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) increases when it absorbs water vapor and converts to its decahydrate (Na2SO4·10H2O), we can follow these steps:

### Step 1: Calculate the molar mass of anhydrous sodium sulfate (Na2SO4)
- Sodium (Na) has an atomic mass of approximately 23 g/mol. Since there are 2 sodium atoms:
\[ 2 \times 23 = 46 \text{ g/mol} \]
- Sulfur (S) has an atomic mass of approximately 32 g/mol.
- Oxygen (O) has an atomic mass of approximately 16 g/mol. Since there are 4 oxygen atoms:
\[ 4 \times 16 = 64 \text{ g/mol} \]
- Now, sum these values to find the molar mass of Na2SO4:
\[ 46 + 32 + 64 = 142 \text{ g/mol} \]

### Step 2: Calculate the molar mass of the decahydrate (Na2SO4·10H2O)
- The molar mass of Na2SO4 is already calculated as 142 g/mol.
- Each water molecule (H2O) has a molar mass of approximately 18 g/mol. For 10 water molecules:
\[ 10 \times 18 = 180 \text{ g/mol} \]
- Now, sum these values to find the molar mass of Na2SO4·10H2O:
\[ 142 + 180 = 322 \text{ g/mol} \]

### Step 3: Calculate the increase in mass when converting from anhydrous to decahydrate
- The increase in mass when converting from Na2SO4 to Na2SO4·10H2O is:
\[ 322 \text{ g/mol} - 142 \text{ g/mol} = 180 \text{ g/mol} \]

### Step 4: Calculate the increase in mass for a 1 g sample
- To find the increase in mass for a 1 g sample of anhydrous sodium sulfate, we can set up a proportion based on the molar masses:
\[ \text{Increase in mass} = \left(\frac{180 \text{ g}}{142 \text{ g}}\right) \times 1 \text{ g} \]
- Calculating this gives:
\[ \text{Increase in mass} = \frac{180}{142} \approx 1.27 \text{ g} \]

### Conclusion
The mass of a 1 g sample of anhydrous sodium sulfate would increase by approximately **1.27 grams** when it is converted to its decahydrate.

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