How many equivalents of Mg would have to react in order to liberate `4 N_(A)` electrons ? `(Mg-2e^(-)rarrMg^(2+))`

Answer

To determine how many equivalents of magnesium (Mg) are needed to liberate 4 Na electrons, we can follow these steps:

### Step 1: Understand the Reaction
The given reaction is:
\[ \text{Mg} - 2e^- \rightarrow \text{Mg}^{2+} \]
This indicates that 1 mole of magnesium (Mg) loses 2 moles of electrons.

### Step 2: Determine the Relationship Between Moles of Mg and Electrons
From the reaction, we see that:
- 1 mole of Mg liberates 2 moles of electrons.

### Step 3: Calculate the Moles of Mg Required for 4 Na Electrons
We need to liberate 4 Na electrons. Since 1 mole of Mg liberates 2 moles of electrons, we can set up a proportion:
- If 1 mole of Mg liberates 2 moles of electrons, then to liberate 4 moles of electrons, we need:
\[ \text{Moles of Mg} = \frac{4 \text{ moles of electrons}}{2 \text{ moles of electrons per mole of Mg}} = 2 \text{ moles of Mg} \]

### Step 4: Calculate the Equivalents of Mg
The number of equivalents is calculated using the formula:
\[ \text{Number of equivalents} = \frac{\text{Number of moles}}{n \text{ factor}} \]
Where the n factor is the number of electrons lost per mole of substance. For Mg, the n factor is 2 (since it loses 2 electrons).

Now substituting the values:
- Number of moles of Mg = 2
- n factor = 2

Thus:
\[ \text{Number of equivalents} = \frac{2 \text{ moles}}{2} = 1 \text{ equivalent} \]

### Conclusion
Therefore, **1 equivalent of Mg** would have to react in order to liberate **4 Na electrons**.

---