every 100 mL of the solution, 35 mL is ethylene glycol.
Ethylene glycol at this concentration lowers the freezing point of water to 255.4K (-17.6°C).

Volume percentage (V/V) is a useful way to specify the concentration of liquid components in solutions, particularly in applications such as chemistry, industry, and automotive maintenance.

3. Mass by Volume Percentage (w/V):

Mass by volume percentage (w/V) is a commonly used unit in medicine and pharmacy to express the concentration of a solute in a solution.
This unit represents the mass of the solute (in grams) dissolved in 100 mL of the solution.
It is particularly important in fields where precise dosing of medications or chemicals is necessary, as it provides a clear measure of concentration.
The formula for calculating mass by volume percentage (w/V) is as follows:
Mass by Volume % (w/V) = (Mass of the solute in grams / Volume of the solution in mL) x 100
For example, if you have a medication described as “5% (w/V) glucose solution,” it means that:
- There are 5 grams of glucose dissolved in 100 mL of the solution.
- This concentration is important in medical practice where accurately dosing medications is crucial.

Mass by volume percentage is an important unit for healthcare professionals, pharmacists, and researchers dealing with solutions where the concentration of a solute in a specific volume is critical.

4. Parts per Million (ppm) as a Concentration Unit:

Parts per million (ppm) is a unit used to express extremely low concentrations of a solute in a solution, especially when it is present in trace amounts.
It quantifies the number of parts of a particular component per one million parts of the entire solution.
The formula for calculating parts per million (ppm) is as follows:
Parts per Million (ppm) = (Number of parts of the component / Total number of parts of all components of the solution) x 1,000,000
Concentrations in ppm can be expressed in various ways, including:
- Mass to mass: Mass of the solute in grams per million grams of the solution.
- Volume to volume: Volume of the solute in milliliters per million milliliters of the solution.
- Mass to volume: Mass of the solute in grams per million milliliters (or liters) of the solution.
For example, in a liter of sea water (which weighs approximately 1030 grams), if there are about 6 x 10^-3 grams of dissolved oxygen (O2), this concentration can be expressed as 5.8 grams per million grams (5.8 ppm) of sea water.
Parts per million is commonly used to express the concentration of pollutants in water or the atmosphere. For example, the concentration of pollutants might be expressed as milligrams per milliliter (mg/mL) or ppm in environmental studies and quality control.
ppm is a valuable unit for measuring trace amounts of substances and is essential for environmental monitoring, quality control, and other applications where even tiny concentrations matter.

5. Mole Fraction (x) as a Concentration Measure:

Mole fraction (x) is a unitless measure used to express the concentration of a component in a mixture or solution.
It is represented by the symbol “x,” and the subscript on the right-hand side of “x” denotes the component for which the mole fraction is being calculated.
The mole fraction of a component is defined as:
Mole Fraction of a Component = (Number of moles of the component) / (Total number of moles of all components)
In a binary mixture containing two components A and B with the number of moles of A and B being nA and nB respectively, the mole fraction of A is calculated as:
xA = nA / (nA + nB)
For a solution containing i number of components, the mole fraction of each component can be calculated using the formula:
xi = (ni / n_total)
Where xi is the mole fraction of component i, ni is the number of moles of component i, and n_total is the total number of moles of all components in the solution.
It is important to note that the sum of all mole fractions in a solution is always equal to 1. This reflects the fact that mole fractions represent the fraction of moles contributed by each component in the total moles of the mixture.
Mole fraction is a valuable unit in relating various physical properties of solutions, such as vapor pressure, to the concentration of the solution. It is particularly useful in calculations involving gas mixtures where the behavior of individual gases in the mixture needs to be understood and quantified.

Mole fraction provides a precise way to describe the composition of a mixture and is widely used in chemistry and chemical engineering for various calculations and property correlations.

6. Molarity (M) as a Concentration Unit:

Molarity (M) is a unit of concentration used to express the amount of solute dissolved in a solution in relation to the volume of the solution.
It is commonly represented as moles of solute per liter (or one cubic decimeter) of solution.
The formula for calculating molarity is as follows:
Molarity (M) = (Moles of solute) / (Volume of solution in liters)
For example, a solution described as 0.25 mol L^–1 (or 0.25 M) solution of NaOH means that 0.25 moles of NaOH have been dissolved in one liter (or one cubic decimeter) of solution.
Molarity is particularly important in chemistry and chemical analysis because it allows for precise control of the concentration of solutions. It is commonly used in laboratory work and in the preparation of solutions for experiments and reactions.
When performing calculations involving molarity, it is essential to convert the volume of the solution to liters to ensure that the units align correctly.
Molarity is often used in stoichiometry, dilution, and titration calculations, where the precise amount of a substance in a solution needs to be determined or controlled.

