The heat of reaction of
`A+(1)/(2)O_(2)rarr AO` is -50 K call and
`AO+(1)/(2)O_(2)rarr AO_(2)` is 100 Kcal. The heat of reaction for `A+O_(2)rarr AO_(2)` is :-

Options

A. `-50` K cal.
B. `+50` K cal
C. 100 K cal.
D. 150 K cal.

Answer

To find the heat of reaction for the equation \( A + O_2 \rightarrow AO_2 \), we can use Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps of the reaction.

### Step-by-Step Solution:

1. **Identify the Given Reactions and Their Heats of Reaction:**
- Reaction 1: \( A + \frac{1}{2} O_2 \rightarrow AO \) with \( \Delta H_1 = -50 \) Kcal
- Reaction 2: \( AO + \frac{1}{2} O_2 \rightarrow AO_2 \) with \( \Delta H_2 = +100 \) Kcal

2. **Write the Target Reaction:**
- Target Reaction: \( A + O_2 \rightarrow AO_2 \)

3. **Manipulate the Given Reactions:**
- We can add Reaction 1 and Reaction 2 together to achieve the target reaction.
- First, we keep Reaction 1 as it is:
\[ A + \frac{1}{2} O_2 \rightarrow AO \quad (\Delta H_1 = -50 \text{ Kcal}) \]
- Then, we keep Reaction 2 as it is:
\[ AO + \frac{1}{2} O_2 \rightarrow AO_2 \quad (\Delta H_2 = +100 \text{ Kcal}) \]

4. **Add the Two Reactions:**
- When we add these two reactions, the \( AO \) on the product side of Reaction 1 will cancel with the \( AO \) on the reactant side of Reaction 2:
\[ A + \frac{1}{2} O_2 + AO + \frac{1}{2} O_2 \rightarrow AO + AO_2 \]
- This simplifies to:
\[ A + O_2 \rightarrow AO_2 \]

5. **Calculate the Total Heat of Reaction:**
- Now, we sum the heats of reaction:
\[ \Delta H = \Delta H_1 + \Delta H_2 = -50 \text{ Kcal} + 100 \text{ Kcal} = +50 \text{ Kcal} \]

6. **Final Result:**
- Therefore, the heat of reaction for \( A + O_2 \rightarrow AO_2 \) is \( +50 \) Kcal.

### Summary:
The heat of reaction for \( A + O_2 \rightarrow AO_2 \) is \( +50 \) Kcal.