The lattice energy of LiF calculated from Born-Lande equation – ...
From Born-Lande equation
because ‘n’ is always greater than one.
LiF = 1000 kJ mole
–1 ... (1)
MgO = x =
... (2)
x = 4000 kJ mole–1 Correct option is (d)
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The lattice energy of LiF calculated from Born-Lande equation – ...
Explanation:
Introduction:
The lattice energy is the energy released when gaseous ions combine to form an ionic solid. It can be calculated using the Born-Lande equation, which relates the lattice energy to the Madelung constant, interionic distances, and Born exponent.
Given:
- Lattice energy of LiF calculated from Born-Lande equation = 1000 kJ mol⁻¹
- Madelung constants, interionic distances, and Born exponents are the same for LiF and MgO
Explanation:
Step 1: Determine the relationship between the lattice energies of LiF and MgO.
Since the Madelung constants, interionic distances, and Born exponents are the same for both LiF and MgO, the only difference between the two compounds is the charges on the ions.
Step 2: Compare the charges on the ions in LiF and MgO.
LiF: Lithium ion (Li⁺) and fluoride ion (F⁻)
MgO: Magnesium ion (Mg²⁺) and oxide ion (O²⁻)
The charge on the ions affects the strength of the ionic bond and, consequently, the lattice energy. The higher the charge on the ions, the greater the lattice energy.
Step 3: Compare the charges on the ions in LiF and MgO.
The charge on the lithium ion (Li⁺) is +1, while the charge on the magnesium ion (Mg²⁺) is +2. Therefore, the charge on the magnesium ion is higher than that on the lithium ion.
Step 4: Determine the relationship between the lattice energies of LiF and MgO.
Since the charge on the magnesium ion is higher than that on the lithium ion, the lattice energy of MgO should be greater than that of LiF.
Step 5: Calculate the lattice energy of MgO.
Since the lattice energy of LiF calculated from the Born-Lande equation is 1000 kJ mol⁻¹, we can conclude that the lattice energy of MgO is greater than 1000 kJ mol⁻¹.
Step 6: Determine the correct answer.
The only option greater than 1000 kJ mol⁻¹ is option 'D', which is 4000 kJ mol⁻¹. Therefore, the correct answer is option 'D' (4000 kJ mol⁻¹).