The number of atoms in 0.1 mole of a triatomic gas is `(N_(A) = 6.02 xx 10^(23) "mol"^(-1))`

Options

A. `6.026 xx 10^(22)`
B. `1.806 xx 10^(23)`
C. `3.600 xx 10^(23)`
D. `1.800 xx 10^(22)`

Answer

To find the number of atoms in 0.1 mole of a triatomic gas, we can follow these steps:

### Step 1: Understand the concept of moles and atoms
- A triatomic gas consists of molecules that each contain three atoms.

### Step 2: Calculate the number of moles of atoms in 0.1 mole of triatomic gas
- Since each molecule of the triatomic gas has 3 atoms, 1 mole of triatomic gas will have 3 moles of atoms.
- Therefore, in 0.1 mole of triatomic gas, the number of moles of atoms can be calculated as:
\[ \text{Moles of atoms} = 0.1 \, \text{mole of triatomic gas} \times 3 \, \text{atoms/molecule} = 0.3 \, \text{moles of atoms} \]

### Step 3: Use Avogadro's number to find the number of atoms
- Avogadro's number (\(N_A\)) is \(6.022 \times 10^{23} \, \text{atoms/mole}\).
- To find the total number of atoms, we multiply the number of moles of atoms by Avogadro's number:
\[ \text{Number of atoms} = \text{Moles of atoms} \times N_A = 0.3 \, \text{moles of atoms} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]

### Step 4: Perform the calculation
- Now, calculate the number of atoms:
\[ \text{Number of atoms} = 0.3 \times 6.022 \times 10^{23} = 1.806 \times 10^{23} \, \text{atoms} \]

### Conclusion
- Therefore, the number of atoms in 0.1 mole of a triatomic gas is \(1.806 \times 10^{23} \, \text{atoms}\).

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