Revision: Mole Concept and Stoichiometry >> Gay-Lussac's Law and Avogadro's Law Chemistry (English Medium) ICSE Class 10 CISCE

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.

The reactant which is completely used up in a reaction is known as Limiting reagent or Limiting reactant.

When gases react, they do so in volumes that bear a simple ratio to one another and to the volume of the gaseous product, provided all volumes are measured at the same temperature and pressure.

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. 

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.

The number of atoms in a molecule of an element is called its atomicity. 

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.

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

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

"When gases combine or are produced in a chemical reaction, they do so in a simple ratio by volume, provided all gases are at the same temperature and pressure."

• Proposed by Gay-Lussac in 1808.
• e.g. 100 mL H₂ + 50 mL O₂ → 100 mL H₂O vapour (ratio = 2 : 1 : 2).
• The volume ratio of gaseous reactants to products agrees with their molar ratio.
• Volume of a gas is directly proportional to the number of moles (not inversely).

Statement: The volume remaining constant, the pressure of a given mass of gas increases or decreases by 1/273.15 of its pressure at 0°C for each 1°C rise or fall in temperature.

where β = pressure expansion coefficient = 1/273 per °C.

"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.

• Types of Molecules: Monoatomic (He), Diatomic (H₂), Triatomic (O₃), Tetratomic (P₄), Octatomic (S₈).
• Homoatomic & Heteroatomic: Same atoms = homoatomic (O₃), different atoms = heteroatomic (HCl).
• Gay-Lussac’s Law: Gases react in simple volume ratios at the same temperature and pressure.
• Avogadro’s Law: Equal gas volumes at the same conditions have an equal number of molecules.
• Molecular Formula from Volumes: Volume ratios help find formulas, e.g., NH₃ from 2 NH₃ → 1 N₂ + 3.