Give the products available on the cathode and the anode respectively during the electrolysis of an aqueous solution of `MgSO_(4)` between inert electrodes.

Options

A. `H_(2)(g) and O_2(g)`
B. `O_(2) (g) and H_(2) (g)`
C. `O_(2)(g) andMg (s)`
D. `O_(2)(g) and SO_(2) (g)`

Explanation

To determine the products formed at the cathode and anode during the electrolysis of an aqueous solution of magnesium sulfate (MgSO₄) using inert electrodes, we can follow these steps:

### Step 1: Identify the Electrolysis Setup
In electrolysis, we have two electrodes: the anode (positive electrode) and the cathode (negative electrode). An aqueous solution of MgSO₄ contains Mg²⁺ ions and SO₄²⁻ ions, along with water (H₂O).

### Step 2: Determine the Reactions at the Anode
At the anode, oxidation occurs. We need to consider the possible species that can be oxidized:
- The sulfate ion (SO₄²⁻) does not undergo oxidation under these conditions.
- Water (H₂O) can be oxidized to produce oxygen gas (O₂).

The half-reaction for the oxidation of water is:
\[ 2 H₂O \rightarrow O₂ + 4 H⁺ + 4 e⁻ \]

Thus, the product at the anode is oxygen gas (O₂).

### Step 3: Determine the Reactions at the Cathode
At the cathode, reduction occurs. We need to consider the possible species that can be reduced:
- Magnesium ions (Mg²⁺) can be reduced to magnesium metal (Mg).
- Water (H₂O) can also be reduced to produce hydrogen gas (H₂).

The reduction half-reaction for magnesium is:
\[ Mg^{2+} + 2 e⁻ \rightarrow Mg \]

The reduction half-reaction for water is:
\[ 2 H₂O + 2 e⁻ \rightarrow H₂ + 2 OH⁻ \]

To determine which reaction occurs, we compare the standard reduction potentials:
- The standard reduction potential for Mg²⁺ is -2.37 V.
- The standard reduction potential for water is -0.42 V.

Since the reduction potential for water is higher (less negative), water will be reduced instead of magnesium ions.

Thus, the product at the cathode is hydrogen gas (H₂).

### Conclusion
The products formed during the electrolysis of an aqueous solution of MgSO₄ are:
- At the anode: Oxygen gas (O₂)
- At the cathode: Hydrogen gas (H₂)

### Final Answer
- Products at the anode: O₂
- Products at the cathode: H₂