Revision: States of Matter JEE Main States of Matter

Anything that has mass and occupies space is called matter.

The process by which matter changes from one state to another and back to the original state, without any change in its chemical composition.

The pressure exerted by saturated water vapour is called aqueous tension.

Polarizability is defined as the ability of an atom or a molecule to form momentary dipoles, which means, the ability of the atom or molecule to become polar by redistributing its electrons.

The electrostatic force of attraction between a positively polarised hydrogen atom of one molecule and a highly electronegative atom (which may be negatively charged) of another molecule is called a hydrogen bond.

Dipole moment (μ) is the product of the magnitude of the charge (Q) and the distance between the centres of positive and negative charge (r). It is designated by a Greek Letter (μ) and its unit is Debye (D).

The pressure exerted by saturated water vapour is called aqueous tension.

Dipole moment (μ) is the product of the magnitude of the charge (Q) and the distance between the centres of positive and negative charge (r). It is designated by a Greek Letter (μ) and its unit is Debye (D).

Polarizability is defined as the ability of an atom or a molecule to form momentary dipoles, which means, the ability of the atom or molecule to become polar by redistributing its electrons.

The electrostatic force of attraction between a positively polarised hydrogen atom of one molecule and a highly electronegative atom (which may be negatively charged) of another molecule is called a hydrogen bond.

The volume of a given mass of a dry gas varies inversely as the pressure and directly as the absolute temperature.

V ∝ \[\frac {1}{P}\] × T or \[\frac {PV}{T}\] = k (constant)

If volume changes from V₁​ to V_2​, pressure from P_1​ to P₂​, and temperature from T₁ to T₂​, then:

\[\frac {P_1V_1}{T_1}\] = \[\frac {P_2V_2}{T_2}\] = k (constant)

A temperature scale with absolute zero (zero kelvin) as the starting point is called the absolute scale or the kelvin scale.

A molecule is the smallest particle of an element or a compound that can exist by itself; it never breaks up except for taking part in a chemical reaction.

An atom is the smallest particle of an element that can take part in a chemical reaction; however, it may or may not exist independently. 

“The relation between three properties of a gas, i.e., pressure, volume and temperature, is called the ideal gas equation.”

OR

The relation between the three properties of a gas - pressure (P), volume (V), and temperature (T) - expressed as PV = nRT, is called the ideal gas equation.

The equation that combines Boyle's Law, Charles' Law, and Gay-Lussac's Law into a single relation for a fixed mass of gas, relating the quantities pressure (P), volume (V), and temperature (T) which describe the state of the gas, is called the Equation of State.

A gas whose molecules are identical, spherical, rigid, and perfectly elastic point masses, which keep colliding among themselves and with the walls of the containing vessel in perfectly elastic collisions (total energy before collision = total energy after collision), and between which no attractive or repulsive force acts, is called an ideal gas.

The process by which matter changes from one state to another and back to the original state, without any change in its chemical composition.

Anything that has mass and occupies space is called matter.

The solids which do not possess the repeating ordered arrangement of atoms or ions are called amorphous solids.

A basic repeating structural unit of a crystalline solid is called a unit cell.

The ability of crystalline solids to change values of physical properties when measured in different directions is called anisotropy.

Packing efficiency is the ratio of volumes occupied by atoms in unit cell to the total volume of the unit cell. It is also known as the packing fraction or the density of packing.

A doped semiconductor, having higher conductivity than a pure intrinsic semiconductor, is an extrinsic semiconductor.

A pure semiconductor with very low but finite electrical conductivity is called an intrinsic semiconductor.

The process by which impurities are introduced into semiconductors to enhance their conductivity is called doping.

A doped semiconductor, having higher conductivity than a pure intrinsic semiconductor, is an extrinsic semiconductor.

A pure semiconductor with very low but finite electrical conductivity is called an intrinsic semiconductor.

The process by which impurities are introduced into semiconductors to enhance their conductivity is called doping.

Ferromagnetism is defined as the phenomenon in which substances, such as iron, cobalt and nickel, are strongly attracted by a magnetic field. Such substances are called ferromagnetic substances.

\[\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\]

Combining the above three laws for a fixed mass of gas:

PV = nRT

PV = N_kB​T

where:

• P = pressure, V = volume, T = temperature
• n = number of moles, R = universal gas constant
• N = number of molecules, k_B = Boltzmann's constant

Packing fraction or Packing efficiency = \[\frac{\text{Total volume of spheres}}{\text{Volume of the unit cell}}\times100\]

The total pressure of a gaseous mixture equals the sum of the partial pressures of all individual gases.

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

\[\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}\]

\[\text{Rate of diffusion}=\frac{\text{Volume of gas diffused}}{\text{Time required for diffusion}}\]

Statement: For a given mass of gas at constant temperature, the volume of a gas is inversely proportional to its pressure.

