🌡️ Vapour Pressure of Liquid Solutions

Introduction:
Liquid solutions are formed when the solvent is a liquid. The solute in such solutions can be a gas, a liquid, or a solid. In this section, we will discuss binary solutions, i.e., solutions containing two components. These include:

• (i) Solutions of liquids in liquids

• (ii) Solutions of solids in liquids

Such solutions may contain one or more volatile components, with the solvent generally being volatile.

🔹 Vapour Pressure of Liquid–Liquid Solutions

Let us consider a binary solution made of two volatile liquids, denoted by components 1 and 2.

When this mixture is placed in a closed container, both liquids evaporate. Eventually, an equilibrium is established between the vapour phase and the liquid phase.

Let:

• $p_1$ = Partial vapour pressure of component 1

• $p_2$ = Partial vapour pressure of component 2

• $p_{\text{total}}$ = Total vapour pressure of the solution

• $x_1$ = Mole fraction of component 1 in the liquid phase

• $x_2$ = Mole fraction of component 2 in the liquid phase

📘 Raoult’s Law:

Given by: François-Marie Raoult (1886)

Statement: For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution.

So,

$$p_1 \propto x_1 \quad \Rightarrow \quad p_1 = p_1^0 \cdot x_1 \tag{1.12}$$
$$p_2 \propto x_2 \quad \Rightarrow \quad p_2 = p_2^0 \cdot x_2 \tag{1.13}$$

Where:

• $p_1^0$ and $p_2^0$ = Vapour pressures of pure components 1 and 2 respectively.

🧪 Total Vapour Pressure:

According to Dalton’s Law of Partial Pressures, the total pressure is the sum of partial vapour pressures:

$$p_{\text{total}} = p_1 + p_2 \tag{1.14}$$

Substituting from equations (1) and (2):

$$p_{\text{total}} = x_1 p_1^0 + x_2 p_2^0 \tag{1.15}$$

Since $x_1 + x_2 = 1$, we can write:

$$p_{\text{total}} = p_1^0 + (p_2^0 - p_1^0)x_2 \tag{1.16}$$

📊 Interpretation of Equation :

• (i) Total vapour pressure depends on mole fraction of any one component.

• (ii) The relation is linear with respect to mole fraction $x_{2.}$

• (iii) If $p_1^0 < p_2^0$, then total vapour pressure increases with increasing $x_2$.

🧩 Graphical Representation:

A plot of:

• $p_1$ vs. $x_1$

• $p_2$ vs. $x_2$

• $p_{\text{total}}$ vs. $x_2$

gives straight lines, intersecting at the points where mole fractions = 1 (i.e., pure components).

The line for $p_{\text{total}}$ lies between those of $p_1$ and $p_2$.

🌫️ Composition of Vapour Phase at Equilibrium:

Let:

• $y_1$ = Mole fraction of component 1 in vapour phase

• $y_2$ = Mole fraction of component 2 in vapour phase

Using Dalton’s law:

$$p_1 = y_1 \cdot p_{\text{total}} \tag{1.17}$$
$$p_2 = y_2 \cdot p_{\text{total}} \tag{1.18}$$

In general, for any component $i$:

$$p_i = y_i \cdot p_{\text{total}}$$

This shows that mole fraction in vapour phase ( $y_i$ ) is not necessarily equal to mole fraction in liquid phase ( $x_i$ ).

🔍 Important Points to Remember:

• Raoult’s law applies to ideal solutions.

• For non-ideal solutions, deviations occur due to intermolecular interactions.

• Mole fractions in liquid and vapour phases differ unless the solution is ideal and forms an azeotrope.

• Vapour pressure is a colligative property, depending on the number of particles, not their nature.

📘 Application in Daily Life:

• Perfumes and essential oils use volatile liquid mixtures.

• Distillation techniques (like in petrochemicals) rely on vapour pressure principles.

• Meteorology and humidity studies use vapour pressure data of water.

✍️ Practice Questions:

1. State Raoult’s law and write its mathematical form.

2. Derive the expression for total vapour pressure in a binary liquid solution.

3. Explain why total vapour pressure changes with mole fraction.

4. A solution has $x_1 = 0.6$, $p_1^0 = 80 \, \text{kPa}$, $p_2^0 = 60 \, \text{kPa}$. Calculate $p_{\text{total}}$.

5. Define ideal and non-ideal solutions with examples.

Solubility of a Gas in a Liquid

 📘 Class 12 CBSE Chemistry Study Material

Chapter: Solutions
Topic: Solubility of a Gas in a Liquid

Many gases dissolve in liquids to form homogeneous mixtures. This is an important phenomenon not just in chemistry but also in environmental science, biology, and industry.

