Anhydrous sodium sulphate can absorb water vapour and convert to its decahydrate. By how many gram would the mass of a 1 g sample of the thoroughly dried sodium sulphate increase, if its is exposed to sufficient water vapour to be converted to the decahydrate.

Options

A. 0.85 gm
B. 1.27 gm
C. 3.17 gm
D. 2.42 gm

Answer

To solve the problem of how much the mass of a 1 g sample of anhydrous sodium sulfate (Na2SO4) would increase when converted to its decahydrate (Na2SO4·10H2O), we can follow these steps:

### Step-by-Step Solution

1. **Write the Reaction**:
The hydration reaction of sodium sulfate can be represented as:
\[ \text{Na}_2\text{SO}_4 + 10\text{H}_2\text{O} \rightarrow \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O} \]

2. **Calculate Molar Mass of Anhydrous Sodium Sulfate (Na2SO4)**:
- Sodium (Na): 23 g/mol (2 atoms) = 2 × 23 = 46 g/mol
- Sulfur (S): 32 g/mol (1 atom) = 32 g/mol
- Oxygen (O): 16 g/mol (4 atoms) = 4 × 16 = 64 g/mol
- Total molar mass of Na2SO4:
\[ 46 + 32 + 64 = 142 \text{ g/mol} \]

3. **Calculate Molar Mass of Decahydrate Sodium Sulfate (Na2SO4·10H2O)**:
- Molar mass of water (H2O): 18 g/mol (10 molecules) = 10 × 18 = 180 g/mol
- Total molar mass of Na2SO4·10H2O:
\[ 142 + 180 = 322 \text{ g/mol} \]

4. **Determine the Mass Increase**:
- From the reaction, we see that 142 g of Na2SO4 absorbs water to form 322 g of Na2SO4·10H2O.
- The increase in mass when 142 g of Na2SO4 is converted to its decahydrate is:
\[ 322 \text{ g} - 142 \text{ g} = 180 \text{ g} \]

5. **Use Unitary Method to Find Increase for 1 g of Na2SO4**:
- If 142 g of Na2SO4 gives an increase of 180 g, then for 1 g of Na2SO4:
\[ \text{Increase} = \frac{180 \text{ g}}{142 \text{ g}} \times 1 \text{ g} \approx 1.27 \text{ g} \]

6. **Final Calculation**:
- The increase in mass when 1 g of anhydrous sodium sulfate is converted to its decahydrate is approximately:
\[ 1.27 \text{ g} \]

### Conclusion
Thus, the mass of a 1 g sample of thoroughly dried sodium sulfate would increase by approximately **1.27 grams** when exposed to sufficient water vapor to convert it to the decahydrate.