Q.Which one of the following will have the largest number of atoms?

Concept: Molecular Mass Calculation — the number of atoms in a given mass is inversely proportional to the atomic/molecular mass (smaller molar mass → more moles → more atoms).

Step 1: Find moles of each substance using $n = \frac{\text{mass}}{\text{molar mass}}$.

• Au: $n = \frac{1}{197} \approx 0.00508$ mol
• Na: $n = \frac{1}{23} \approx 0.0435$ mol
• Li: $n = \frac{1}{6.94} \approx 0.144$ mol
• Cl$_2$: $n = \frac{1}{71} \approx 0.0141$ mol …

The question asks: for the same mass (1 g), which substance gives the most atoms? The key is that atoms are counted in moles, and one mole of any substance contains the same number of entities (Avogadro’s number, $6.022 \times 10^{23}$). So the number of atoms in a sample depends directly on the number of moles of atoms present.

Number of moles of atoms = $\frac{\text{mass}}{\text{molar mass of the atom (or molecule, adjusted)}}$.

For a given mass, the substance with the smallest molar mass per atom will yield the largest number of atoms. That’s the core idea.

Let’s work through each option.

1. 1 g Au (s) — Gold is monatomic. Atomic mass of Au = 197 g mol⁻¹.

   Moles of Au atoms = $\frac{1}{197} \approx 5.08 \times 10^{-3}$ mol.

   Number of atoms = $5.08 \times 10^{-3} \times 6.022 \times 10^{23} \approx 3.06 \times 10^{21}$.

2. 1 g Na (s) — Sodium is also monatomic. Atomic mass of Na = 23 g mol⁻¹.

   Moles of Na atoms = $\frac{1}{23} \approx 4.35 \times 10^{-2}$ mol.

   Number of atoms = $4.35 \times 10^{-2} \times 6.022 \times 10^{23} \approx 2.62 \times 10^{22}$.

3. 1 g Li (s) — Lithium is monatomic. Atomic mass of Li = 6.94 g mol⁻¹.

   Moles of Li atoms = $\frac{1}{6.94} \approx 0.144$ mol.

   Number of atoms = $0.144 \times 6.022 \times 10^{23} \approx 8.68 \times 10^{22}$.

4. 1 g Cl₂ (g) — Chlorine gas is diatomic. Molecular mass of Cl₂ = 2 × 35.5 = 71 g mol⁻¹.

   Moles of Cl₂ molecules = $\frac{1}{71} \approx 1.41 \times 10^{-2}$ mol.

   Each Cl₂ molecule contains 2 atoms, so moles of Cl atoms = $2 \times 1.41 \times 10^{-2} = 2.82 \times 10^{-2}$ mol. …

Method: Mole Concept & Avogadro's Number Comparison

Concept: The number of atoms in a given mass depends on:

• The molar mass (lower molar mass → more moles → more atoms)
• The atomicity (number of atoms per molecule)

Steps

1. Write the molar masses

   • Au: $197 \, \text{g/mol}$
   • Na: $23 \, \text{g/mol}$
   • Li: $7 \, \text{g/mol}$
   • Cl$_2$: $2 \times 35.5 = 71 \, \text{g/mol}$

2. Calculate moles in 1 g

• Au: $\frac{1}{197} \approx 0.00508 \, \text{mol}$
• Na: $\frac{1}{23} \approx 0.0435 \, \text{mol}$
• Li: $\frac{1}{7} \approx 0.1429 \, \text{mol}$
• Cl$_2$: $\frac{1}{71} \approx 0.0141 \, \text{mol}$

3. Convert moles to number of atoms Multiply moles by Avogadro's number ($6.022 \times 10^{23}$) and by atomicity:
   • Au (atomicity = 1): $0.00508 \times N_A$
   • Na (atomicity = 1): $0.0435 \times N_A$ …

Here are the most common mistakes students make on this exact type of question, along with how to avoid each one.

✗ Mistake 1: Comparing masses directly instead of moles

What students do:

They see "1 g" for each option and think all have the same number of atoms. They forget that different elements have different atomic masses.

Why it’s wrong:

Number of atoms depends on number of moles, not mass.

$\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

Since molar masses differ, 1 g of each substance contains a different number of moles — and therefore a different number of atoms.

✓ How to avoid:

Always convert mass to moles first. Then multiply by Avogadro’s number ($6.022 \times 10^{23}$) to get the number of atoms.

✗ Mistake 2: Forgetting that $Cl_2$ is diatomic

What students do:

They treat $Cl_2$ as if it were monatomic (like Cl), so they use 35.5 g/mol instead of 71 g/mol.

Why it’s wrong:

$Cl_2$ is a molecule with two atoms. Its molar mass is $2 \times 35.5 = 71$ g/mol.

Using 35.5 g/mol gives double the actual number of moles, leading to a wrong answer.

✓ How to avoid:

Always check the chemical formula. If it’s a diatomic molecule ($H_2$, $N_2$, $O_2$, $F_2$, $Cl_2$, $Br_2$, $I_2$), use the molecular mass, not atomic mass.

✗ Mistake 3: Confusing "number of molecules" with "number of atoms"

What students do:

For $Cl_2$, they calculate the number of molecules and stop there — forgetting that each molecule has 2 atoms.

Why it’s wrong:

The question asks for number of atoms, not molecules.

For $Cl_2$:

$\text{Number of atoms} = 2 \times (\text{number of molecules})$

✓ How to avoid: …