The heat of solution of one mole of `Na_2SO_(4).10H_2O ` is -78.7 kJ ,and that of dehydration , `-81.6 kJ. ` The heat of solution (kJ) of anhydrous sodium sulphate is

Options

A. `+2.9 kJ`
B. `+160.3 kJ`
C. `-2.9 kJ`
D. `-160.3 kJ`

Answer

To find the heat of solution of anhydrous sodium sulfate (Na2SO4), we will use the given data about the heat of solution of sodium sulfate decahydrate (Na2SO4·10H2O) and the heat of dehydration. Here’s how we can solve the problem step by step:

### Step 1: Write down the given data
- Heat of solution of Na2SO4·10H2O = -78.7 kJ
- Heat of dehydration (removal of water) = -81.6 kJ

### Step 2: Write the equations for the processes
1. The dissolution of sodium sulfate decahydrate:
\[ \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O (s)} \rightarrow 2\text{Na}^+ (aq) + \text{SO}_4^{2-} (aq) + 10\text{H}_2\text{O (l)} \quad \Delta H = -78.7 \text{ kJ} \]

2. The dehydration of sodium sulfate decahydrate:
\[ \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O (s)} \rightarrow \text{Na}_2\text{SO}_4 (s) + 10\text{H}_2\text{O (l)} \quad \Delta H = -81.6 \text{ kJ} \]

### Step 3: Reverse the dehydration equation
To find the heat of solution of anhydrous sodium sulfate, we need to reverse the dehydration equation:
\[ \text{Na}_2\text{SO}_4 (s) + 10\text{H}_2\text{O (l)} \rightarrow \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O (s)} \quad \Delta H = +81.6 \text{ kJ} \]

### Step 4: Add the two equations
Now we can add the two reactions together:
1. The dissolution of Na2SO4·10H2O:
\[ \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O (s)} \rightarrow 2\text{Na}^+ (aq) + \text{SO}_4^{2-} (aq) + 10\text{H}_2\text{O (l)} \quad \Delta H = -78.7 \text{ kJ} \]

2. The reversed dehydration:
\[ \text{Na}_2\text{SO}_4 (s) + 10\text{H}_2\text{O (l)} \rightarrow \text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O (s)} \quad \Delta H = +81.6 \text{ kJ} \]

When we add these two reactions, the Na2SO4·10H2O on the left cancels out:
\[ \text{Na}_2\text{SO}_4 (s) \rightarrow 2\text{Na}^+ (aq) + \text{SO}_4^{2-} (aq) \quad \Delta H = -78.7 \text{ kJ} + 81.6 \text{ kJ} \]

### Step 5: Calculate the total heat of solution
Now we can calculate the total heat of solution for anhydrous sodium sulfate:
\[ \Delta H = -78.7 \text{ kJ} + 81.6 \text{ kJ} = +2.9 \text{ kJ} \]

### Final Answer
The heat of solution of anhydrous sodium sulfate is **+2.9 kJ**.

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