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States of Matter JEE Notes: Important Concepts and Gas Laws

States of Matter is an important Physical Chemistry chapter for JEE because most questions involve selecting the correct gas law, applying the ideal gas equation, handling temperature conversions and understanding molecular behaviour. These JEE questions commonly test gas laws, ideal gas calculations, Dalton's law, Graham's law, kinetic theory and real gas behaviour. These States of Matter JEE notes cover important concepts, formulas, solved examples and revision points required for JEE preparation.

The Three States of Matter

Matter mainly exists in three states: solid, liquid and gas. The state of matter depends on the competition between intermolecular forces and thermal energy.

Intermolecular forces are attractive forces between molecules. These include van der Waals forces, dipole-dipole interactions and hydrogen bonding.

The chapter mainly focuses on gases and liquids because their properties can be described using mathematical relationships and experimental laws.

Gas Laws for JEE

Boyle's Law

Boyle's law describes the relationship between pressure and volume of a gas at constant temperature and number of moles.

According to Boyle's law:

Pressure of a fixed amount of gas is inversely proportional to its volume at constant temperature.

$$P_1V_1=P_2V_2$$

Important points:

• Increasing pressure decreases volume.
• Decreasing pressure increases volume.
• Temperature remains constant.

Worked example: A gas occupies 500 mL at 1 atm pressure. Find its volume at 2.5 atm if temperature remains constant.

Using Boyle's law:

$$P_1V_1=P_2V_2$$

$$1\times500=2.5\times V_2$$

$$V_2=200\ mL$$

Answer: 200 mL

Charles's Law

Charles's law explains the relationship between volume and temperature of a gas at constant pressure.

Volume of a fixed mass of gas is directly proportional to absolute temperature at constant pressure.

$$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$

Important: Temperature must always be converted into Kelvin.

$$T(K)=T(^{\circ}C)+273.15$$

Worked example: A gas occupies 2 L at 27°C. Find its volume at 127°C at constant pressure.

Convert temperatures:

$$T_1=300K,\ T_2=400K$$

Using Charles's law:

$$V_2=2\times\frac{400}{300}$$

V₂ = 2.67 L

Gay-Lussac's Law

Gay-Lussac's law gives the relationship between pressure and temperature at constant volume.

Pressure of a gas is directly proportional to absolute temperature when volume remains constant.

$$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$

Example: A tyre has pressure 2 atm at 27°C. If temperature increases to 87°C, find the new pressure.

Temperatures:

$$T_1=300K,\ T_2=360K$$

$$P_2=2\times\frac{360}{300}$$

P₂ = 2.4 atm

Avogadro's Law

Avogadro's law relates the volume of a gas with the number of moles at constant temperature and pressure.

Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

$$\frac{V_1}{n_1}=\frac{V_2}{n_2}$$

Important JEE point:

• At STP, one mole of an ideal gas occupies 22.4 litres.
• At 27°C and 1 atm, one mole occupies approximately 24.6 litres.

Ideal Gas Equation

The four gas laws combine to form the ideal gas equation.

An ideal gas is a theoretical gas whose molecules have negligible volume and no intermolecular attraction.

$$PV=nRT$$

where:

• P = pressure
• V = volume
• n = number of moles
• R = universal gas constant
• T = absolute temperature

Values of Gas Constant R

Worked example: Find the volume of 2 moles of an ideal gas at 27°C and 1 atm pressure.

Temperature:

$$T=300K$$

Using ideal gas equation:

$$V=\frac{nRT}{P}$$

$$V=\frac{2\times0.0821\times300}{1}$$

V = 49.26 L

Density and Molar Mass Form of Ideal Gas Equation

Since:

$$n=\frac{m}{M}$$

The ideal gas equation can be rewritten as:

$$d=\frac{PM}{RT}$$

where:

• d = density of gas
• M = molar mass

This form is frequently used in JEE questions involving density and molecular mass calculations.

