Which one of the following samples contains the smallest number of atoms ?

Options

A. 1 g of `CO_(2)`
B. 1 g of `C_(8) H_(18)`
C. 1 g of `C_(2) H_(6)`
D. 1 g of LIF

Answer

To determine which sample contains the smallest number of atoms, we will calculate the number of atoms in each of the given samples (1 g of CO2, C8H18, C2H6, and LiF) by following these steps:

### Step 1: Calculate the number of moles for each compound
1. **For CO2:**
- Molar mass of CO2 = 12 (C) + 16*2 (O) = 44 g/mol
- Moles of CO2 = mass / molar mass = 1 g / 44 g/mol = 0.02273 moles

2. **For C8H18:**
- Molar mass of C8H18 = 12*8 (C) + 1*18 (H) = 114 g/mol
- Moles of C8H18 = 1 g / 114 g/mol = 0.00877 moles

3. **For C2H6:**
- Molar mass of C2H6 = 12*2 (C) + 1*6 (H) = 30 g/mol
- Moles of C2H6 = 1 g / 30 g/mol = 0.03333 moles

4. **For LiF:**
- Molar mass of LiF = 6.94 (Li) + 19 (F) = 26 g/mol
- Moles of LiF = 1 g / 26 g/mol = 0.03846 moles

### Step 2: Calculate the number of molecules for each compound
Using Avogadro's number (NA = 6.022 x 10^23 molecules/mol):
1. **For CO2:**
- Number of molecules = moles × NA = 0.02273 moles × 6.022 x 10^23 = 1.367 x 10^22 molecules

2. **For C8H18:**
- Number of molecules = 0.00877 moles × 6.022 x 10^23 = 5.27 x 10^21 molecules

3. **For C2H6:**
- Number of molecules = 0.03333 moles × 6.022 x 10^23 = 2.01 x 10^22 molecules

4. **For LiF:**
- Number of molecules = 0.03846 moles × 6.022 x 10^23 = 2.31 x 10^22 molecules

### Step 3: Calculate the number of atoms in each compound
1. **For CO2 (3 atoms per molecule):**
- Number of atoms = number of molecules × 3 = 1.367 x 10^22 × 3 = 4.10 x 10^22 atoms

2. **For C8H18 (26 atoms per molecule):**
- Number of atoms = number of molecules × 26 = 5.27 x 10^21 × 26 = 1.37 x 10^23 atoms

3. **For C2H6 (8 atoms per molecule):**
- Number of atoms = number of molecules × 8 = 2.01 x 10^22 × 8 = 1.61 x 10^23 atoms

4. **For LiF (2 atoms per molecule):**
- Number of atoms = number of molecules × 2 = 2.31 x 10^22 × 2 = 4.62 x 10^22 atoms

### Step 4: Compare the number of atoms
- CO2: 4.10 x 10^22 atoms
- C8H18: 1.37 x 10^23 atoms
- C2H6: 1.61 x 10^23 atoms
- LiF: 4.62 x 10^22 atoms

### Conclusion
The sample with the smallest number of atoms is **1 g of CO2**.

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