Molarity is a fundamental concept in chemistry and plays a crucial role in quantitative analysis and chemical reactions, helping chemists accurately measure and manipulate the concentration of solutions.

7. Molality (m) as a Concentration Unit:

Molality (m) is a unit of concentration used to express the amount of solute dissolved in a solution relative to the mass of the solvent.
It is represented as moles of solute per kilogram (kg) of solvent.
The formula for calculating molality is as follows:
Molality (m) = (Moles of solute) / (Mass of solvent in kg)
For example, a solution described as 1.00 mol kg^–1 (or 1.00 m) solution of KCl means that 1 mole (74.5 grams) of KCl is dissolved in 1 kilogram (1000 grams) of water.
Molality is particularly useful in situations where changes in temperature might affect the volume of a solution, as it is independent of temperature changes. This makes it a preferred concentration unit in many laboratory applications.
Unlike molarity, which depends on the volume of the solution (and can change with temperature), molality remains constant with temperature variations because it is based on mass.
Molality is often used in chemistry, particularly in colligative properties, freezing-point depression, and boiling-point elevation calculations. It is also used in various industries, such as pharmaceuticals and food chemistry, where precise control of solute concentrations is essential.

Molality provides a reliable way to express concentration in solutions and is especially valuable in situations where temperature fluctuations must be considered.

Solubility and Its Factors:

Definition of Solubility:

Solubility is the maximum amount of a substance (solute) that can be dissolved in a specified amount of solvent at a particular temperature and pressure. It’s a fundamental concept in chemistry that depends on various factors.

Factors Affecting Solubility:

Nature of Solute and Solvent:
- The chemical and physical properties of the solute and solvent play a significant role in determining solubility.
- Like dissolves like: Polar solutes tend to dissolve better in polar solvents, while nonpolar solutes dissolve better in nonpolar solvents.
Temperature:
- In general, the solubility of most solids in liquids increases with an increase in temperature. This is because higher temperatures provide more energy to overcome the attractive forces between solute particles.
- However, there are exceptions. For example, the solubility of some salts decreases with increasing temperature (e.g., calcium sulfate).
Pressure (for Gases in Liquids):
- For gases dissolved in liquids, Henry’s law describes how the solubility depends on pressure.
- According to Henry’s law, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
- An increase in pressure leads to an increase in the solubility of gases in liquids.
Pressure (for Solids in Liquids):
- Pressure generally has little effect on the solubility of solids in liquids. It’s typically considered a constant factor.
Stirring or Agitation:
- Mechanical agitation or stirring can increase the rate at which a solute dissolves but doesn’t typically change the maximum solubility.
Surface Area of the Solute:
- Increasing the surface area of the solute, such as by grinding it into smaller particles, can increase the rate of dissolution but not necessarily the maximum solubility.
Nature of the Solution (Previous Dissolution):
- The presence of a previously dissolved solute in a solution can sometimes affect the solubility of another solute. This phenomenon is called salting in or salting out.

Solubility of Solids in Liquids:

1. Solubility Depends on Intermolecular Interactions:

Not all solids dissolve in a given liquid. The solubility of a solid in a liquid depends on the nature of the solute and solvent.
Polar solutes tend to dissolve in polar solvents, and nonpolar solutes tend to dissolve in nonpolar solvents. This principle is summarized as “like dissolves like.”

2. Dissolution and Crystallization:

When a solid solute is added to a solvent, two processes occur: dissolution and crystallization.
Dissolution is the process in which some solute particles dissolve in the solvent, increasing the concentration of the solute in the solution.
Crystallization is the process in which some solute particles in the solution collide with solid solute particles and separate out of the solution.
When the rates of dissolution and crystallization are equal, a dynamic equilibrium is reached.

3. Dynamic Equilibrium:

The dynamic equilibrium is represented by the equation: Solute + Solvent ⇌ Solution (1.10).
At this stage, the concentration of solute in the solution remains constant under given conditions of temperature and pressure.

4. Saturated and Unsaturated Solutions:

A saturated solution is one in which no more solute can be dissolved at the same temperature and pressure. It contains the maximum amount of solute that can be dissolved in a given amount of solvent.
An unsaturated solution is one in which more solute can be dissolved at the same temperature.

