Q.Which of the following has the largest number of atoms?
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Mole Concept
The Intuition: Why Do We Need a "Mole"?
Imagine you run a bakery and need to buy eggs. You don't go to the shop and say "I want 12 eggs" — you say "I want a dozen eggs." The word dozen is just a convenient name for the number 12. It saves you from counting out every single egg.
Now think about chemistry. Atoms and molecules are unimaginably tiny. A single grain of sand contains about 1019 atoms. If you tried to count them one by one, you'd be counting for billions of years. So chemists needed a "dozen" — but for particles that are astronomically small. That's the mole.
Just as 1 dozen = 12 things, 1 mole = 6.022×1023 things. That number is called Avogadro's number (NA).
Why that specific number? Because it was chosen so that one mole of any substance has a mass in grams equal to its atomic/molecular mass in atomic mass units (u). For example:
- One atom of carbon-12 has mass 12 u. One mole of carbon-12 atoms has mass exactly 12 grams.
- One molecule of water (H2O) has mass 18 u. One mole of water molecules has mass exactly 18 grams.
This is the bridge between the invisible atomic world and the measurable laboratory world.
The Precise Definition
One mole is the amount of a substance that contains exactly 6.02214076×1023 elementary entities (atoms, molecules, ions, electrons, etc.). This number is Avogadro's constant, NA.
The mole is a counting unit, like a dozen or a gross. It tells you how many particles you have, not how heavy they are.
The Three Pillars of the Mole Concept
The mole connects three measurable quantities: mass, number of particles, and volume of a gas. Here's how.
1. Mass ↔ Moles ↔ Number of Particles
The molar mass (M) of a substance is the mass of one mole of it, in grams per mole (g/mol).
Number of moles (n)=Molar mass (g/mol)Mass of substance (g)
Number of particles=n×NA=MMass×6.022×1023
Example: How many atoms are in 24 g of carbon?
Molar mass of carbon = 12 g/mol.
n=1224=2 moles.
Number of atoms = 2×6.022×1023=1.2044×1024 atoms.
Always check: if you have a mass in grams, divide by the molar mass to get moles. Then multiply by NA to get particles.
2. Volume of a Gas ↔ Moles
For gases, there's a special shortcut. At Standard Temperature and Pressure (STP) — 0°C and 1 atm pressure — one mole of any gas occupies 22.4 litres. This is called the molar volume.
Number of moles (n)=22.4 L/molVolume of gas at STP (L)
This 22.4 L/mol applies only at STP. If temperature or pressure changes, the volume changes. Use the ideal gas law (PV=nRT) for non-STP conditions.
Example: What is the volume of 2 moles of oxygen gas at STP?
Volume = 2×22.4=44.8 litres.
Putting It All Together: The Mole Triangle
You can visualise the relationships as a triangle:
Mass (g)÷MMoles×NAParticles
Volume of gas at STP (L)÷22.4Moles
Any problem in mole concept is just a matter of converting along these paths. You never need to memorise a hundred formulas — just these three conversions.
A Worked Example …
Comparing the number of atoms means converting every option to moles of Cu atoms (atomic mass of Cu = 63.5 u) and multiplying by Avogadro's number. …
0.5 g atom of Cu contains the most atoms (0.5 mol x N_A).
Convert each option into moles of Cu atoms:
- (a) 0.5 g atom of Cu = 0.5 mol Cu atoms = 0.5 x 6.022x10^23 = 3.011x10^23 atoms.
- (b) 0.635 g Cu / 63.5 g mol^-1 = 0.01 mol = 6.02x10^21 atoms.
- (c) 0.25 mol Cu atoms = 0.25 x 6.022x10^23 = 1.5055x10^23 atoms. …
Showing the 12 most recent of 45 on this concept.
- CBSE 2026Set sz1 markMCQQ.Select the correct one: The number of molecules in 89.6 litre of a gas at NTP are:(a) 6.023 x 10^23(b) 2 x 6.023 x 10^23(c) 3 x 6.023 x 10^23(d) 4 x 6.023 x 10^23
›Reveal solutionSolution
Moles = Volume at NTP / 22.4 L mol^-1; here that gives 4 moles, so molecules = 4 x 6.023 x 10^23.
At NTP (Normal Temperature and Pressure, taken as 0 degC and 1 atm), the molar volume of any ideal gas is 22.4 L/mol (Avogadro's law consequence).
Number of moles, n = Given volume / Molar volume at NTP
n = 89.6 L / 22.4 L mol^-1 = 4 mol
…
- CBSE 2026Set ANNUAL1 markMCQQ."At the same temperature and pressure, equal volumes of all gases contain equal number of molecules." This statement is based on which law ?(a) Berzelius' law(b) Avogadro's hypothesis(c) Graham's law(d) Charles' law
›Reveal solutionSolution
This is Avogadro's hypothesis (law).
Avogadro (1811) proposed that equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules. This explained Gay-Lussac's law of combining v …
- CBSE 2026Set ANNUAL1 markMCQQ.A group of 6.022 × 10^23 particles is called(a) Mole(b) Atomic mass unit(c) Graham's law(d) Charles' law
›Reveal solutionSolution
6.022 × 10^23 particles = 1 mole.
