If `x_(1)` , `x_(2)` and `x_(3)` are enthalpies of `H-H` , `O=O` and `O-H` bonds respective, and `x_(4)` is the enthaply of vaporisation of water, estimate the standard enthalpy opf combustion of hydrogen.

Options

A. `x_1 + (x_2)/(2) - 2x_(3) + x_(4)`
B. `x_1 + (x_2)/(2) - 2x_(3) - x_(4)`
C. `x_1 + (x_2)/(2) + x_(3) + x_(4)`
D. `2x_(3) - x_(1) -(x_2)/2 - x_(4)`

Explanation

To estimate the standard enthalpy of combustion of hydrogen, we can follow these steps:

### Step 1: Write the combustion reaction
The standard enthalpy of combustion of hydrogen can be represented by the following reaction:
\[ \text{H}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{H}_2O(l) \]
This reaction shows hydrogen gas reacting with oxygen gas to form liquid water.

### Step 2: Identify bond energies
Let:
- \( x_1 \) = Enthalpy of the H-H bond
- \( x_2 \) = Enthalpy of the O=O bond
- \( x_3 \) = Enthalpy of the O-H bond
- \( x_4 \) = Enthalpy of vaporization of water

### Step 3: Calculate the bond energies of reactants
In the reactants, we have:
- 1 H-H bond in H2: contributes \( x_1 \)
- 1 O=O bond in O2: contributes \( \frac{1}{2} x_2 \)

Thus, the total bond energy of the reactants is:
\[ \text{Total bond energy of reactants} = x_1 + \frac{1}{2} x_2 \]

### Step 4: Calculate the bond energies of products
In the products, we have:
- 2 O-H bonds in H2O: contributes \( 2 \times x_3 \)
- The enthalpy of vaporization of water \( x_4 \) must also be considered since we are forming liquid water from gaseous water.

Thus, the total bond energy of the products is:
\[ \text{Total bond energy of products} = 2x_3 + x_4 \]

### Step 5: Apply Hess's Law
According to Hess's Law, the standard enthalpy change for the reaction can be calculated as:
\[ \Delta H = \text{Bond energy of reactants} - \text{Bond energy of products} \]
Substituting the values we calculated:
\[ \Delta H = \left( x_1 + \frac{1}{2} x_2 \right) - \left( 2x_3 + x_4 \right) \]

### Step 6: Rearrange the equation
Rearranging the equation gives:
\[ \Delta H = x_1 + \frac{1}{2} x_2 - 2x_3 - x_4 \]

### Step 7: Finalize the expression
To express it in a more standard form, we can write:
\[ \Delta H = \frac{x_1 + x_2}{2} - 2x_3 - x_4 \]

### Conclusion
Thus, the standard enthalpy of combustion of hydrogen is given by:
\[ \Delta H = \frac{x_1 + x_2}{2} - 2x_3 - x_4 \]

### Answer
The correct option is:
\[ \Delta H = \frac{x_1 + x_2}{2} - 2x_3 - x_4 \]