For any acid catalysed reaction, `Aoverset(H^(+))rarrB`
half- life period is independent of concentration of A at given pH. At definite concentration of A half- time is 10min at pH=2 and half- time is 100 min at pH=3. If the rate law expression of reaction is `r=k[A]^(x)[H^(+)]^(y)` then calulate the value of (x+y).

Answer

To solve the problem, we need to analyze the information given about the acid-catalyzed reaction and the relationship between half-life and the concentrations of the reactants.

### Step-by-Step Solution:

1. **Understanding Half-Life in Reactions**:
- The half-life period (t_half) of a reaction is the time taken for the concentration of a reactant to reduce to half of its initial concentration.
- For different orders of reactions, the relationship between half-life and concentration varies:
- **Zero-order**: t_half is directly proportional to the initial concentration.
- **First-order**: t_half is independent of the initial concentration.
- **Second-order**: t_half is inversely proportional to the initial concentration.

2. **Given Data**:
- At pH = 2, t_half = 10 minutes.
- At pH = 3, t_half = 100 minutes.
- The reaction is catalyzed by H⁺ ions, and the rate law is given as:
\[ r = k[A]^x[H^+]^y \]

3. **Analyzing the pH Values**:
- pH = 2 corresponds to [H⁺] = 10⁻² M.
- pH = 3 corresponds to [H⁺] = 10⁻³ M.
- The concentration of H⁺ decreases by a factor of 10 when pH changes from 2 to 3.

4. **Relating Half-Life to Concentration**:
- Since t_half is independent of the concentration of A at a given pH, we can conclude that the reaction is first-order with respect to A (x = 1).
- The change in half-life from 10 minutes to 100 minutes indicates that the half-life is affected by the concentration of H⁺ ions.

5. **Determining the Order with Respect to H⁺**:
- When the concentration of H⁺ decreases by a factor of 10, the half-life increases by a factor of 10 (from 10 min to 100 min).
- This implies that t_half is directly proportional to [H⁺] raised to some power.
- If we denote the order with respect to H⁺ as y, we can express this relationship as:
\[ t_{half} \propto [H^+]^{-y} \]
- Since t_half increases by a factor of 10 when [H⁺] decreases by a factor of 10, we can conclude that y = 2.

6. **Calculating x + y**:
- We have determined that:
- x = 1 (first-order with respect to A)
- y = 2 (second-order with respect to H⁺)
- Therefore, x + y = 1 + 2 = 3.

### Final Answer:
The value of (x + y) is **3**.