An imaginary reaction `X rarr Y` takes place in three steps
`X rarr A, DeltaH=-q_(1), " "BrarrA, DeltaH=-q_(2), " "BrarrY, DeltaH=-q_(3)`
If Hess's law is applicable, then the heat of the reaction `(X rarr Y)` is :

Options

A. `q_(1)-q_(2)+q_(3)`
B. `q_(2)-q_(3)-q_(1)`
C. `q_(1)-q_(2)-q_(3)`
D. `q_(3)-q_(2)-q_(1)`

Explanation

To solve the problem, we will apply 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 that lead to that reaction.

### Step-by-Step Solution:

1. **Identify the Steps of the Reaction:**
The reaction occurs in three steps:
- Step 1: \( X \rightarrow A \) with \( \Delta H = -q_1 \)
- Step 2: \( A \rightarrow B \) with \( \Delta H = -q_2 \)
- Step 3: \( B \rightarrow Y \) with \( \Delta H = -q_3 \)

2. **Write the Enthalpy Changes:**
From the steps, we can write the enthalpy changes:
- For Step 1: \( \Delta H_1 = -q_1 \)
- For Step 2: \( \Delta H_2 = -q_2 \)
- For Step 3: \( \Delta H_3 = -q_3 \)

3. **Apply Hess's Law:**
According to Hess's law, the total enthalpy change for the overall reaction \( X \rightarrow Y \) is the sum of the enthalpy changes of the individual steps:
\[ \Delta H_{total} = \Delta H_1 + \Delta H_2 + \Delta H_3 \]

4. **Substitute the Enthalpy Changes:**
Substituting the values from the steps:
\[ \Delta H_{total} = (-q_1) + (-q_2) + (-q_3) \]
This simplifies to:
\[ \Delta H_{total} = -q_1 - q_2 - q_3 \]

5. **Rearranging the Equation:**
To express the heat of the reaction \( X \rightarrow Y \) in a more useful form, we can rearrange the equation:
\[ \Delta H_{total} = -(q_1 + q_2 + q_3) \]
However, if we want to express it in terms of absorbed and released heat, we can consider the heat absorbed in the reverse direction.

6. **Final Expression:**
The heat of the reaction \( X \rightarrow Y \) can be expressed as:
\[ \Delta H_{reaction} = q_2 - q_1 - q_3 \]
Thus, the heat of the reaction \( X \rightarrow Y \) is:
\[ \Delta H_{reaction} = q_2 - q_1 - q_3 \]

### Conclusion:
The heat of the reaction \( X \rightarrow Y \) is given by:
\[ \Delta H_{reaction} = q_2 - q_1 - q_3 \]