Question

Calculate the lattice energy for the reaction $L{{i}^{+}}(g)+C{{l}^{-}}(g)\to LiCl(s)$given that: $\Delta {{H}_{sub}}(Li)=160;\Delta {{H}_{diss}}(C{{l}_{2}})=244;IP(Li)=520;{{E}_{A}}(Cl)=-365\text{ } and \text{ } \Delta {{H}_{f}}(LiCl)=400$ (all in kJ $mol{{e}^{-1}}$)
A.-837
B.-959
C.-1567
D.-37

Answer 1

Hint: $\Delta {{H}_{f}}$ or molar heat of sublimation is the amount of energy that must be added to a mole of solid at constant pressure to turn it directly into a gas. $\Delta {{H}_{diss}}$ is the bond dissociation enthalpy which describes the amount of energy stored in a bond between atoms in a molecule.
So, to form LiCl the formation energy required is given by $\Delta {{H}_{f}}$ which equals the molar heat of sublimation of Li, bond dissociation energy in Cl, ionization potential of Li, electron affinity of Cl and internal energy or lattice energy.

Formula Used: $\Delta {{H}_{f}}=\Delta {{H}_{sub}}+\dfrac{1}{2}\Delta {{H}_{diss}}+IP+{{E}_{A}}+U$ where U is lattice energy

Complete Step By Step Solution: Lithium (Li) will ionize to form LiCl so ionization potential of Li is required. $\dfrac{1}{2}\Delta {{H}_{diss}}$ is required, because we need only one Cl atom in the equation so it is halved. Electron affinity is taken as negative as it is the amount of energy released when an electron is attached to a neutral atom.
So, using the above formula $\Delta {{H}_{f}}=\Delta {{H}_{sub}}+\dfrac{1}{2}\Delta {{H}_{diss}}+IP+{{E}_{A}}+U$ we get,
$\begin {align}
  & -400=160+\dfrac{1}{2}(244)+520-365+U \\
 & -400=160+122+520-365+U \\
 & -400=282+520-365+U \\
 & -400=282+155+U \\
 & -400=437+U \\
 & U=-400-437 \\
 & U=-837 kJ mol{{e}^{-1}} \\
\end{align}$

So, the correct option is (A)


Additional Information:
A particular set of equations known as a Born-Haber cycle demonstrates how chemists are able to use the first law of thermodynamics—that the energy of the universe is conserved in any chemical or physical change—to find an unknown energy value that is difficult or impossible to measure experimentally. Some energy quantities, such as the lattice energy of a mineral or the electron affinity of an atom, can be difficult to measure in the lab. Examining a Born-Haber cycle we see that there is more than one path to the formation of a substance in a particular state, and that if we use consistent definitions, an energy value that we seek can be calculated from energy values that we already know.
Standard enthalpy of formation: The change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states.
 Ionization potential: The energy required to remove the outermost electron of each atom in one mole of an element in its gaseous state.
Enthalpy of sublimation: The energy needed to transform one mole of a substance from the solid to the gaseous state.
Bond Dissociation Energy: The energy required to break one mole of bonds between two atoms.


Note: The energy which is released is taken as negative as electron affinity is the energy released when an electron is added to the atom to form a negative ion. The enthalpy of formation tells whether the formation reaction releases heat (negative) or requires heat (positive). Reactions where two species will combine into one typically releases heat to counteract the loss in entropy. This is the reason why in the above calculation enthalpy of formation is taken as negative as Li and Cl are combining to form LiCl.