A hypothetical reaction `Ato2B`, proceeds through following sequence of steps
(i) `A to C,DeltaH=q`
(ii) `C to D,DeltaH=v`
(iii) `(1)/(2)D to B,DeltaH=x`
Then, the heat of reaction is

Options

A. `q - v + 2x`
B. `q + v - 2x`
C. `q + v + 2x`
D. `q + 2v - 2x`

Explanation

To find the heat of reaction for the hypothetical reaction \( A \to 2B \) that proceeds through the given steps, we can apply Hess's law. Here’s a step-by-step solution:

### Step 1: Understand the Reaction Steps
We have three steps with their respective enthalpy changes:
1. \( A \to C \), with \(\Delta H = q\)
2. \( C \to D \), with \(\Delta H = v\)
3. \( \frac{1}{2}D \to B \), with \(\Delta H = x\)

### Step 2: Write the Overall Reaction
We need to combine these steps to find the overall reaction \( A \to 2B \).

### Step 3: Modify the Third Step
Since the third step produces only \( B \) from \( \frac{1}{2}D \), we need to multiply this step by 2 to produce 2 moles of \( B \):
- \( D \to 2B \) will have an enthalpy change of \( 2x \).

### Step 4: Combine the Reactions
Now we can combine the three steps:
1. \( A \to C \) (enthalpy change = \( q \))
2. \( C \to D \) (enthalpy change = \( v \))
3. \( D \to 2B \) (enthalpy change = \( 2x \))

### Step 5: Write the Overall Enthalpy Change
According to Hess's law, the total enthalpy change for the overall reaction is the sum of the enthalpy changes of the individual steps:
\[ \Delta H_{\text{net}} = q + v + 2x \]

### Conclusion
Thus, the heat of reaction for \( A \to 2B \) is:
\[ \Delta H = q + v + 2x \]