For the reaction,
`2H_(2)(g)+O_(2)(g) to 2H_(2)O(g), DeltaH=-573.2kJ`
The heat of decomposition of water per mole

Options

A. `286.6 kJ`
B. `573.2 kJ`
C. `-28.66 kJ`
D. zero

Explanation

To find the heat of decomposition of water per mole from the given reaction:

**Given Reaction:**
\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(g), \quad \Delta H = -573.2 \text{ kJ} \]

This indicates that when 2 moles of water are formed, 573.2 kJ of heat is released. We need to determine the heat required to decompose 1 mole of water.

### Step-by-Step Solution:

1. **Understanding the Reaction:**
The given reaction is an exothermic reaction where 2 moles of water are formed, and heat is released. The negative sign in \(\Delta H\) indicates that heat is released during the formation of water.

2. **Reversing the Reaction:**
To find the heat of decomposition, we need to reverse the reaction. The decomposition of water can be represented as:
\[ 2H_2O(g) \rightarrow 2H_2(g) + O_2(g) \]
When we reverse the reaction, the sign of \(\Delta H\) also changes:
\[ \Delta H = +573.2 \text{ kJ} \]
This means that 573.2 kJ of heat is required to decompose 2 moles of water.

3. **Calculating Heat per Mole:**
Since the reversed reaction gives the heat required for 2 moles of water, we need to find the heat required for 1 mole of water. We do this by dividing the total heat by 2:
\[ \text{Heat for 1 mole} = \frac{573.2 \text{ kJ}}{2} = 286.6 \text{ kJ} \]

4. **Conclusion:**
Therefore, the heat of decomposition of water per mole is:
\[ \Delta H_{decomposition} = 286.6 \text{ kJ/mol} \]

### Final Answer:
The heat of decomposition of water per mole is **286.6 kJ/mol**.

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