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Q3.32(b):
Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (b) Magnesium and nitrogen

Solution :

Step 1: Identification of Electronic Configuration and Valency

To determine the stable binary compound, we must first establish the ground-state electronic configuration of each element and identify their preferred oxidation states based on the Octet Rule [Per the Octet Rule, atoms gain, lose, or share electrons to achieve a stable noble gas configuration].

  • Magnesium ($Mg$): Atomic number $Z = 12$. The electronic configuration is $1s^2 2s^2 2p^6 3s^2$.
    Magnesium belongs to Group 2 (Alkaline Earth Metals). It loses two valence electrons to achieve the stable configuration of Neon ($1s^2 2s^2 2p^6$), resulting in the $Mg^{2+}$ cation.
  • Nitrogen ($N$): Atomic number $Z = 7$. The electronic configuration is $1s^2 2s^2 2p^3$.
    Nitrogen belongs to Group 15 (Pnictogens). It requires three additional electrons to complete its valence shell (achieving an octet of $2s^2 2p^6$), resulting in the $N^{3-}$ anion (nitride ion).

Step 2: Determining the Stoichiometry (Criss-Cross Method)

For a binary ionic compound to be electrically neutral, the total positive charge from the cations must balance the total negative charge from the anions [Per the Principle of Electroneutrality].

Ion Charge
Magnesium Ion $+2$
Nitride Ion $-3$

Let the formula be $Mg_x N_y$. The condition for electrical neutrality is:

$x(+2) + y(-3) = 0$

By inspection, the smallest integer values that satisfy this equation are $x = 3$ and $y = 2$.

Step 3: Structural Representation of the Compound

The resulting compound is Magnesium Nitride ($Mg_3N_2$). Below is a conceptual representation of the ionic lattice arrangement:

Mg²⁺ Mg²⁺ Mg²⁺ N³⁻ N³⁻ Ionic Structure: Mg₃N₂

Step 4: Final Chemical Formulation

Combining the ions in the required stoichiometry:

$3Mg^{2+} + 2N^{3-} \rightarrow Mg_3N_2$

This compound, Magnesium Nitride, is a high-melting-point crystalline solid formed through ionic bonding [Per the Bohr-Kossel Theory of ionic bonding].

Final Solution: The stable binary compound is Magnesium Nitride, with the chemical formula $Mg_3N_2$.


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