Lattice energy of crystal

Chemistry Level 3

Calculate the electrostatic part of the lattice energy of sodium chloride, given that the inter-nuclear separation between Na + \text{Na}^{+} and Cl \text{Cl}^{-} ions, R 0 , R_{0}, is 3.6 × 1 0 10 3.6 \times 10^{-10} m and its Madelung constant M M is 1.7476. 1.7476.

187 kJ mol 1 187\text{ kJ mol}^{-1} 239 kJ mol 1 239\text{ kJ mol}^{-1} 674 kJ mol 1 674\text{ kJ mol}^{-1} 861 kJ mol 1 861\text{ kJ mol}^{-1}

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1 solution

Vilakshan Gupta
Jun 6, 2020

The electrostatic attractive energy for 1 1 mole of an ionic crystal is given by E = N o M z + z e 2 4 π ϵ o R o 2 E=-\dfrac{N_{o}Mz^{+}z^{-}e^2}{4\pi\epsilon_{o} R_{o}^2}

Where N o N_{o} denotes the Avogadro constant which is equal to 6.023 × 1 0 23 6.023\times 10^{23} , M M denotes the Madelung's constant , which depends on the geometry of the crystal, z + z^{+} and z z^{-} denotes the charges on cations and anions respectively , e e denotes the electronic charge which is 1.6 × 1 0 19 1.6\times 10^{-19} coulombs and finally R o R_{o} is the internuclear separation between the ions.

Plugging in all the values gives the answer as 674 kJ mol 1 \boxed{\approx 674~ \text{kJ mol}^{-1}} .

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