5. Solubility:

The concentration of solute in a saturated solution is called its solubility. Solubility is a specific property of a substance and depends on the nature of the substances involved.

Effect of Temperature on Solubility:

The solubility of a solid in a liquid is significantly influenced by temperature changes.
In general, if the dissolution process is endothermic (Δsol H > 0), solubility increases with rising temperature.
If the dissolution process is exothermic (Δsol H < 0), solubility typically decreases with rising temperature.
This temperature effect is due to the dynamic equilibrium and is consistent with Le Chatelier’s Principle.

Effect of Pressure on Solubility:

Pressure has no significant effect on the solubility of solids in liquids.
Solids and liquids are highly incompressible and are practically unaffected by changes in pressure.

Solubility of Gases in Liquids and Henry’s Law:

Solubility of Gases in Liquids:

Many gases can dissolve in liquids, and the extent of their solubility varies with different gases and conditions.
For example, oxygen dissolves only to a small extent in water, while hydrogen chloride gas (HCl) is highly soluble in water.

Factors Affecting Solubility:

The solubility of gases in liquids is greatly influenced by two factors: pressure and temperature.
The solubility of gases generally increases with an increase in pressure.
Gases dissolved in a liquid exist in dynamic equilibrium with the gas phase above the liquid.

Henry’s Law:

Henry’s law provides a quantitative relationship between the pressure of a gas and its solubility in a liquid at a constant temperature.
Henry’s law states that the solubility of a gas is directly proportional to the partial pressure of the gas above the liquid or solution.
It can be expressed as: p = KH x, where p is the partial pressure of the gas, KH is the Henry’s law constant, and x is the mole fraction of the gas in the solution.
Different gases have different Henry’s law constants, and these constants vary with temperature.

Effect of Temperature on Solubility:

The solubility of gases in liquids decreases with an increase in temperature.
This temperature effect is consistent with Le Chatelier’s Principle, as the dissolution of gases is an exothermic process that releases heat.
Therefore, when the temperature rises, the equilibrium shifts toward the gas phase, resulting in lower gas solubility in the liquid.

Applications of Henry’s Law:

Henry’s law finds applications in various fields, including:
- Carbonation of Soft Drinks: High-pressure sealing of bottles with CO2 increases its solubility, creating carbonated beverages.
- Scuba Diving: Divers breathe high-pressure air underwater, leading to higher gas solubility in their blood. When ascending, dissolved gases can form bubbles, causing decompression sickness (“the bends”).
- High-Altitude Climbing: Lower oxygen partial pressure at high altitudes reduces oxygen solubility in blood, leading to altitude sickness.

Effect of Temperature on Gas Solubility in Liquids:

The effect of temperature on the solubility of gases in liquids is an important factor to consider in various scientific and industrial processes. Here’s a summary of how temperature affects gas solubility in liquids:

General Trend: In most cases, the solubility of gases in liquids decreases with an increase in temperature.
Exothermic Process: Dissolution of gases in liquids is often considered an exothermic process, meaning it releases heat. During dissolution, gas molecules move from the gas phase to the liquid phase, and this transition is accompanied by the release of thermal energy.
Le Chatelier’s Principle: The behavior of gas solubility with respect to temperature change can be understood through Le Chatelier’s Principle. According to this principle, if a system at equilibrium experiences a change in conditions (such as temperature), it will adjust to counteract that change and re-establish a new equilibrium.
Exothermic Nature: Since the dissolution of gases in liquids is an exothermic process, an increase in temperature disrupts the equilibrium. To counteract the temperature increase and restore equilibrium, the system shifts in the direction that consumes heat. In this case, it means that gas molecules tend to leave the liquid phase and return to the gas phase when the temperature rises.
Lower Solubility at Higher Temperatures: Due to the exothermic nature of gas dissolution, higher temperatures lead to lower gas solubility in the liquid. In other words, gases are less likely to remain dissolved in the liquid phase at elevated temperatures.
Practical Implications: This temperature effect is important in various applications. For example, in the beverage industry, when carbonating soft drinks, it’s more challenging to dissolve carbon dioxide (CO2) at higher temperatures. Additionally, in scuba diving, understanding how temperature affects gas solubility is critical for managing the risk of decompression sickness.

