To find the energy required to break down water molecules, we need to consider the energies associated with breaking and forming the relevant chemical bonds. Here is the step-by-step solution:
1. Identify the Chemical Bonds:
- In water (H[tex]\(_2\)[/tex]O), each molecule consists of two hydrogen-oxygen (H-O) bonds.
2. Bond Energies:
- The energy required to break one H-H bond is 436 kJ/mol.
- The energy required to break one O=O bond is 498 kJ/mol.
3. Energy Calculations:
- When breaking down water molecules, we'll be breaking two H-O bonds in each molecule of H[tex]\(_2\)[/tex]O.
- Conversely, we will form one H-H bond and half of an O=O bond by breaking the water molecule.
4. Total Energy Calculation:
- The energy required to break down the water molecule will be:
[tex]\[
\text{Energy required} = \text{Energy to form H\(_2\)O} = -(2 \times \text{Energy of H-H bond} + \frac{1}{2} \times \text{Energy of O=O bond})
\][/tex]
- Substituting the values:
[tex]\[
= - (2 \times 436 + \frac{1}{2} \times 498) \text{ kJ/mol}
\][/tex]
[tex]\[
= - (872 + 249) \text{ kJ/mol}
\][/tex]
[tex]\[
= -1121 \text{ kJ/mol}
\][/tex]
Therefore, the energy required to break down water molecules is [tex]\( -1121 \)[/tex] kJ/mol.
