Question

The number of atoms in 0.1 mole of a triatomic gas will be (NA = \( 6.02 \times 10^{23} \)):

• A. \( 1.800 \times 10^{22} \)
• B. \( 6.026 \times 10^{22} \)
• C. \( 1.806 \times 10^{23} \)
• D. \( 3.600 \times 10^{23} \)

Hint:

To find the total number of atoms, multiply: \[ \text{Moles of gas} \times N_A \times \text{Atoms per molecule} \] For triatomic gases, multiply by 3.

Answer 1

The Correct Option is C

Given:

• Number of moles of gas \( = 0.1 \)
• Nature of gas: Triatomic \( \Rightarrow \) Each molecule contains 3 atoms
• Avogadro's number \( N_A = 6.02 \times 10^{23} \) molecules per mole

Calculation: \[\n\text{Number of molecules} = 0.1 \times 6.02 \times 10^{23} = 6.02 \times 10^{22}\n\] Total number of atoms: \[\n\text{Number of atoms} = 6.02 \times 10^{22} \times 3 = 18.06 \times 10^{22} = 1.806 \times 10^{23}\n\] The initial calculation was correct. Recalculating for clarity: \[\n0.1 \text{ mole} \times 6.02 \times 10^{23} \text{ molecules/mole} = 6.02 \times 10^{22} \text{ molecules}\n\] Each molecule has 3 atoms: \[\n6.02 \times 10^{22} \times 3 = 18.06 \times 10^{22} = \boxed{1.806 \times 10^{23}}\n\] Therefore, the answer is: \[\n\boxed{\text{(3) } 1.806 \times 10^{23}}\n\]