26.8 gm `Na_(2)SO_(4). nH_(2)O` contains 12.6 of water here the value of 'n' is ?

Answer

To find the value of 'n' in the compound \( \text{Na}_2\text{SO}_4 \cdot n\text{H}_2\text{O} \), we can follow these steps:

### Step 1: Determine the mass of anhydrous \( \text{Na}_2\text{SO}_4 \)
We are given that the total mass of the hydrate \( \text{Na}_2\text{SO}_4 \cdot n\text{H}_2\text{O} \) is 26.8 g and the mass of water in it is 12.6 g.

To find the mass of anhydrous \( \text{Na}_2\text{SO}_4 \):
\[ \text{Mass of } \text{Na}_2\text{SO}_4 = \text{Total mass} - \text{Mass of water} = 26.8 \, \text{g} - 12.6 \, \text{g} = 14.2 \, \text{g} \]

### Step 2: Calculate the number of moles of \( \text{Na}_2\text{SO}_4 \)
The molar mass of \( \text{Na}_2\text{SO}_4 \) can be calculated as follows:
- Sodium (Na): 23 g/mol, and there are 2 Na: \( 2 \times 23 = 46 \, \text{g/mol} \)
- Sulfur (S): 32 g/mol
- Oxygen (O): 16 g/mol, and there are 4 O: \( 4 \times 16 = 64 \, \text{g/mol} \)

Adding these together:
\[ \text{Molar mass of } \text{Na}_2\text{SO}_4 = 46 + 32 + 64 = 142 \, \text{g/mol} \]

Now, we can calculate the number of moles of \( \text{Na}_2\text{SO}_4 \):
\[ \text{Number of moles of } \text{Na}_2\text{SO}_4 = \frac{\text{Mass}}{\text{Molar mass}} = \frac{14.2 \, \text{g}}{142 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 3: Calculate the number of moles of water
The molar mass of water \( \text{H}_2\text{O} \) is:
- Hydrogen (H): 1 g/mol, and there are 2 H: \( 2 \times 1 = 2 \, \text{g/mol} \)
- Oxygen (O): 16 g/mol

Thus, the molar mass of water is:
\[ \text{Molar mass of } \text{H}_2\text{O} = 2 + 16 = 18 \, \text{g/mol} \]

Now, we can calculate the number of moles of water:
\[ \text{Number of moles of water} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{12.6 \, \text{g}}{18 \, \text{g/mol}} = 0.7 \, \text{mol} \]

### Step 4: Set up the equation to find 'n'
In the hydrate \( \text{Na}_2\text{SO}_4 \cdot n\text{H}_2\text{O} \), the number of moles of water is equal to \( n \) times the number of moles of \( \text{Na}_2\text{SO}_4 \):
\[ n \cdot \text{moles of } \text{Na}_2\text{SO}_4 = \text{moles of water} \]
Substituting the values we found:
\[ n \cdot 0.1 = 0.7 \]

### Step 5: Solve for 'n'
To find 'n', we rearrange the equation:
\[ n = \frac{0.7}{0.1} = 7 \]

Thus, the value of 'n' is 7.

### Final Answer
The value of \( n \) is 7.

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