Worked example: A gas has density 1.96 g/L at STP. Find its molar mass.

Using:

$$M=\frac{dRT}{P}$$

$$M=\frac{1.96\times0.0821\times273}{1}$$

M ≈ 44 g/mol

The gas is likely carbon dioxide.

Dalton's Law of Partial Pressures

Dalton's law applies when non-reacting gases are mixed together.

According to Dalton's law:

Total pressure of a mixture is equal to the sum of individual partial pressures of all gases.

$$P_{total}=p_1+p_2+p_3+...$$

The partial pressure of a gas depends on its mole fraction.

$$p_i=x_iP_{total}$$

where:

• xᵢ = mole fraction of gas
• Ptotal = total pressure

Worked example: A mixture contains 2 mol nitrogen and 3 mol oxygen. Find mole fractions.

Total moles:

$$n=2+3=5$$

Nitrogen mole fraction:

$$x_{N_2}=\frac25$$

Oxygen mole fraction:

$$x_{O_2}=\frac35$$

Therefore, nitrogen contributes 40% and oxygen contributes 60% of the total pressure.

Graham's Law of Diffusion and Effusion

Diffusion and Effusion

Diffusion is the process in which gas molecules move from a region of higher concentration to a region of lower concentration due to random molecular motion.

Effusion is the process in which gas molecules escape through a very small hole into a region of lower pressure.

Graham studied the rate of diffusion and effusion of gases and established a relationship between the rate and molar mass.

Graham's Law

The rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

$$r\propto\frac{1}{\sqrt M}$$

For two gases:

$$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}$$

where:

• r = rate of diffusion
• M = molar mass of gas

Important JEE points:

• Lighter gases diffuse faster.
• Higher molar mass gases diffuse slower.
• Rate of diffusion depends on temperature and molar mass.

Worked example: Compare the rates of diffusion of hydrogen and oxygen.

Molar masses:

H₂ = 2 g/mol

O₂ = 32 g/mol

Using Graham's law:

$$\frac{r_{H_2}}{r_{O_2}}=\sqrt{\frac{32}{2}}$$

$$=\sqrt{16}$$

Ratio = 4 : 1

Hydrogen diffuses four times faster than oxygen.

Kinetic Molecular Theory of Gases

The kinetic molecular theory explains the behaviour of gases by considering molecules as continuously moving particles.

Assumptions of Kinetic Theory

• Gas molecules are in continuous random motion.
• The actual volume of gas molecules is negligible compared to the container volume.
• Molecules collide elastically with each other and the walls of the container.
• No intermolecular forces exist between ideal gas molecules.
• The average kinetic energy depends only on absolute temperature.

Pressure According to Kinetic Theory

The pressure of a gas is produced due to collisions of gas molecules with the walls of the container.

$$P=\frac13\rho c^2$$

where:

• ρ = density of gas
• c = root mean square velocity

Molecular Speeds in Gases

Gas molecules do not move with the same velocity. Different molecules have different speeds at a particular temperature.

Root Mean Square Velocity

The root mean square velocity represents the square root of the average of squares of molecular velocities.

$$u_{rms}=\sqrt{\frac{3RT}{M}}$$

Average Velocity

$$u_{avg}=\sqrt{\frac{8RT}{\pi M}}$$

Most Probable Velocity

$$u_{mp}=\sqrt{\frac{2RT}{M}}$$

The relationship between different molecular speeds is:

$$u_{rms}>u_{avg}>u_{mp}$$

Effect of temperature:

• Increasing temperature increases molecular speed.
• Increasing molar mass decreases molecular speed.

Effect of temperature and molar mass:

Kinetic Energy of Gas Molecules

The kinetic energy of gas molecules depends only on temperature.

Average kinetic energy is directly proportional to absolute temperature.

Therefore:

• All gases at the same temperature have the same average kinetic energy.
• Kinetic energy does not depend on the nature of the gas.

