calculate the lattice enthalpy of potassium fluoride from the following data:
enthalpy of formation of K(g):
+89 kJ · mol−1
first ionization energy of K(g):
+418 kJ · mol−1
enthalpy of formation of F(g):
+79 kJ · mol−1
electron affinity of F(g):
+328 (�H = −328) kJ · mol−1
enthalpy of formation of KF(s):
−567 kJ · mol−1
Options:
1. 1481 kJ · mol−1
2. 904 kJ · mol−1
3. 497 kJ · mol−1
4. 347 kJ · mol−1
5. 825 kJ · mol−1
5. 825
The answer is 5) 825 kJ · mol−1
You want to use the Born-Haber cycle.
To calculate the lattice enthalpy of potassium fluoride (KF), we need to use the Born-Haber cycle, which is a series of steps that represent the formation of an ionic compound from its elements.
The Born-Haber cycle involves several key steps:
1. Formation of gaseous atoms: K(g) + 1/2 F2(g) → K(g) + F(g)
2. Formation of gaseous ions: K(g) → K+(g) + e- and F(g) + e- → F-(g)
3. Formation of solid KF: K+(g) + F-(g) → KF(s)
We can use the given enthalpy values to calculate the lattice enthalpy of KF.
First, we need to consider the formation of gaseous atoms. The enthalpy change for this step is the sum of the enthalpy of formation of K(g) and the enthalpy of formation of F(g):
ΔH1 = enthalpy of formation of K(g) + enthalpy of formation of F(g)
= +89 kJ · mol-1 + +79 kJ · mol-1
= +168 kJ · mol-1
Next, we consider the ionization energy of K, which represents the energy required to remove one electron from K(g) to form K+(g):
ΔH2 = first ionization energy of K(g)
= +418 kJ · mol-1
We also consider the electron affinity of F, which represents the energy change when one electron is added to F(g) to form F-(g):
ΔH3 = -electron affinity of F(g)
= -328 kJ · mol-1
Finally, we consider the enthalpy change for the formation of solid KF from gaseous ions:
ΔH4 = enthalpy of formation of KF(s)
= -567 kJ · mol-1
According to the Born-Haber cycle, the lattice enthalpy of KF is equal to the sum of these enthalpy changes:
Lattice enthalpy of KF = ΔH1 + ΔH2 + ΔH3 + ΔH4
Substituting the values we calculated:
Lattice enthalpy of KF = +168 kJ · mol-1 + +418 kJ · mol-1 -328 kJ · mol-1 -567 kJ · mol-1
= -309 kJ · mol-1
The correct option is 4. 347 kJ · mol-1.