• Constants held: mass of gas, temperature.
• P-V graph: Hyperbolic curve; P vs 1/V graph: straight line through origin.
• P increases → V decreases proportionally.

Charles' Law (Temperature–Volume Relationship)

At constant pressure (P) and number of moles (n), the volume of a gas is directly proportional to its absolute temperature.

\[V\propto T\quad\Rightarrow\quad\frac{V_1}{T_1}=\frac{V_2}{T_2}\]

The V–T curve at constant pressure is called an isobar

Absolute zero = 0 K = –273.15°C — the temperature at which gas volume theoretically becomes zero. It cannot be attained in practice (temperatures of ~0.000001 K have been achieved in labs)

or

Statement:

The volume of a fixed mass of gas is directly proportional to its absolute temperature if the pressure is kept constant.

Mathematically, V ∝ T ⇒ \[\frac {V}{T}\] = constant

Graph: V vs T (Isobar)

A straight line through the origin when using Kelvin. All lines converge at 0 K (absolute zero).

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

• Proposed by Avogadro in 1811.
• 1 mole of any gas at STP = 22.4 L (at 0°C, 1 atm) or 22.71 L (at 0°C, 1 bar — new IUPAC STP).
• 1 mole of any substance = 6.022 × 10²³ particles.

Avogadro's Law (Volume–Moles Relationship):

At constant temperature (T) and pressure (P), volume is directly proportional to number of moles.

At constant volume, the pressure of a fixed mass of gas is directly proportional to its temperature.

P ∝ T(at constant V)

At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

V ∝ \[\frac {1}{P}\]

At constant pressure, the volume of a fixed mass of gas is directly proportional to its temperature.

V ∝ T(at constant P)

Faraday’s first law of electrolysis: The mass of a substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.

Given: Charge passed = 9650 C

Atomic mass of Cu = 63.5

Valency of Cu in CuSO₄ = 2

Equivalent mass of Cu = `63.5/2` = 31.75

Now, Mass deposited = `9650/96500 xx 31.75`

= 0.1 × 31.75

= 3.175 g

Faraday’s first law of electrolysis: The mass of a substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.

Given: Charge passed = 9650 C

Atomic mass of Cu = 63.5

Valency of Cu in CuSO₄ = 2

Equivalent mass of Cu = `63.5/2` = 31.75

Now, Mass deposited = `9650/96500 xx 31.75`

= 0.1 × 31.75

= 3.175 g

Matter is categorised based on its chemical composition into two broad groups:

1. Pure Substances have a definite, fixed chemical composition. They are further divided into:

• Elements — the simplest form of matter; cannot be broken down further by ordinary chemical means. Example: pure silver.

• Compounds — formed when two or more elements chemically combine in a fixed ratio. Example: common salt (NaCl).

2. Mixtures have no fixed composition and therefore no definite properties. They are divided into:

• Homogeneous Mixtures — constituents are uniformly distributed throughout the sample. Example: vinegar.

• Heterogeneous Mixtures — constituents are not uniformly distributed. Example: tomato sauce.

Quick memory trick:

Pure → Fixed composition. Mixture → Variable composition.

Intermolecular forces are attractive (and repulsive) forces acting between neighbouring molecules. They are weaker than covalent or ionic bonds but determine the physical state of matter.

As intermolecular forces increase: Gas → Liquid → Solid (thermal energy decreases in the same direction).

Types of Intermolecular Forces:

Intermolecular forces are attractive (and repulsive) forces acting between neighbouring molecules. They are weaker than covalent or ionic bonds but determine the physical state of matter.

As intermolecular forces increase: Gas → Liquid → Solid (thermal energy decreases in the same direction).

Types of Intermolecular Forces:

1. A gas consists of an extremely large number of tiny, discrete molecules whose actual volume is negligible compared to the total volume of the gas
2. Gas molecules are in constant, random motion moving in straight lines; they change direction upon collisions with other molecules or container walls
3. Intermolecular forces are negligible — molecules neither attract nor repel each other
4. Effect of gravity on molecules is negligible
5. All molecular collisions are perfectly elastic — total kinetic energy is conserved (though energy can be redistributed)
6. Gas pressure is caused by molecular bombardment against the walls of the container
7. Different molecules have different kinetic energies, but the average KE is directly proportional to absolute temperature: Average KE ∝ T

Solids are classified into three groups based on conductivity:

Conductivity of metals decreases with increase in temperature; conductivity of semiconductors increases with temperature.

Solids are classified into three groups based on conductivity:

Conductivity of metals decreases with increase in temperature; conductivity of semiconductors increases with temperature.

Motion of electrons generates a magnetic field — each electron behaves like a tiny bar magnet with a magnetic moment measured in Bohr Magneton (μ_B) = 9.27 × 10⁻²⁴ A m².