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: Understanding the Concept:
A mole of any substance contains Avogadro's number (\( \text{N}_A \)) of constituent particles (molecules or atoms).
For a gas, the total number of atoms depends on both the number of moles of the gas molecules and its atomicity.

Step 2: Key Formula or Approach:
The formula to compute the total number of individual atoms is given by:
\[ \text{Total number of atoms} = \text{Number of moles} \times \text{N}_A \times \text{Atomicity} \]
where atomicity is the total number of atoms present inside a single molecule of the gas.

Step 3: Detailed Explanation:
Given parameters:
- Number of moles of gas = \( 0.1 \text{ mole} \)
- Gas type = Triatomic (which explicitly means \( \text{Atomicity} = 3 \), such as \( \text{O}_3 \) or \( \text{CO}_2 \))
- Avogadro's number (\( \text{N}_A \)) = \( 6.02 \times 10^{23} \text{ molecules/mole} \)
First, let us calculate the total number of molecules present in $0.1$ mole:
\[ \text{Number of molecules} = 0.1 \times 6.02 \times 10^{23} = 6.02 \times 10^{22} \text{ molecules} \]
Next, since every molecule contains $3$ constituent atoms, we multiply the total molecules by the atomicity:
\[ \text{Total number of atoms} = 3 \times (6.02 \times 10^{22}) \]
\[ \text{Total number of atoms} = 18.06 \times 10^{22} \]
Converting this value into scientific standard notation:
\[ \text{Total number of atoms} = 1.806 \times 10^{23} \]

Step 4: Final Answer:
The total number of atoms is \( 1.806 \times 10^{23} \).