Vapor Pressure of Liquid Solutions:

In the context of liquid solutions, particularly binary solutions containing two components (a solvent and a solute), understanding vapor pressure is crucial. Here’s an overview of the vapor pressure of liquid solutions:

Binary Liquid Solutions: Liquid solutions consist of a solvent and a solute. The solvent is typically a liquid, and the solute can be a liquid or a solid. Binary solutions are those containing exactly two components.
Volatility: In many cases, the solvent is volatile, meaning it has the tendency to evaporate and form vapor at a given temperature. Volatility is a key factor in determining the vapor pressure of the solution.
Vapor Pressure: The vapor pressure of a liquid solution is the pressure exerted by the vapor (gaseous phase) above the liquid surface when the system is in a state of dynamic equilibrium. This equilibrium involves molecules of the solvent both evaporating from the liquid and condensing back into the liquid phase at the same rate.
Components and Vapor Pressure: The vapor pressure of a liquid solution is influenced by the nature and concentration of its components, as well as the temperature. Several important points to note:
- Raoult’s Law: Raoult’s Law is a fundamental principle that applies to ideal solutions. It states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of each component in the solution. Mathematically, for a binary solution:
- P_total = x_A * P_A^0 + x_B * P_B^0
- Where:
  - P_total is the total vapor pressure of the solution.
  - x_A and x_B are the mole fractions of the solvent (A) and solute (B), respectively.
  - P_A^0 and P_B^0 are the vapor pressures of the pure solvent and solute, respectively.
- Ideal vs. Non-Ideal Solutions: In ideal solutions, the vapor pressure follows Raoult’s Law precisely. In non-ideal solutions, interactions between solvent and solute molecules (deviations from ideal behavior) can affect vapor pressure. Deviations can result in either higher or lower vapor pressures compared to what would be predicted by Raoult’s Law.
Temperature Dependence: Vapor pressure is highly temperature-dependent. An increase in temperature generally leads to an increase in vapor pressure. This relationship is exploited in various applications, such as distillation and evaporation.
Boiling Point: The boiling point of a liquid is the temperature at which its vapor pressure equals atmospheric pressure. When the vapor pressure reaches this level, the liquid starts to boil and convert into vapor.

Vapor Pressure of Liquid Solutions – Raoult’s Law:

In liquid solutions consisting of two volatile components, Raoult’s law provides a quantitative relationship between the vapor pressures of the components and their mole fractions. Here are the key points:

Binary Volatile Liquid Solutions: Consider a binary solution comprising two volatile liquids, denoted as component 1 and component 2. When placed in a closed vessel, both components will evaporate, establishing an equilibrium between the vapor and liquid phases.
Partial Vapor Pressures: Let p1 and p2 represent the partial vapor pressures of component 1 and component 2, respectively. These partial pressures are related to the mole fractions x1 and x2 of the two components:
1. For component 1: p1 ∝ x1 and p1= p1^0.x1, where p1^0 is the vapor pressure of pure component 1 at the same temperature.
2. For component 2: p2 ∝ x2 and p2= p2^0.x2, where p2^0 is the vapor pressure of pure component 2 at the same temperature.
Raoult’s Law: Raoult’s Law states that for a solution of volatile liquids, the partial vapor pressure of each component in the solution is directly proportional to its mole fraction present in the solution.
Total Vapor Pressure: According to Dalton’s law of partial pressures, the total pressure (P total) over the solution in the container is the sum of the partial pressures of the components. Mathematically, it is expressed as p(total) = p1 + p2.
Linear Relationship: The total vapor pressure over the solution p(total) varies linearly with the mole fraction of component 2(x2).
varies linearly with the mole fraction of component (y1 and y2) of components 1 and 2 in the vapor phase. According to Dalton’s law of partial pressures, p1=y1.p(total) and p2=y2.p(total).
Generally, pi=yi.p(total) for any component i.

Raoult’s Law as a Special Case of Henry’s Law:

Raoult’s law and Henry’s law are two fundamental principles used to describe the behavior of solute components in solutions. Raoult’s law applies primarily to liquid solutions, while Henry’s law is used to describe the behavior of gases in liquids. Interestingly, Raoult’s law can be considered a special case of Henry’s law when dealing with a specific scenario. Here’s how they relate:

Raoult’s Law: This law describes the behavior of volatile components in liquid-liquid solutions. It states that the partial vapor pressure (pi) of a volatile component in a solution is directly proportional to its mole fraction (xi) in the solution and can be expressed as p_i = x_i * p_i⁰ In this equation, p_i⁰ is the vapor pressure of pure component _i at the same temperature.
Henry’s Law: Henry’s law, on the other hand, is applicable to the solubility of gases in liquids. It states that the partial pressure (p) of a gas in the vapor phase is directly proportional to its mole fraction (x) in the liquid phase and is expressed as p = K_H * x. In this equation, K_H is the Henry’s law constant, specific to the gas-solvent system.