The mole is the SI unit for amount of substance. One mole of any species contains exactly Avogadro's number of particles, 6.022 × 10^23. So 6.0 …
- CBSE 2026Set ANNUAL1 markMCQQ.The total number of moles in 720 gm of water is(a) 4(b) 10(c) 40(d) 72
›Reveal solutionSolution
720 g of water = 720/18 = 40 moles.
Molar mass of water (H2O) = 2(1) + 16 = 18 g/mol. …
- CBSE 2026Set ANNUAL1 markMCQQ.The necessary volume of oxygen that should be required to convert 10 ml of SO2 to SO3 by complete oxidation is(a) 10 ml(b) 20 ml(c) 30 ml(d) 5 ml
›Reveal solutionSolution
2SO2 + O2 → 2SO3, so 10 mL SO2 needs 5 mL O2.
Balanced reaction: 2SO2(g) + O2(g) → 2SO3(g). By Gay-Lussac's law of combining volumes, the volume ratio equals the mole ratio: 2 volumes …
- CBSE 2026Set ANNUAL1 markMCQQ.The volume of 4.4 gm of CO2 at standard temperature and pressure is(a) 22.4 L(b) 11.2 L(c) 5.6 L(d) 2.24 L
›Reveal solutionSolution
4.4 g CO2 = 0.1 mol → 2.24 L at STP.
Molar mass of CO2 = 12 + 2(16) = 44 g/mol.
Moles = 4.4 / 44 = 0.1 mol. …
- CBSE 2026Set ANNUAL1 markMCQQ.Candela is the S.I. unit of(a) a) Luminous intensity(b) b) Thermodynamic temperature(c) c) Amount of substance(d) d) Electric current
›Reveal solutionSolution
[!TLDR]
a) Luminous intensity
Why
Candela (cd) is the SI base unit of luminous inten …
- CBSE 2025Set ANNUAL1 markMCQQ.What is the SI unit of the amount of chemical substance?(a) kilogram(b) gram(c) mole(d) tonne
›Reveal solutionSolution
The SI unit for amount of substance is the mole (symbol mol).
The mole is defined as the amount of substance that contains as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in exactly 12 g of carbon-12, i.e. Avogadro's number (6.022 …
- CBSE 2025Set ANNUAL1 markMCQQ.Which of the following has the largest number of atoms?(a) 0.5 g atom of Cu(b) 0.635 g of Cu(c) 0.25 mole of Cu atom(d) 1 g of Cu
›Reveal solutionSolution
0.5 g atom of Cu contains the most atoms (0.5 mol x N_A).
Convert each option into moles of Cu atoms:
- (a) 0.5 g atom of Cu = 0.5 mol Cu atoms = 0.5 x 6.022x10^23 = 3.011x10^23 atoms.
- (b) 0.635 g Cu / 63.5 g mol^-1 = 0.01 mol = 6.02x10^21 atoms.
- (c) 0.25 mol Cu atoms = 0.25 x 6.022x10^23 = 1.5055x10^23 atoms. …
- CBSE 2025Set ANNUAL1 markMCQQ.How much of NaOH is required to neutralise 1500 cc of 0.1 N HCl?(a) 40 g(b) 4 g(c) 6 g(d) 60 g
›Reveal solutionSolution
6 g of NaOH exactly neutralises 1500 mL of 0.1 N HCl.
Equivalents of HCl = Normality x Volume(L) = 0.1 x 1.5 = 0.15 equivalents.
At neutralisation, equivalents of NaOH required = 0.15.
…
- CBSE 2025Set ANNUAL1 markMCQQ.The amount of CO2 that could be produced when one mole of carbon is burnt in air, is(a) 22 g(b) 50 g(c) 44 g(d) 56 g
›Reveal solutionSolution
C + O2 -> CO2 is a 1:1 mole reaction, so 1 mole of carbon gives exactly 1 mole (44 g) of CO2.
Write the balanced combustion equation for carbon burning completely in air (excess oxygen):
C(s) + O2(g) -> CO2(g)
The stoichiometric coefficients show a 1:1:1 mole ratio between C, O2, and CO2. So 1 mole of carbon reacts with 1 mole of O2 to give exactly 1 mole of CO2.
…
- CBSE 2025Set sz1 markMCQQ.Select the correct one: Which of the following contours (contains) maximum number of atoms?(a) 6.023 x 10^21 molecules of CO2(b) 22.4 L of CO2 at STP(c) 0.44 g of CO2(d) None of these
›Reveal solutionSolution
22.4 L of CO2 at STP = 1 mole of CO2 = 3 moles of atoms, the largest amount among the four options.
Each CO2 molecule has 3 atoms (1 C + 2 O), so moles of atoms = 3 x moles of CO2.
(A) 6.023 x 10^21 molecules of CO2 = 6.023x10^21 / 6.022x10^23 = 0.01 mol CO2 -> 0.03 mol atoms.
(B) 22.4 L of CO2 at STP = 1 mol of gas (since 1 mole of any ideal gas occupies 22.4 L at STP) -> 1 mol CO2 -> 3 mol atoms.
(C) 0.44 g of CO2: molar mass of CO2 = 44 g/mol, so 0.44 g = 0.01 mol CO2 -> 0.03 mol atoms.
…
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