For the given reactions, `A rightarrow D, Delta H = x`. Steps involved are
`A rightarrow B, Delta H_(1) = x_(1)`
`B rightarrow C, Delta H_(2) = ?`
`C rightarrow D, Delta H_(3) = x_(3)`

Options

A. `Delta H_(2) = x-(x_(1) + x_(3))`
B. `Delta H_(2) = x + x_(1) + x_(3)`
C. `Delta H_(2) = x_(1) - x_(3) - x`
D. `Delta H_(2) = (x_(1) + x) - x_(3)`

Answer

To solve the problem using Hess's Law, we need to express the enthalpy change for the overall reaction \( A \rightarrow D \) in terms of the enthalpy changes for the individual steps.

### Step-by-Step Solution:

1. **Identify the Overall Reaction and its Enthalpy Change**:
- The overall reaction is given as \( A \rightarrow D \) with an enthalpy change \( \Delta H = x \).

2. **Break Down the Overall Reaction into Steps**:
- The reaction can be broken down into three steps:
- Step 1: \( A \rightarrow B \) with \( \Delta H_{1} = x_{1} \)
- Step 2: \( B \rightarrow C \) with \( \Delta H_{2} = ? \)
- Step 3: \( C \rightarrow D \) with \( \Delta H_{3} = x_{3} \)

3. **Apply Hess's Law**:
- According to Hess's Law, the total enthalpy change for the reaction can be expressed as the sum of the enthalpy changes for each step:
\[ \Delta H = \Delta H_{AB} + \Delta H_{BC} + \Delta H_{CD} \]
- Substituting the known values:
\[ x = x_{1} + \Delta H_{2} + x_{3} \]

4. **Rearranging to Solve for \( \Delta H_{2} \)**:
- To find \( \Delta H_{2} \), we rearrange the equation:
\[ \Delta H_{2} = x - x_{1} - x_{3} \]

5. **Final Expression**:
- Thus, the enthalpy change for the step \( B \rightarrow C \) is:
\[ \Delta H_{2} = x - x_{1} - x_{3} \]

### Conclusion:
The final answer for \( \Delta H_{2} \) is:
\[ \Delta H_{2} = x - x_{1} - x_{3} \]