To determine the correct formula for magnesium nitride, we must consider the charges of the ions involved in forming this compound.
1. Identify the charges on the ions:
- Magnesium (Mg) is an alkaline earth metal found in Group 2 of the periodic table. As such, it forms a cation with a charge of +2 ([tex]$Mg^{2+}$[/tex]).
- Nitrogen (N) is a nonmetal found in Group 15 of the periodic table. When it forms an anion, it typically gains three electrons, resulting in a charge of -3 ([tex]$N^{3-}$[/tex]).
2. Combine the ions to neutralize charges:
- For a neutral compound, the total positive charge must balance the total negative charge.
- If one [tex]$Mg^{2+}$[/tex] ion combines with one [tex]$N^{3-}$[/tex] ion, the total charge would be [tex]$+2 + (-3) = -1$[/tex], which is not neutral.
- To balance the charges, we need to find the smallest whole number ratio that allows the positive and negative charges to cancel out.
3. Determine the formula using the lowest whole number ratios:
- If we have three [tex]$Mg^{2+}$[/tex] ions, their total charge is [tex]$3 \times +2 = +6$[/tex].
- If we have two [tex]$N^{3-}$[/tex] ions, their total charge is [tex]$2 \times -3 = -6$[/tex].
- Combining three [tex]$Mg^{2+}$[/tex] ions with two [tex]$N^{3-}$[/tex] ions results in a neutral compound since [tex]$+6$[/tex] and [tex]$-6$[/tex] cancel each other out.
4. Write the empirical formula:
- The empirical formula, which shows the smallest whole number ratio of ions, is [tex]$Mg_3N_2$[/tex].
Therefore, the correct answer is:
A. [tex]$Mg_3 N_2$[/tex].