Now, let’s consider the relationship between these two laws:

Special Case – Raoult’s Law as a Special Case of Henry’s Law:

When dealing with the solubility of a gas in a liquid, we can consider one component to be a gas (the solute) and the other component to be the liquid (the solvent).
In this scenario, Henry’s law applies to describe the solubility of the gas in the liquid, and we have p = K_H * x for the gas component.

Now, here’s the key insight:

If we compare this Henry’s law equation to the Raoult’s law equation (p_i = x_i * p_i⁰) we notice that both equations describe the same concept: the partial pressure of a component is directly proportional to its mole fraction.

To make Raoult’s law a special case of Henry’s law in this context:

The proportionality constant in Henry’s law K_H should be equal to the product of the vapor pressure of the pure component p_i⁰ and the proportionality constant in Raoult’s law p_i⁰. That is, K_H = p_i⁰ * p_i⁰ = (p_i⁰)².

So, when K_H s equal to (p_i⁰)². Raoult’s law becomes a special case of Henry’s law, where the solute component is considered a gas with a solubility constant equal to This specific condition demonstrates the relationship between the two laws and shows how Raoult’s law can be viewed as a subset of Henry’s law in the context of gas-liquid solutions.

Vapor Pressure of Solutions of Solids in Liquids

Some solutions include solids dissolved in liquids, like salt, sugar, and urea in water, or iodine and sulfur in carbon disulfide.
These solutions have different properties than pure solvents, such as vapor pressure.
Vapor pressure refers to the pressure exerted by a liquid’s vapor in equilibrium with the liquid at a given temperature.
In pure liquids, the entire surface is occupied by liquid molecules. But in a solution with a non-volatile solute, the vapor pressure is solely from the solvent, and it’s lower than that of the pure solvent at the same temperature.
This happens because the surface has both solute and solvent molecules, reducing the fraction of the surface covered by solvent molecules, which, in turn, reduces the number of solvent molecules escaping, thus lowering vapor pressure.
The decrease in vapor pressure depends on the amount of non-volatile solute, regardless of its type. For example, adding 1.0 mol of sucrose or urea to water at the same temperature will have a similar effect on vapor pressure.
Raoult’s law states that the partial vapor pressure of each volatile component in a solution is directly proportional to its mole fraction.
In a binary solution (solvent and solute), if the solute is non-volatile, only solvent molecules contribute to vapor pressure.
Let p₁ be the vapor pressure of the solvent, x₁ its mole fraction, and p₁⁰ its vapor pressure in pure form. Raoult’s law can be expressed as p₁ ∝ x₁, and p₁ = x₁ * p₁⁰.
The proportionality constant is equal to the vapor pressure of the pure solvent, denoted as p₁⁰.
A plot of vapor pressure against the mole fraction of the solvent in a binary solution results in a linear relationship.

Ideal and Non-Ideal Solutions

In the realm of liquid-liquid solutions, we can categorize them as either ideal or non-ideal solutions based on Raoult’s law.

Ideal Solutions

Ideal solutions are those that adhere to Raoult’s law throughout their entire concentration range.
Ideal solutions possess two distinctive characteristics:
1. Zero Enthalpy of Mixing: When the pure components are combined to form the solution, there is neither absorption nor evolution of heat. Mathematically, this is represented as ΔmixH = 0.
2. Zero Volume of Mixing: The volume of the solution is equal to the sum of the volumes of the individual components. In other words, there is no change in volume upon mixing. This is expressed as ΔmixV = 0.
On a molecular level, ideal behavior in solutions is a result of balanced intermolecular attractive forces. For two components, A and B, in a pure state, attractive interactions occur as A-A and B-B. When they are mixed to form a binary solution, A-B interactions also come into play. In ideal solutions, the attractive forces between A-A and B-B are roughly equivalent to those between A-B, resulting in ideal behavior.
While perfectly ideal solutions are rare, some solutions, such as n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene, come very close to ideal behavior.

