Calculate the number of atoms in
(i) 0.5 mole atoms of carbon (`C^12`)
(ii) 3.2 g of sulphur
(iii) 18.0 g of glucose (`C_6 H_12O_6`)
(iv) 0.20 mole molecules of oxygen

Explanation

To solve the problem of calculating the number of atoms in the given substances, we will follow a systematic approach for each part of the question.

### (i) Calculate the number of atoms in 0.5 mole of carbon (`C^12`)

1. **Identify Avogadro's number**: Avogadro's number is \(6.022 \times 10^{23}\) atoms/mole. This number tells us how many atoms are in one mole of any substance.

2. **Calculate the number of atoms in 0.5 mole**:
\[ \text{Number of atoms} = 0.5 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]
\[ = 3.011 \times 10^{23} \, \text{atoms} \]

### (ii) Calculate the number of atoms in 3.2 g of sulfur

1. **Find the molar mass of sulfur**: The atomic weight of sulfur (S) is 32 g/mole.

2. **Calculate the number of moles in 3.2 g of sulfur**:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{3.2 \, \text{g}}{32 \, \text{g/mole}} = 0.1 \, \text{moles} \]

3. **Calculate the number of atoms**:
\[ \text{Number of atoms} = 0.1 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]
\[ = 6.022 \times 10^{22} \, \text{atoms} \]

### (iii) Calculate the number of atoms in 18.0 g of glucose (`C_6H_{12}O_6`)

1. **Find the molar mass of glucose**:
\[ \text{Molar mass} = (6 \times 12) + (12 \times 1) + (6 \times 16) = 72 + 12 + 96 = 180 \, \text{g/mole} \]

2. **Calculate the number of moles in 18.0 g of glucose**:
\[ \text{Number of moles} = \frac{18.0 \, \text{g}}{180 \, \text{g/mole}} = 0.1 \, \text{moles} \]

3. **Calculate the number of molecules**:
\[ \text{Number of molecules} = 0.1 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 6.022 \times 10^{22} \, \text{molecules} \]

4. **Calculate the number of atoms in glucose**: Each molecule of glucose contains \(6 + 12 + 6 = 24\) atoms.
\[ \text{Total number of atoms} = 6.022 \times 10^{22} \, \text{molecules} \times 24 \, \text{atoms/molecule} = 1.445 \times 10^{24} \, \text{atoms} \]

### (iv) Calculate the number of atoms in 0.20 mole of oxygen

1. **Calculate the number of molecules in 0.20 mole of oxygen**:
\[ \text{Number of molecules} = 0.20 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 1.2044 \times 10^{23} \, \text{molecules} \]

2. **Calculate the number of atoms in oxygen**: Each molecule of oxygen (O₂) contains 2 atoms.
\[ \text{Total number of atoms} = 1.2044 \times 10^{23} \, \text{molecules} \times 2 \, \text{atoms/molecule} = 2.4088 \times 10^{23} \, \text{atoms} \]

### Summary of Answers:
- (i) \(3.011 \times 10^{23}\) atoms of carbon
- (ii) \(6.022 \times 10^{22}\) atoms of sulfur
- (iii) \(1.445 \times 10^{24}\) atoms in glucose
- (iv) \(2.4088 \times 10^{23}\) atoms of oxygen