The overall reactions of a hydrogen -oxygen fuel cell is

Options

A. `2H_(2(g)) + O_(2(g)) to 2H_2O_((l))`
B. `2H_(2(g)) + 4OH_((aq)) to 4H_2O_((l)) + 4e^(-)`
C. `O_(2(g)) + 2H_2O_((l)) + 4e^(-) to 4OH_((aq))^-`
D. `4OH_((aq))^(-) + 4e^(-) to 2H_2O_((l))`

Explanation

To find the overall reaction of a hydrogen-oxygen fuel cell, we can follow these steps:

### Step 1: Identify the half-reactions
In a hydrogen-oxygen fuel cell, there are two half-reactions: one occurs at the anode and the other at the cathode.

- **Anode Reaction:** At the anode, hydrogen gas (H2) is oxidized.
\[ 2 H_2 \rightarrow 4 H^+ + 4 e^- \]

- **Cathode Reaction:** At the cathode, oxygen gas (O2) is reduced.
\[ O_2 + 4 H^+ + 4 e^- \rightarrow 2 H_2O \]

### Step 2: Combine the half-reactions
To find the overall reaction, we need to combine the two half-reactions. We can add them together while ensuring that the electrons cancel out.

1. Write the anode reaction:
\[ 2 H_2 \rightarrow 4 H^+ + 4 e^- \]

2. Write the cathode reaction:
\[ O_2 + 4 H^+ + 4 e^- \rightarrow 2 H_2O \]

3. Combine the two reactions:
\[ 2 H_2 + O_2 \rightarrow 4 H^+ + 4 e^- + 4 H^+ + 4 e^- \rightarrow 2 H_2O \]

### Step 3: Simplify the overall reaction
After canceling out the electrons and protons, we are left with the overall reaction:
\[ 2 H_2 + O_2 \rightarrow 2 H_2O \]

### Conclusion
The overall reaction of a hydrogen-oxygen fuel cell is:
\[ 2 H_2 + O_2 \rightarrow 2 H_2O \]