Which of the following gases contains the least number of atoms at s.t.p?

Analysis

To determine which gas contains the least number of atoms, we need to calculate the total number of atoms in each sample.

Key Concept: The number of atoms in a substance is calculated as:

Since $N_A$ is a constant ($6.02 \times 10^{23}$), we can simply compare the product of (moles $\times$ atoms per molecule) for each option.

Step-by-Step Calculation

A. 1 mole of butane ($C_4H_{10}$)

• Number of atoms per molecule = $4 \text{ (carbon)} + 10 \text{ (hydrogen)} = 14$ atoms.
• Total = $1 \text{ mole} \times 14 = \mathbf{14 \text{ units}}$

B. 4 moles of chlorine ($Cl_2$)

• Number of atoms per molecule = $2$ atoms.
• Total = $4 \text{ moles} \times 2 = \mathbf{8 \text{ units}}$

C. 3 moles of ozone ($O_3$)

• Number of atoms per molecule = $3$ atoms.
• Total = $3 \text{ moles} \times 3 = \mathbf{9 \text{ units}}$

D. 7 moles of argon ($Ar$)

• Argon is a noble gas and exists as a monatomic molecule.
• Number of atoms per molecule = $1$ atom.
• Total = $7 \text{ moles} \times 1 = \mathbf{7 \text{ units}}$

Conclusion

Comparing the results:

• Butane: 14
• Chlorine: 8
• Ozone: 9
• Argon: 7

The sample with the lowest value is 7 units (Argon). Therefore, 7 moles of argon contains the least number of atoms.

Exam Tip

Always check the atomicity of the gas! Many students forget that noble gases (like Argon, Helium, Neon) are monatomic (1 atom per molecule), while diatomic gases (like $Cl_2, O_2, N_2$) have 2 atoms per molecule. Misidentifying the atomicity is the most common trap in this type of JAMB question.