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, we will use Hess's Law, which states that the total enthalpy change for a reaction is equal to the sum of the enthalpy changes for the individual steps of the reaction.

### Step-by-Step Solution:

1. **Identify the Overall Reaction and Enthalpy Change**:
We have the overall reaction:
\[ A \rightarrow D \quad \Delta H = x \]
This means that the enthalpy change for the reaction from A to D is \(x\).

2. **Identify the Steps and Their Enthalpy Changes**:
The steps involved in the reaction are:
- Step 1: \(A \rightarrow B\) with \(\Delta H_1 = x_1\)
- Step 2: \(B \rightarrow C\) with \(\Delta H_2 = ?\) (this is what we need to find)
- 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 overall reaction can be expressed as the sum of the enthalpy changes for each step:
\[ \Delta H = \Delta H_1 + \Delta H_2 + \Delta H_3 \]
Substituting the known values:
\[ x = x_1 + \Delta H_2 + x_3 \]

4. **Rearranging the Equation to Solve for \(\Delta H_2\)**:
To isolate \(\Delta H_2\), we can rearrange the equation:
\[ \Delta H_2 = x - x_1 - x_3 \]

5. **Final Expression**:
Thus, we can express \(\Delta H_2\) as:
\[ \Delta H_2 = x - (x_1 + x_3) \]
This can also be written as:
\[ \Delta H_2 = x - x_1 + x_3 \]