Some common examples include:

• Oxygen dissolving in water, which is vital for aquatic life.

• Hydrogen chloride (HCl), which is highly soluble in water and forms hydrochloric acid.

However, the solubility of gases is highly affected by pressure and temperature, unlike solids, which are mostly unaffected by pressure.

Dynamic Equilibrium in Gas-Liquid Solutions

Consider a container partly filled with a liquid and some gas above it, both at constant pressure (p) and temperature (T). Initially, gas molecules start dissolving in the liquid. Eventually, an equilibrium is reached when:

Rate of gas molecules entering the solution = Rate of gas molecules escaping from the solution

This is called dynamic equilibrium, represented as:

                         Gas(g) ⇌ Gas (in solution)

When this equilibrium is disturbed (e.g., by changing pressure or temperature), the system shifts to restore balance, as predicted by Le Chatelier’s Principle.

Effect of Pressure on Gas Solubility

As pressure increases, more gas molecules are forced into the solution.

➤ Henry’s Law

Henry’s Law gives a quantitative relationship between pressure and gas solubility.

Statement: At constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the surface of the liquid.

Mathematically:

p = K_H. x     …… (1.11)

Where,

• p = partial pressure of the gas above the liquid

• x = mole fraction of the gas in the solution

• K_H = Henry’s Law constant (depends on nature of the gas and temperature)

Graphical Representation:

If we plot p vs x, we get a straight line with slope K_H 

Interpretation:

• A high K_H value indicates low solubility of the gas.

• A low K_H value means high solubility of the gas.

K_H  increases with temperature, so gas solubility decreases as temperature rises.

Effect of Temperature on Gas Solubility

The dissolution of gases in liquids is typically an exothermic process:

Gas (g) → Gas (in solution) + Heat

Hence, by Le Chatelier’s Principle:

When temperature increases, the equilibrium shifts backwards (i.e., towards the gaseous state), reducing gas solubility.

This is why:

• Cold water contains more dissolved oxygen than warm water.

• Aquatic animals thrive better in cold water due to higher oxygen content.

Applications of Henry’s Law

🔹 Carbonated Beverages:

• CO₂ is dissolved under high pressure in soda bottles.

• When opened, pressure is released, solubility drops, and CO₂ escapes as bubbles.

🔹 Scuba Diving and Bends:

• At high underwater pressures, more N₂ dissolves in blood.

• Upon sudden ascent, pressure drops quickly, and nitrogen comes out as bubbles in blood.

• This causes "bends" (decompression sickness), which can be fatal.

• Helium, a less soluble gas, is used in diving tanks along with oxygen.

🔹 High Altitude Anoxia:

• At high altitudes, pO₂ (partial pressure of oxygen) is low.

• Less oxygen dissolves in blood, leading to anoxia – a condition marked by weakness, confusion, and difficulty in thinking clearly.

Conclusion

• Solubility of gases is governed primarily by Henry’s Law, pressure, and temperature.

• Higher pressure = higher gas solubility

• Higher temperature = lower gas solubility

• Understanding this is crucial for real-world applications like scuba diving, soda bottling, and managing oxygen supply at high altitudes.

Key Formula:

p = K_H . x

Where:

• p = partial pressure of the gas

• x = mole fraction of the gas in the solution

• K_H = Henry's Law constant

Important Terms:

Term	Definition
Solubility	Maximum amount of a substance that can dissolve in a solvent at given T and p
Dynamic Equilibrium	Equal rate of dissolution and escape of gas
Henry’s Law	Solubility ∝ partial pressure of the gas
KH	Henry’s law constant; varies with gas and temperature

 

Study Notes: Solubility of Solids in Liquids

 1. What is a Solution?

A solution is a homogeneous mixture of two or more components.

• Homogeneous means the composition and properties are uniform throughout the mixture.

• The component present in the largest quantity is called the solvent.

• The physical state of the solution is determined by the solvent.

• All other components in the mixture are called solutes.

Example: In a sugar-water solution, water is the solvent and sugar is the solute.

2. Types of Solutions Covered

In this unit, we focus on binary solutions, i.e., those containing only two components – one solute and one solvent.

3. Solubility of a Solid in a Liquid

Not all solids dissolve in all liquids.
Some examples:

• Sodium chloride (NaCl) and sugar dissolve readily in water.

• Naphthalene and anthracene do not dissolve in water but dissolve in benzene.

Rule of Solubility:

"Like dissolves like"

• Polar solutes dissolve in polar solvents.

• Non-polar solutes dissolve in non-polar solvents.

4. Dissolution and Crystallisation

When a solid solute is added to a solvent:

• Some solute dissolves and increases the solute concentration. This process is called dissolution.