Important: A heavier gas molecule moves slower than a lighter molecule at the same temperature, but both have the same average kinetic energy.

Maxwell-Boltzmann Distribution Curve

The Maxwell-Boltzmann distribution explains how molecular speeds are distributed among gas molecules at a particular temperature.

The curve shows that:

• Most molecules have speeds near the most probable velocity.
• Only a small number of molecules have extremely high or low speeds.
• Increasing temperature shifts the curve towards higher velocities.

Effect of increasing temperature:

• Peak height decreases.
• Curve becomes broader.
• Average molecular speed increases.

Effect of increasing molar mass:

• Distribution shifts towards lower velocities.
• Gas molecules move slower.

Real Gases and Ideal Gas Behaviour

Ideal Gas

An ideal gas is a theoretical gas that follows gas laws perfectly under all conditions.

Assumptions of an ideal gas:

• No intermolecular attraction.
• Molecules have negligible volume.
• Collisions are perfectly elastic.

Real Gas

Real gases deviate from ideal behaviour because gas molecules have:

• Finite molecular volume.
• Intermolecular attractions.

Real gases behave approximately like ideal gases at:

• High temperature.
• Low pressure.

Real gases show maximum deviation at:

• Low temperature.
• High pressure.

Compressibility Factor

The compressibility factor measures the deviation of a real gas from ideal behaviour.

$$Z=\frac{PV}{nRT}$$

For an ideal gas:

Z = 1

Van der Waals Equation for Real Gases

Van der Waals modified the ideal gas equation by considering:

• Volume occupied by molecules.
• Intermolecular attractions.

$$\left(P+\frac{an^2}{V^2}\right)(V-nb)=nRT$$

where:

• a represents correction for intermolecular attraction.
• b represents correction for molecular volume.

Effect of constants:

• Higher value of a indicates stronger intermolecular attraction.
• Higher value of b indicates larger molecular size.

Liquefaction of Gases

Liquefaction is the process of converting a gas into a liquid by applying suitable temperature and pressure conditions.

Conditions Required for Liquefaction

• Temperature must be below critical temperature.
• Pressure must be sufficiently high.
• Intermolecular attraction should be significant.

Critical Temperature

Critical temperature is the maximum temperature above which a gas cannot be liquefied, regardless of pressure applied.

Important:

• Higher critical temperature means easier liquefaction.
• Gases with stronger intermolecular forces have higher critical temperatures.

Liquid State Properties for JEE

Liquids have properties that are intermediate between solids and gases. Unlike gases, liquids have definite volume because of intermolecular attraction, but they do not have a fixed shape because molecules can move freely.

The important properties of liquids frequently tested in JEE are:

• Vapour pressure
• Surface tension
• Viscosity
• Capillary action

Vapour Pressure

Concept of Vapour Pressure

When a liquid is kept in a closed container, some molecules at the surface gain enough energy to escape into the vapour phase. These vapour molecules exert pressure on the liquid surface, which is called vapour pressure.

Vapour pressure: The pressure exerted by vapour molecules in equilibrium with the liquid at a given temperature.

Factors Affecting Vapour Pressure

Important JEE points:

• Liquids with weak intermolecular forces have higher vapour pressure.
• Liquids with strong intermolecular forces evaporate slowly.
• Higher vapour pressure means greater volatility.

Boiling Point and Vapour Pressure

A liquid boils when its vapour pressure becomes equal to the external pressure.

Normal boiling point: Temperature at which vapour pressure becomes equal to atmospheric pressure.

Effect of pressure on boiling point:

• Increase in external pressure increases boiling point.
• Decrease in external pressure decreases boiling point.

Example: Food cooks faster in a pressure cooker because increased pressure raises the boiling point of water.

Surface Tension

Concept of Surface Tension

Surface tension is the tendency of a liquid surface to behave like a stretched elastic membrane.

Molecules inside a liquid experience balanced attractive forces, but surface molecules experience a net inward force because they have fewer neighbouring molecules.