Non-Ideal Solutions

Solutions that do not conform to Raoult’s law throughout their entire concentration range are referred to as non-ideal solutions.
In non-ideal solutions, the vapor pressure of the solution deviates from what is predicted by Raoult’s law. This deviation can either be positive or negative.
Positive Deviation: When the vapor pressure of the solution is higher than what is predicted by Raoult’s law, the solution exhibits positive deviation.
Negative Deviation: Conversely, when the vapor pressure of the solution is lower than predicted by Raoult’s law, the solution exhibits negative deviation.
The causes for these deviations can be attributed to the interactions between molecules at the molecular level. In cases of positive deviation, the A-B interactions (solute-solvent) are weaker compared to the A-A or B-B interactions (solute-solute or solvent-solvent). This implies that in these solutions, molecules of A (or B) find it easier to escape compared to when they are in the pure state. As a result, vapor pressure is increased.
Non-ideal solutions may also exhibit variations in other properties, such as enthalpy of mixing and volume of mixing, which further distinguish them from ideal solutions.

Positive Deviation from Raoult’s Law:

Positive deviation from Raoult’s law occurs when the vapor pressure of a solution is higher than that predicted by Raoult’s law. This is often due to weaker intermolecular attractive forces between solute-solvent molecules compared to those between solute-solute or solvent-solvent molecules.
An example of positive deviation is the mixture of ethanol and acetone. In pure ethanol, molecules are hydrogen bonded. When acetone is added, its molecules come between the host ethanol molecules and break some of the hydrogen bonds. Weakened interactions lead to positive deviation from Raoult’s law.
Another example is a solution formed by adding carbon disulphide to acetone, where dipolar interactions between solute-solvent molecules are weaker than the interactions among solute-solute and solvent-solvent molecules.

Negative Deviation from Raoult’s Law:

Negative deviation from Raoult’s law occurs when the vapor pressure of a solution is lower than that predicted by Raoult’s law. This is often due to stronger intermolecular attractive forces between solute-solute or solvent-solvent molecules compared to those between solute-solvent molecules.
An example of negative deviation is a mixture of phenol and aniline. In this case, the intermolecular hydrogen bonding between the phenolic proton and the lone pair on the nitrogen atom of aniline is stronger than the interactions between similar molecules. This results in negative deviation.
Another example is a mixture of chloroform and acetone, where chloroform molecules can form hydrogen bonds with acetone molecules, reducing the escaping tendency of each component and decreasing vapor pressure.

Azeotropes:

Some liquid mixtures, known as azeotropes, have the same composition in both the liquid and vapor phases and boil at a constant temperature. Azeotropes cannot be separated by fractional distillation.
There are two types of azeotropes: minimum boiling azeotropes and maximum boiling azeotropes. Minimum boiling azeotropes are formed by solutions that show large positive deviations from Raoult’s law at specific compositions. For example, the ethanol-water mixture obtained by sugar fermentation forms an azeotrope composition of approximately 95% ethanol by volume.
Maximum boiling azeotropes are formed by solutions that show large negative deviations from Raoult’s law at specific compositions. An example is the azeotrope of nitric acid and water, which has an approximate composition of 68% nitric acid and 32% water by mass and a boiling point of 393.5 K.

Colligative Properties and Determination of Molar Mass

In solutions, there are several properties that depend on the number of solute particles rather than the nature of the solute. These properties are known as colligative properties. Colligative properties are essential in determining the molar mass of solutes. Here are four important colligative properties:

Relative Lowering of Vapor Pressure: The vapor pressure of a solvent decreases when a non-volatile solute is added. The extent of lowering is directly proportional to the mole fraction of the solute particles. This property can be used to determine the molar mass of the solute.
Depression of Freezing Point: Adding a non-volatile solute lowers the freezing point of the solvent. The extent of depression in freezing point is related to the molality (moles of solute per kilogram of solvent) of the solution. This property is used in techniques like cryoscopy to find the molar mass of the solute.
Elevation of Boiling Point: A non-volatile solute increases the boiling point of the solvent. The extent of elevation in boiling point is also related to the molality of the solution. This property is utilized in boiling point elevation experiments to determine the molar mass of the solute.
Osmotic Pressure: Osmotic pressure is the pressure required to prevent osmosis (the flow of solvent molecules through a semipermeable membrane into a solution). It is directly proportional to the molarity of the solution and can be used to determine the molar mass of the solute.

These colligative properties provide a means to determine the molar mass of a solute, even if the identity of the solute is unknown. By measuring these properties and applying appropriate equations, chemists can calculate the molar mass of solutes in a variety of solutions.