• At the same time, dissolved solute particles may recombine and settle back as solid. This process is called crystallisation.

Over time, the system reaches a dynamic equilibrium:

                               Solute (solid)+Solvent (liquid)⇌Solution

At dynamic equilibrium, the rate of dissolution equals the rate of crystallisation, and the concentration of solute in solution becomes constant (under given temperature and pressure).

5. Saturated and Unsaturated Solutions

• A saturated solution is one where no more solute can dissolve at a given temperature and pressure.

• An unsaturated solution is one where more solute can still dissolve at the same temperature and pressure.

• A saturated solution is in dynamic equilibrium with the undissolved solute.

• The concentration of solute in a saturated solution represents its solubility

6. Factors Affecting Solubility

(i) Nature of Solute and Solvent

Solubility depends on:

• Type of bonding

• Intermolecular forces

• Polarity

(ii) Temperature

• Solubility of solids is greatly affected by temperature.

• According to Le Chatelier’s Principle:

  • If dissolution is endothermic (ΔH_sol > 0), solubility increases with temperature.

  • If dissolution is exothermic (ΔH_sol < 0), solubility decreases with temperature.

Example: Most salts dissolve better in warm water (endothermic dissolution).

(iii) Pressure

• Pressure has no significant effect on the solubility of solids in liquids.

• Reason: Solids and liquids are incompressible; hence, they are not affected by pressure changes.

8. Summary

• A solution is a homogeneous mixture of solute and solvent.

• Solubility depends on the nature of the solute and solvent, temperature, and pressure.

• Temperature affects solubility greatly, especially depending on whether the process is endothermic or exothermic.

• Pressure has negligible impact on solid-liquid solubility due to incompressibility of solids and liquids.

• A saturated solution is in dynamic equilibrium and defines the solubility of the solute at specific conditions.

 

CLASS 7: ENVIRONMENT

 

 

Lecture 1: CLASS VIII: SCIENCE: CHAPTER 5: CLASSIFICATION OF NATURAL RESOURCES -2

 

Lecture 1: CLASS VIII: SCIENCE: CHAPTER 5: CLASSIFICATION OF NATURAL RESOURCES

 Natural Resources and Coal

Classification of Natural Resources:

Natural resources are materials provided by nature that are useful to humans. They are broadly classified into two categories:

1. Inexhaustible Natural Resources:

   • These are available in unlimited quantity and cannot be depleted by human use.

   • Examples: Sunlight, Air.

2. Exhaustible Natural Resources:

   • These are limited in amount and can be exhausted due to overuse by humans.

   • Examples: Coal, Petroleum, Natural Gas, Forests, Minerals, Wildlife.

An activity analogy is given where eatables in a container represent exhaustible resources. Different groups may consume these differently. Some earlier generations may have used too much (being greedy), while others may have been thoughtful and left some for future generations. This introduces the idea of sustainable use of resources.

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Fossil Fuels

Exhaustible natural resources like coal, petroleum, and natural gas are called fossil fuels because they are formed from the dead remains of living organisms over millions of years.

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Coal – A Fossil Fuel

• Appearance: Hard, black, stone-like substance.

• Uses:

  • Fuel for cooking (in some places)

  • Earlier used in steam engines of trains

  • Important in thermal power plants for electricity generation

  • Fuel in various industries

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Formation of Coal (Carbonisation):

• About 300 million years ago, dense forests in wetland areas were buried due to natural events like flooding.

• Over time, these were compressed under layers of soil.

• With increased pressure and temperature, the dead plant matter slowly turned into coal.

• This slow chemical change is called carbonisation.

• Since coal comes from plant remains, it is classified as a fossil fuel.

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By-products of Coal and Their Uses:

1. Coke:

   • Tough, porous, black substance

   • Almost pure carbon

   • Used in steel manufacturing and metal extraction

2. Coal Tar:

   • Thick, black liquid with an unpleasant smell

   • Contains over 200 different substances

   • Used for making:

     • Synthetic dyes

     • Drugs

     • Explosives

     • Perfumes

     • Plastics

     • Paints

     • Photographic and roofing materials

     • Naphthalene balls (used to repel insects)

   • Note: Bitumen (a petroleum product) has replaced coal tar for road construction in modern times.

3. Coal Gas:

   • Obtained when coal is processed to make coke

   • Used as a fuel in nearby industries

   • Historically used for street lighting (London: 1810, New York: 1820)

   • Now used mainly as a heat source

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Conclusion:

Coal is a vital fossil fuel that has powered industries and households for centuries. However, being an exhaustible resource, it must be used judiciously. Understanding its origin, uses, and by-products helps us make better decisions about its consumption and environmental impact.

NUTRITION IN PLANTS: CLASS 7