Avogadro’s Law

Avogadro’s Law

Statement of Avogadro’s Law

Avogadro’s Law states that:

“Equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules (or moles).”

In other words, if you take the same volume of any ideal gas under identical temperature and pressure conditions, they will contain the same number of gas molecules, regardless of the type of gas.

Mathematical Expression

Avogadro’s Law can be mathematically expressed as:

V₁ / n₁ = V₂ / n₂

or simply,

V / n = k (where k is a constant at constant temperature and pressure)

• V = Volume of the gas
• n = Number of moles of gas
• k = Proportionality constant

Connection of Avogadro’s Law with Molar Volume at STP

At standard temperature and pressure (STP) — 273.16 K and 1 atm — it has been experimentally determined that:

• One mole of any ideal gas occupies 22.414 dm³ of volume.
• One mole contains Avogadro’s number of molecules, i.e., 6.022 × 10²³ molecules.

This means:

• 22.414 dm³ of any ideal gas at STP contains 6.022 × 10²³ molecules.

For example, if you have 1 dm³ of any gas at STP, the number of molecules will be:

(6.022 × 10²³) ÷ 22.414 ≈ 2.68 × 10²² molecules

This value applies to any gas: whether it’s hydrogen (H₂), helium (He), nitrogen (N₂), oxygen (O₂), or carbon monoxide (CO).

Example

Suppose you have separate containers each containing 1 dm³ of H₂, He, N₂, O₂, and CO gases at STP:

• The number of molecules in each container will be approximately 2.68 × 10²² molecules.

Even though their masses are different (because molecular masses differ), the number of molecules remains the same!

• For instance, 1 dm³ of hydrogen (H₂) at STP weighs approximately 0.0899 g.
• Whereas, 1 dm³ of oxygen (O₂) at STP weighs about 1.4384 g.

The mass differs because oxygen molecules are heavier (O₂ is 16 times heavier than H₂), but the number of molecules per volume is the same!

Why Mass Doesn’t Affect Volume at STP

Even though molecules have different masses, gases at STP behave similarly because their particles are widely separated. The size of the individual molecules becomes negligible compared to the distances between them.

At room temperature, the average distance between two neighboring gas molecules is approximately 300 times the diameter of a single molecule!

Explanation of Avogadro’s Law with Kinetic Molecular Theory (KMT)

According to KMT, gas particles are constantly moving and colliding with container walls, creating pressure.

If we add more gas molecules (increase n) into the same volume at constant temperature:

• The number of collisions would increase.
• The pressure would increase.

To maintain the same pressure, the volume must increase so that the number of collisions per unit area remains constant.

This explains why volume is directly proportional to the number of moles at constant temperature and pressure, as stated by Avogadro’s Law.

Key Takeaways:

• Equal volumes of gases at the same temperature and pressure contain the same number of molecules.
• The volume of a gas is directly proportional to the number of moles.
• The nature or type of gas does not affect this relationship.
• The molar volume of any ideal gas at STP is 22.414 dm³ per mole.

🌟 Key Insight: Even though different gases have different masses and molecular sizes, they occupy the same volume at STP if the number of molecules is the same.