Question

Lattice energy of $NaCl$ is ${}^{\prime }{X}^{\prime }$. If the ionic size of $A^{+2}$ is equal to that of $N{a}^{+}$ and $B^{-2}$ is equal to $C{l}^{-}$, then lattice energy associated with the crystal $AB$ is:

• A. $X$
• B. $2X$
• C. $4X$
• D. $8X$

Answer 1

The correct option is C $4X$

The lattice energy of crystal $AB$ is $4X$.

Lattice energy is the energy associated to the crystal lattice of a compound.

Mathematically,

$E_{lattice}=k\frac{Q_1{Q}_2}{d}$

where, $k=$ proportionality constant

$Q_1$ and $Q_2$ are the charges on the ions in coulombs.

$d=$ distance between the ion charges.

Lattice energy of $NaCl=X$

$E_{lattice}\left(NaCl\right)=\frac{Q_1{Q}_2}{d}=X$

As the ionic size remains same when $AB$ crystal is formed, d remains same

Lattice energy of $AB$,

$E_{lattice}\left(AB\right)=\frac{\left(2Q_1\right)\left(2Q_2\right)}{d}$

$E_{lattice}\left(AB\right)=4\left(\frac{Q_1{Q}_2}{d}\right)=4X$

The lattice energy of crystal $AB$ is $4X$.