How many molecules approximately do you expect to be present in (i) a small sugar crystal which weighs 10 mg (ii) one drop of water with 0.05 cc volume ?

Explanation

To solve the question of how many molecules are present in (i) a small sugar crystal weighing 10 mg and (ii) one drop of water with a volume of 0.05 cc, we will follow these steps:

### Part (i): Small Sugar Crystal (10 mg)

1. **Convert the weight of sugar from mg to grams**:
\[ 10 \, \text{mg} = 10 \times 10^{-3} \, \text{g} = 0.01 \, \text{g} \]

2. **Determine the molar mass of sucrose (C\(_{12}\)H\(_{22}\)O\(_{11}\))**:
- Carbon (C): 12 g/mol × 12 = 144 g/mol
- Hydrogen (H): 1 g/mol × 22 = 22 g/mol
- Oxygen (O): 16 g/mol × 11 = 176 g/mol
- Total molar mass = 144 + 22 + 176 = 342 g/mol

3. **Calculate the number of moles of sugar**:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{0.01 \, \text{g}}{342 \, \text{g/mol}} \approx 2.92 \times 10^{-5} \, \text{moles} \]

4. **Use Avogadro's number to find the number of molecules**:
\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 2.92 \times 10^{-5} \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \approx 1.76 \times 10^{19} \, \text{molecules} \]

### Part (ii): One Drop of Water (0.05 cc)

1. **Convert the volume of water to grams**:
- Since the density of water is approximately 1 g/cc, 0.05 cc of water weighs about 0.05 g.

2. **Determine the molar mass of water (H\(_2\)O)**:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Oxygen (O): 16 g/mol × 1 = 16 g/mol
- Total molar mass = 2 + 16 = 18 g/mol

3. **Calculate the number of moles of water**:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{0.05 \, \text{g}}{18 \, \text{g/mol}} \approx 2.78 \times 10^{-3} \, \text{moles} \]

4. **Use Avogadro's number to find the number of molecules**:
\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 2.78 \times 10^{-3} \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \approx 1.67 \times 10^{21} \, \text{molecules} \]

### Final Answers:
- (i) Approximately \(1.76 \times 10^{19}\) molecules in a small sugar crystal weighing 10 mg.
- (ii) Approximately \(1.67 \times 10^{21}\) molecules in one drop of water with a volume of 0.05 cc.