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). The process involves oxidation at the anode and reduction at the cathode.

### Step 2: Determine the Possible Reactions at the Cathode
At the cathode, reduction occurs. The possible species that can be reduced in an aqueous solution of MgSO₄ are:
- Magnesium ions (Mg²⁺)
- Water (H₂O)

The reduction half-reaction for magnesium ions is:
\[ \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg (s)} \]
The reduction half-reaction for water is:
\[ 2\text{H}_2\text{O} + 2e^- \rightarrow \text{H}_2(g) + 2\text{OH}^- \]

### Step 3: Compare Standard Reduction Potentials
To determine which reaction occurs, we compare the standard reduction potentials (E°):
- For Mg²⁺: E° = -2.37 V
- For water: E° = -0.42 V

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

### Step 4: Determine the Products at the Cathode
Thus, at the cathode, hydrogen gas (H₂) is produced:
\[ \text{Cathode product: H}_2(g) \]

### Step 5: Determine the Possible Reactions at the Anode
At the anode, oxidation occurs. The possible species that can be oxidized are:
- Sulfate ions (SO₄²⁻)
- Water (H₂O)

The oxidation half-reaction for water is:
\[ 2\text{H}_2\text{O} \rightarrow \text{O}_2(g) + 4\text{H}^+ + 4e^- \]

The sulfate ion (SO₄²⁻) contains sulfur in its highest oxidation state (+6), meaning it cannot be oxidized further. Therefore, water will be oxidized instead.

### Step 6: Determine the Products at the Anode
Thus, at the anode, oxygen gas (O₂) is produced:
\[ \text{Anode product: O}_2(g) \]

### Final Conclusion
In summary, during the electrolysis of an aqueous solution of MgSO₄:
- **At the cathode:** Hydrogen gas (H₂) is produced.
- **At the anode:** Oxygen gas (O₂) is produced.

### Final Answer:
The products available on the cathode and the anode respectively are:
- Cathode: H₂(g)
- Anode: O₂(g)

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