Question

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

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

Hint:

Always read carefully whether the question asks for the total number of molecules or atoms. Multiplying by the atomicity (3 for triatomic, 2 for diatomic) is essential to get the correct atom count.

Answer 1

The Correct Option is C

Step 1: List what we know.
We have $0.1$ mole of a triatomic gas, so each molecule holds $3$ atoms. Take $N_A = 6.02 \times 10^{23}$.

Step 2: Find the molecules.
Number of molecules equals moles times $N_A$:
\[ 0.1 \times 6.02 \times 10^{23} = 6.02 \times 10^{22} \]

Step 3: Switch to atoms.
Each molecule has $3$ atoms, so multiply by $3$:
\[ 3 \times 6.02 \times 10^{22} = 18.06 \times 10^{22} \]

Step 4: Tidy the form.
Writing this neatly gives $1.806 \times 10^{23}$ atoms.
\[ \boxed{1.806 \times 10^{23}} \]