Assertion `(A) : (H_(2)+O_(2))` fuel cell gives a constant voltages throughout its life.
Reason `(R): `In this fuel cell, `H_(2)` reacts with `overset(-)(OH)` ions, yet the over all `[overset(c-)(O)H]` does not change.

Options

A. If both `(A)` and `(R)` are correct, and `(R)` is the correct explanation of `(A)`.
B. If both `(A)` and `(R)` are correct, but `(R)` is not the correct explanation of `(A)`.
C. If `(A)` is correct, but `(R)` is incorrect.
D. If `(A)` is incorrect, `(R)` is correct.

Answer

To solve the question regarding the assertion and reason related to the hydrogen-oxygen fuel cell, we will analyze both statements step by step.

### Step 1: Understanding the Assertion
**Assertion (A):** The hydrogen-oxygen fuel cell gives a constant voltage throughout its life.

- A hydrogen-oxygen fuel cell operates by continuously converting chemical energy into electrical energy. The reactions occurring in the fuel cell are designed to maintain a stable output voltage as long as reactants (hydrogen and oxygen) are supplied.

**Hint for Step 1:** Consider how the continuous supply of reactants affects the voltage output of the fuel cell.

### Step 2: Understanding the Reason
**Reason (R):** In this fuel cell, hydrogen reacts with OH⁻ ions, yet the overall concentration of OH⁻ ions does not change.

- In the fuel cell, hydrogen gas (H₂) reacts with hydroxide ions (OH⁻) at the anode to produce water (H₂O) and electrons. At the same time, oxygen (O₂) at the cathode reacts with water and electrons to produce more hydroxide ions. This means that for every hydroxide ion consumed at the anode, an equivalent amount is produced at the cathode, maintaining a constant concentration of OH⁻ ions.

**Hint for Step 2:** Think about the stoichiometry of the reactions occurring at both electrodes and how they relate to the concentration of hydroxide ions.

### Step 3: Analyzing the Relationship Between Assertion and Reason
- Both the assertion and the reason are correct. The reason explains why the assertion holds true: the constant concentration of OH⁻ ions ensures that the voltage remains stable.

**Hint for Step 3:** Reflect on how the reactions at the anode and cathode are balanced and how this balance supports the assertion.

### Step 4: Conclusion
- Since both the assertion and the reason are correct, and the reason provides a valid explanation for the assertion, we conclude that the correct answer is that both A and R are correct, and R is the correct explanation of A.

**Final Answer:** Both assertion (A) and reason (R) are correct, and R is the correct explanation of A.