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 solve the problem, we need to find the heat of reaction for the equation:

\[ A + O_2 \rightarrow AO_2 \]

We are given two reactions with their respective heats of reaction:

1. \( A + \frac{1}{2} O_2 \rightarrow AO \) with a heat of reaction \( \Delta H_1 = -50 \, \text{kcal} \)
2. \( AO + \frac{1}{2} O_2 \rightarrow AO_2 \) with a heat of reaction \( \Delta H_2 = 100 \, \text{kcal} \)

### Step 1: Write down the given reactions and their heats of reaction
- Reaction 1:
\[ A + \frac{1}{2} O_2 \rightarrow AO \quad (\Delta H_1 = -50 \, \text{kcal}) \]
- Reaction 2:
\[ AO + \frac{1}{2} O_2 \rightarrow AO_2 \quad (\Delta H_2 = 100 \, \text{kcal}) \]

### Step 2: Combine the reactions
To find the overall heat of reaction for \( A + O_2 \rightarrow AO_2 \), we can add the two reactions together.

When we add the two reactions, we need to ensure that the intermediate product \( AO \) cancels out:

1. From Reaction 1, we have:
\[ A + \frac{1}{2} O_2 \rightarrow AO \]
2. From Reaction 2, we have:
\[ AO + \frac{1}{2} O_2 \rightarrow AO_2 \]

Adding these two reactions gives:
\[ A + \frac{1}{2} O_2 + AO + \frac{1}{2} O_2 \rightarrow AO + AO_2 \]

### Step 3: Simplify the equation
The \( AO \) on the left side cancels with \( AO \) on the right side, and we can combine the \( O_2 \) terms:
\[ A + O_2 \rightarrow AO_2 \]

### Step 4: Calculate the overall heat of reaction
Now, we can find the overall heat of reaction by adding the heats of the two reactions:
\[ \Delta H = \Delta H_1 + \Delta H_2 \]
Substituting the values:
\[ \Delta H = (-50 \, \text{kcal}) + (100 \, \text{kcal}) = 50 \, \text{kcal} \]

### Final Answer
The heat of reaction for \( A + O_2 \rightarrow AO_2 \) is:
\[ \Delta H = 50 \, \text{kcal} \]