Decomposition of a hydrated form of `Na_(2)CO_(3)` cause approximately 63% loss in its mass on strong heating. If the heating only cause removal of water of crystallization then formula of the hydrated salt is

Options

A. `Na_(2)CO_(3).5H_(2)O`
B. `Na_(2)CO_(3).10H_(2)O`
C. `Na_(2)CO_(3).2H_(2)O`
D. `Na_(2)CO_(3).7H_(2)O`

Explanation

To find the formula of the hydrated salt of sodium carbonate (Na₂CO₃) that loses approximately 63% of its mass upon heating, we can follow these steps:

### Step 1: Write the Chemical Equation
The decomposition of the hydrated salt can be represented as:
\[ \text{Na}_2\text{CO}_3 \cdot x\text{H}_2\text{O} \rightarrow \text{Na}_2\text{CO}_3 + x\text{H}_2\text{O} \]

### Step 2: Determine the Molar Masses
Next, we need to calculate the molar mass of the hydrated salt. The atomic masses are:
- Sodium (Na): 23 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol
- Water (H₂O): 18 g/mol

The molar mass of Na₂CO₃ is:
\[ 2 \times 23 + 12 + 3 \times 16 = 46 + 12 + 48 = 106 \text{ g/mol} \]

Thus, the molar mass of the hydrated salt (Na₂CO₃·xH₂O) is:
\[ 106 + 18x \text{ g/mol} \]

### Step 3: Set Up the Percentage Loss Equation
Given that there is a 63% loss in mass upon heating, we can express this mathematically:
\[ \text{Percentage loss} = \frac{\text{mass of water lost}}{\text{total mass of hydrated salt}} \times 100 \]

Substituting the values we have:
\[ 63 = \frac{18x}{106 + 18x} \times 100 \]

### Step 4: Cross-Multiply and Simplify
Cross-multiplying gives us:
\[ 63(106 + 18x) = 1800x \]

Expanding this:
\[ 6678 + 1134x = 1800x \]

### Step 5: Rearranging the Equation
Now, rearranging the equation to isolate x:
\[ 6678 = 1800x - 1134x \]
\[ 6678 = 666x \]

### Step 6: Solve for x
Dividing both sides by 666:
\[ x = \frac{6678}{666} \approx 10.02 \]

Since x must be a whole number, we round it to the nearest integer:
\[ x \approx 10 \]

### Step 7: Write the Final Formula
Thus, the formula of the hydrated salt is:
\[ \text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O} \]

### Conclusion
The formula of the hydrated salt is:
\[ \text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O} \]

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