Relative Lowering of Vapor Pressure:

The vapor pressure of a solvent in a solution is lower than that of the pure solvent due to the presence of solute particles. This reduction in vapor pressure, denoted as Δp₁, is directly related to the concentration of solute particles and is independent of the nature of the solute. Raoult’s law provides a way to calculate this reduction:

Δp₁ = p₁₀ – p₁ = p₁₀(1 – x₁)

Where:

Δp₁ is the reduction in vapor pressure.
p₁₀ is the vapor pressure of the pure solvent.
p₁ is the vapor pressure of the solution.
x₁ is the mole fraction of the solvent.

In a solution with multiple non-volatile solutes, the total reduction in vapor pressure depends on the sum of the mole fractions of all solutes. This can be expressed as:

Δp₁ = x₂p₁₀

Where x₂ is the mole fraction of the solute.

When dealing with dilute solutions where the number of moles of solute (n₂) is much smaller than the number of moles of solvent (n₁), you can simplify the equation to:

Δp₁ ≈ (x₂p₁₀) / n₁

This equation allows you to calculate the molar mass (M₂) of the solute when you know the masses (w₁ and w₂) and molar masses (M₁ and M₂) of the solvent and solute, respectively, along with other quantities.

In summary, the relative lowering of vapor pressure provides a way to determine the molar mass of a solute in a solution, making it a valuable tool in analytical chemistry.

Elevation of Boiling Point:

The boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure. In the presence of a non-volatile solute, the vapor pressure of the solvent decreases. This means that the solvent needs to reach a higher temperature to boil.

Key Points:

The boiling point of a solution is always higher than that of the pure solvent.
The elevation of the boiling point (ΔTb) depends on the number of solute molecules rather than their nature.
Experiments have shown that for dilute solutions, the elevation of boiling point (ΔTb) is directly proportional to the molal concentration (m) of the solute in the solution.
The relationship between ΔTb, molal concentration (m), and a constant (Kb, Boiling Point Elevation Constant) is given by: ΔTb = Kb * m
Molality (m) is defined as the number of moles of solute dissolved in 1 kg of solvent.
The unit of Kb is K kg mol⁻¹.
To determine the molar mass (M2) of the solute, you can use the following equation: M2 = (ΔTb * Kb) / (1000 * m)

To experimentally determine the molar mass of a solute, you need to know the mass of the solute and solvent, measure the elevation in boiling point (ΔTb), and use the known Kb value for the solvent. This allows you to calculate the molar mass (M2) of the solute.

This process is particularly useful in analytical chemistry for identifying unknown substances or verifying the purity of known substances.

Depression of Freezing Point:

When a non-volatile solute is added to a solvent, it lowers the freezing point of the solution compared to that of the pure solvent. The freezing point of a substance is the temperature at which its vapor pressure in the liquid phase equals its vapor pressure in the solid phase. In the presence of a solute, the vapor pressure decreases, causing the freezing point to decrease as well.

Key Points:

The freezing point depression (ΔTf) of a solution is directly proportional to the molality (m) of the solution.
The relationship between ΔTf, molality (m), and a constant (Kf, Freezing Point Depression Constant) is given by: ΔTf = Kf * m.
The unit of Kf is K kg mol⁻¹.
Values of Kf for some common solvents are listed in Table 1.3.
To determine the molar mass (M2) of the solute, you need to know the quantities of solute (w2), solvent (w1), and the depression in freezing point (ΔTf) of the solvent, along with the molal freezing point depression constant (Kf).
The values of Kf and Kb (Boiling Point Elevation Constant) can be determined from the following relations:
- Kf = (1000 * ΔHfus) / (R * M1 * Tf)
- Kb = (1000 * ΔHvap) / (R * M1 * Tb)

Here, R represents the gas constant, M1 is the molar mass of the solvent, Tf and Tb are the freezing and boiling points of the pure solvent in kelvin, and ΔHfus and ΔHvap are the enthalpies of fusion and vaporization of the solvent, respectively.

To calculate the molar mass of the solute, you need these values along with the freezing point depression (ΔTf) of the solvent.

This process is useful in determining the molar mass of unknown substances or verifying the purity of known substances in analytical chemistry.

