The weight of `1xx10^(22)`molecules of `CuSO_4 cdot 5H _2O` is

Options

A. 41.59 g
B. 415.9 g
C. 4.159 g
D. none of these

Answer

To find the weight of \(1 \times 10^{22}\) molecules of \(CuSO_4 \cdot 5H_2O\), we can follow these steps:

### Step 1: Determine the molar mass of \(CuSO_4 \cdot 5H_2O\)

1. **Calculate the molar mass of each component:**
- Copper (Cu): 63.5 g/mol
- Sulfur (S): 32.1 g/mol
- Oxygen (O): 16.0 g/mol (4 from \(CuSO_4\) and 10 from \(5H_2O\))
- Hydrogen (H): 1.0 g/mol (10 from \(5H_2O\))

The molar mass calculation:
\[ \text{Molar mass of } CuSO_4 = 63.5 + 32.1 + (4 \times 16.0) = 63.5 + 32.1 + 64.0 = 159.6 \text{ g/mol} \]
\[ \text{Molar mass of } 5H_2O = 5 \times (2 \times 1.0 + 16.0) = 5 \times 18.0 = 90.0 \text{ g/mol} \]
\[ \text{Total molar mass of } CuSO_4 \cdot 5H_2O = 159.6 + 90.0 = 249.6 \text{ g/mol} \]

### Step 2: Use Avogadro's number to find the weight of 1 molecule

2. **Calculate the weight of one molecule:**
\[ \text{Weight of 1 molecule} = \frac{\text{Molar mass}}{\text{Avogadro's number}} = \frac{249.6 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \]

### Step 3: Calculate the weight of \(1 \times 10^{22}\) molecules

3. **Calculate the weight of \(1 \times 10^{22}\) molecules:**
\[ \text{Weight of } 1 \times 10^{22} \text{ molecules} = \left(\frac{249.6}{6.022 \times 10^{23}}\right) \times (1 \times 10^{22}) \]

### Step 4: Perform the calculation

4. **Calculate the final weight:**
\[ \text{Weight} = \frac{249.6 \times 1 \times 10^{22}}{6.022 \times 10^{23}} \approx 4.15 \text{ grams} \]

### Final Answer

The weight of \(1 \times 10^{22}\) molecules of \(CuSO_4 \cdot 5H_2O\) is approximately **4.15 grams**.

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