Surface tension: Force acting per unit length on the surface of a liquid.

$$T=\frac{F}{l}$$

SI unit of surface tension is N/m.

Factors Affecting Surface Tension

Examples:

• Water droplets are spherical due to surface tension.
• Small insects can walk on water because of surface tension.
• Soap reduces surface tension and improves cleaning ability.

Capillary Action

Capillary action is the rise or fall of a liquid in a narrow tube due to surface tension and adhesive forces.

The behaviour depends on the relative strength of:

• Cohesive forces: Attraction between similar molecules.
• Adhesive forces: Attraction between liquid and container.

Viscosity

Concept of Viscosity

Viscosity is the resistance offered by a fluid to the flow of its layers.

It arises because of intermolecular attraction and internal friction between molecules.

Viscosity: Resistance of a fluid against relative motion between its layers.

$$F=\eta A\frac{dv}{dx}$$

where:

• η = coefficient of viscosity
• A = area of layer
• dv/dx = velocity gradient

Factors Affecting Viscosity

Reason:

• In liquids, increased temperature weakens intermolecular attraction.
• In gases, increased temperature increases molecular collisions.

Complete States of Matter Formula Sheet at a Glance

JEE Important Points, Common Mistakes and Quick Revision

Points JEE Repeatedly Tests

• Gas laws are applicable only when temperature units are converted into Kelvin.
• Ideal gas equation connects pressure, volume, temperature and number of moles.
• Density of a gas increases with increase in pressure.
• Dalton's law applies to mixtures of non-reacting gases.
• Lighter gases diffuse faster according to Graham's law.
• Average kinetic energy of gases depends only on temperature.
• Real gases show maximum deviation at low temperature and high pressure.
• Compressibility factor indicates deviation from ideal behaviour.
• Stronger intermolecular forces make liquefaction easier.
• Critical temperature is the highest temperature at which a gas can be liquefied.
• Vapour pressure increases with temperature.
• Surface tension decreases as temperature increases.
• Viscosity of liquids decreases with increase in temperature.

Common Mistakes to Avoid

1. Using Celsius temperature in gas laws. Always convert temperature into Kelvin.
2. Using incorrect gas constant value. The value of R depends on pressure and volume units.
3. Confusing diffusion and effusion. Diffusion is movement through space, while effusion occurs through a tiny opening.
4. Assuming ideal behaviour at all conditions. Real gases deviate significantly at high pressure and low temperature.
5. Ignoring intermolecular forces. They explain deviations from ideal gas behaviour.
6. Confusing vapour pressure with boiling point. Boiling occurs when vapour pressure equals external pressure.
7. Applying surface tension concepts incorrectly. Surface tension depends on intermolecular attraction and temperature.
8. Forgetting that viscosity behaves differently for liquids and gases. Temperature has opposite effects on them.

Quick Revision Notes for States of Matter

• Gas properties are explained using pressure, volume, temperature and moles.
• Boyle's law relates pressure and volume.
• Charles's law relates volume and temperature.
• Gay-Lussac's law relates pressure and temperature.
• Avogadro's law relates volume and number of moles.
• Ideal gas equation combines all gas laws.
• Dalton's law explains pressure of gas mixtures.
• Graham's law compares rates of diffusion.
• Kinetic theory explains molecular motion in gases.
• Real gases deviate because of molecular volume and attraction.
• Liquefaction requires temperature below critical temperature.
• Surface tension arises due to imbalance of forces at liquid surfaces.
• Viscosity represents resistance to flow.

Problem-solving routine: Start States of Matter questions by identifying the gas law or concept involved. Convert all temperatures into Kelvin, select the correct gas constant based on units and check whether the gas behaves ideally or shows deviation. For mixture problems, use mole fractions and partial pressures. Use a JEE formula sheet during revision to quickly recall gas laws, molecular speed relations, liquid properties and important States of Matter formulas.