Osmosis and Osmotic Pressure

Osmosis is the process in which solvent molecules flow through a semipermeable membrane from an area of lower solute concentration to an area of higher solute concentration. It is driven by the desire to equalize solute concentrations on both sides of the membrane.
A semipermeable membrane allows small solvent molecules, like water, to pass through but restricts the passage of larger solute molecules.
Osmosis can be stopped if extra pressure, called osmotic pressure, is applied to the side with the higher solute concentration to prevent the flow of solvent molecules.
Osmotic pressure is a colligative property, meaning it depends on the number of solute particles in the solution, not their nature.
For dilute solutions, osmotic pressure (P) is directly proportional to the molarity (C) of the solution at a given temperature (T), expressed by the equation: P = C * R * T (where R is the gas constant).
Osmotic pressure can be calculated as P = (n2/V) * R * T, where n2 is the moles of solute, V is the volume of the solution, R is the gas constant, and T is the temperature.
To determine the molar mass (M2) of a solute, you need to know the quantities of solute (w2), temperature (T), osmotic pressure (P), and volume (V), along with the gas constant (R).
Osmotic pressure measurements are particularly useful for determining the molar masses of macromolecules like proteins and polymers.
Isotonic solutions have the same osmotic pressure at a given temperature and do not cause osmosis when separated by a semipermeable membrane.
Hypertonic solutions have a higher solute concentration than the cells they surround, causing cells to lose water and shrink.
Hypotonic solutions have a lower solute concentration than the cells they surround, causing cells to gain water and swell.
Osmosis plays a crucial role in various natural processes, including the preservation of food, water movement in plants, and the functioning of living organisms’ cells.

Reverse Osmosis and Water Purification

Reverse osmosis is the process of reversing the direction of osmosis by applying pressure greater than the osmotic pressure to the solution side of a semipermeable membrane.
In reverse osmosis, pure solvent (usually water) flows out of the solution, leaving behind solute particles and impurities.
Reverse osmosis is a practical and widely used technique for desalinating sea water to obtain fresh drinking water. It’s also used for purifying water from various sources.
The process of reverse osmosis involves applying pressure to force water through a semipermeable membrane that is permeable to water molecules but impermeable to impurities and ions present in the solution.
Cellulose acetate is a common material used to make semipermeable membranes for reverse osmosis. These membranes allow water to pass through while blocking impurities.
Reverse osmosis requires relatively high pressure to overcome the osmotic pressure and force water through the membrane.
Desalination plants in many countries use reverse osmosis to produce potable (drinkable) water from seawater, helping to meet their fresh water needs.

Reverse osmosis is an effective and important technology for water purification, especially in areas with limited access to fresh water sources. It allows the removal of salt and other impurities from seawater, making it safe for drinking and other uses.

Abnormal Molar Masses:

Abnormal molar masses refer to cases where the experimentally determined molar mass of a substance differs from its expected or normal molar mass due to certain chemical phenomena, such as dissociation or association of molecules.

1. Dissociation of Ionic Compounds:

When ionic compounds, such as salts, dissolve in water, they often dissociate into their constituent ions (cations and anions).
For example, when one mole of KCl (potassium chloride) is dissolved in water, it forms one mole of K+ ions and one mole of Cl– ions in the solution.
This dissociation increases the number of particles in the solution, which affects colligative properties like boiling point elevation and freezing point depression.
If we were unaware of this dissociation, we might incorrectly calculate the molar mass of the substance based on the colligative properties.
The experimentally determined molar mass is always lower than the true value for such substances.

2. Association of Molecules:

In some cases, molecules can associate or dimerize in certain solvents due to intermolecular forces like hydrogen bonding.
When molecules associate, the number of particles in the solution is reduced.
For example, molecules of ethanoic acid (acetic acid) can dimerize in solvents like benzene.
If all the molecules associate, the colligative properties, such as boiling point elevation and freezing point depression, would be affected.
In this case, the molar mass calculated based on these properties would be twice the expected value.

Van’t Hoff Factor (i):

The van’t Hoff factor, denoted as i, is introduced to account for the extent of dissociation or association of solute particles.
It is defined as the ratio of the abnormal molar mass (experimentally determined molar mass) to the normal molar mass (calculated based on colligative properties).
The van’t Hoff factor helps quantify the degree of dissociation or association.
For association, the value of i is less than unity, while for dissociation, it is greater than unity.
For example, i is close to 2 for aqueous KCl solution (indicating significant dissociation) and around 0.5 for ethanoic acid in benzene (indicating association).

Modified Equations for Colligative Properties with van’t Hoff Factor (i):

The inclusion of the van’t Hoff factor modifies the equations for colligative properties as follows:
- Relative lowering of vapor pressure of the solvent: ΔP = i * (x2 * P°)
- Elevation of boiling point: ΔTb = i * Kb * m
- Depression of freezing point: ΔTf = i * Kf * m
- Osmotic pressure of solution: P = i * (n2 * R * T) / V