Avogadro Number and Mole Concept in Kinetic Theory
Physics · Kinetic Theory · NEET
The Avogadro number NA = 6.022 x 10^23 is the number of particles in one mole. In Kinetic Theory, a mole of any gas has NA molecules, weighs its molar mass in grams, and occupies 22.4 litres at STP. Memory hook: "One mole = one molar mass in grams = 6.022 x 10^23 particles = 22.4 L of gas at STP." Most NEET numericals start by finding moles: n = given mass / molar mass.
One mole seen four equal ways: it is a counting box (n = mass / molar mass) holding NA = 6.022 x 10^23 particles, weighing its molar mass in grams, and filling 22.4 L only at STP. For any other condition use PV = nRT.
Your doubts, answered
What is the difference between a mole and a molecule?
A molecule is one single particle of a substance (like one O2 unit). A mole is a fixed counting number of such particles, exactly NA = 6.022 x 10^23 of them. So 1 mole of O2 means 6.022 x 10^23 O2 molecules. Think of 'molecule' as one item and 'mole' as a big box that always holds 6.022 x 10^23 items, like a dozen always means 12.
What does the Avogadro number actually count?
It counts the number of basic particles (atoms, molecules, or ions) present in exactly one mole of a substance. The value NA = 6.022 x 10^23 is chosen so that one mole of a substance has a mass equal to its molar mass expressed in grams. For example, 1 mole of water (molar mass 18) is 18 g and contains 6.022 x 10^23 water molecules.
Is 22.4 litres true for all gases or only at STP?
The 22.4 litre molar volume is true for any ideal gas but only at STP (standard temperature 273 K and pressure 1 atm). At other temperatures or pressures the volume changes. This comes straight from PV = nRT: put n = 1, T = 273 K, P = 1.01 x 10^5 Pa, and you get about 22.4 x 10^-3 m^3 = 22.4 L.
How do I find the number of moles from a given mass?
Use n = given mass / molar mass, with both in the same units (usually grams and g per mol). Example: 4500 g of water has n = 4500 / 18 = 250 mol. Once you know n, you can find molecules by N = n x NA, or volume at STP by V = n x 22.4 L.
How many molecules are there in one gram of a gas?
Number of molecules N = (given mass / molar mass) x NA. For 1 g of oxygen (molar mass 32), N = (1 / 32) x 6.022 x 10^23 = 1.88 x 10^22 molecules. Always divide by molar mass first, then multiply by the Avogadro number.
⚠️ The NEET trap ✗ Using V = n x 22.4 L for a gas at any temperature or pressure, or forgetting to convert temperature to kelvin, or leaving mass in kg while molar mass is in grams. ✓ The 22.4 L per mole rule works ONLY at STP (273 K, 1 atm). For any other condition use PV = nRT with T in kelvin. And always match units: n = mass(g) / molar mass(g per mol). 🧠 The 22.4 L trap in gas volume numericals.
Real NEET questions
NEET 2022
The volume occupied by the molecules contained in 4.5 kg of water at STP, if the intermolecular forces vanish away, is:
A · 5.6 x 10^6 m^3
B · 5.6 x 10^3 m^3
C · 5.6 x 10^-3 m^3
D · 5.6 m^3 ✓
Solution: Step 1: If intermolecular forces vanish, water behaves like an ideal gas, so it occupies 22.4 L per mole at STP. Step 2: Find moles. Mass = 4.5 kg = 4500 g, molar mass of water = 18 g per mol, so n = 4500 / 18 = 250 mol. Step 3: Volume at STP = n x 22.4 L = 250 x 22.4 = 5600 L. Step 4: Convert to cubic metres: 5600 L = 5600 x 10^-3 m^3 = 5.6 m^3. Answer: 5.6 m^3 (D).
NEET 2024
The volume occupied by 1.8 g of water vapour at 374 degrees C and 1 bar pressure will be: [Use R = 0.083 bar L K^-1 mol^-1]
A · 96.66 L
B · 55.87 L
C · 3.10 L
D · 5.37 L ✓
Solution: Step 1: This is not STP, so use PV = nRT (the 22.4 L rule does not apply). Step 2: Find moles. n = mass / molar mass = 1.8 / 18 = 0.1 mol. Step 3: Convert temperature to kelvin: T = 374 + 273 = 647 K. Step 4: V = nRT / P = (0.1 x 0.083 x 647) / 1 = 5.37 L. Answer: 5.37 L (D).
Solved Kinetic Theory NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
NA = 6.022 x 10^23 per mole. It is the number of elementary particles in one mole and links the microscopic count of molecules to the measurable macroscopic mole.
How is Avogadro number related to the gas constant R and Boltzmann constant kB?
They are connected by R = NA x kB. Here R = 8.314 J per mol per K is per mole, while kB = 1.38 x 10^-23 J per K is per molecule. So dividing the per-mole constant R by NA gives the per-molecule constant kB.
What is molar volume and its value at STP?
Molar volume is the volume occupied by one mole of an ideal gas. At STP (273 K, 1 atm) it is 22.4 litres for every gas. It comes from PV = nRT with n = 1.
Why does one mole of every gas occupy the same volume at STP?
Because of Avogadro's hypothesis: equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. So one mole (NA molecules) of any gas takes the same 22.4 L at STP, independent of the gas type.
How do I get the mass of one molecule using the Avogadro number?
Mass of one molecule = molar mass / NA. For nitrogen N2 (molar mass 28 g per mol = 0.028 kg per mol), mass = 0.028 / (6.022 x 10^23) = 4.65 x 10^-26 kg.
