Calculate the amount of energy required for the formation of one mole of MgSe bonds (not lattice energy). The radius of the magnesium ion is 0.65 A, and the radius of the selenide ion is 1.98 A. Note that 1 A=10^-10m.
E= 2120 kj/mol
To calculate the energy required for the formation of one mole of MgSe bonds, we will use the Born-Haber cycle and follow these steps:
Step 1: Calculate the energy required to ionize Mg.
The first step in the formation of MgSe is the ionization of Mg. The energy required to remove an electron from Mg is called the first ionization energy.
The first ionization energy of Mg is the energy required to remove one mole of electrons from one mole of gaseous Mg atoms. The first ionization energy of Mg is known to be 737 kJ/mol.
Step 2: Calculate the energy required to form the gaseous Mg+ ion.
The next step in the formation of MgSe is the formation of the gaseous Mg+ ion. This process requires energy equal to the electron affinity of Mg.
The electron affinity of Mg is the energy change when one mole of gaseous Mg atoms accepts one mole of electrons to form the gaseous Mg- ion, which then reacts to form the gaseous Mg+ ion. The electron affinity of Mg is known to be -50 kJ/mol.
Step 3: Calculate the energy required to remove an electron from Se.
The third step in the formation of MgSe is the ionization of Se. The energy required to remove an electron from Se is called the second ionization energy.
The second ionization energy of Se is the energy required to remove one mole of electrons from one mole of gaseous Se atoms. The second ionization energy of Se is known to be 4561 kJ/mol.
Step 4: Calculate the energy released when Mg and Se combine.
The last step in the formation of MgSe is the combination of Mg+ and Se- ions.
The energy released when Mg+ and Se- ions combine to form one mole of MgSe is called the energy of lattice formation or lattice energy. However, in this question, we are asked to calculate the energy required for the formation of MgSe bonds, not the lattice energy. Therefore, the energy released in this step is zero in this context.
Step 5: Calculate the overall energy required for the formation of MgSe.
To calculate the overall energy required for the formation of one mole of MgSe bonds, we add up the energies calculated in the previous steps:
Overall energy = First Ionization Energy of Mg + Electron Affinity of Mg + Second Ionization Energy of Se + Energy of Lattice Formation
Overall energy = 737 kJ/mol + (-50 kJ/mol) + 4561 kJ/mol + 0 kJ/mol
Overall energy = 4858 kJ/mol
Therefore, the overall energy required for the formation of one mole of MgSe bonds is 4858 kJ/mol.
To calculate the amount of energy required for the formation of one mole of MgSe bonds, we need to use the concept of the Born-Haber cycle. The Born-Haber cycle is an energy cycle that relates the lattice energy, ionization energy, electron affinity, and enthalpy of formation to calculate the energy of bond formation.
The energy required for bond formation can be calculated using the following equation:
ΔH°f = ΔH°sub + ΔH°ion + ΔH°ea + ΔH°LE
Where:
ΔH°f = Enthalpy of formation
ΔH°sub = Enthalpy of sublimation of metal
ΔH°ion = Ionization energy of metal
ΔH°ea = Electron affinity of non-metal
ΔH°LE = Lattice energy of compound
To calculate the energy required for the formation of one mole of MgSe bonds, we need to calculate each term in this equation. Let's go step by step:
1. Calculate the enthalpy of sublimation of magnesium (ΔH°sub):
The enthalpy of sublimation is the energy required to convert one mole of solid metal into the gaseous state. Given that the radius of the magnesium ion is 0.65 A, we can use the Born-Lande equation to calculate the enthalpy of sublimation.
ΔH°sub = (2.18 × 10^-18 J) [(Z+/r+) + 0.9 / d]
Where:
Z+ = charge on the cation
r+ = radius of the cation
d = distance between the cations in the solid state
In this case, Z+ = 2, r+ = 0.65 A, and d = 2r+ = 1.3 A.
Substituting the values and converting the units:
ΔH°sub = (2.18 × 10^-18 J) [(2/0.65) + 0.9 / 1.3]
= 4.92 × 10^-18 J
2. Calculate the ionization energy of magnesium (ΔH°ion):
The ionization energy of magnesium is the energy required to remove one mole of electrons from one mole of gaseous magnesium atoms.
The ionization energy of magnesium is 737 kJ/mol.
3. Calculate the electron affinity of selenium (ΔH°ea):
The electron affinity of selenium is the energy released when one mole of electrons is added to one mole of gaseous selenium atoms.
The electron affinity of selenium is -195 kJ/mol.
4. Calculate the lattice energy of magnesium selenide (ΔH°LE):
The lattice energy is the energy released when one mole of an ionic compound is formed from its constituent ions.
The lattice energy can be calculated using the Born-Mayer equation:
ΔH°LE = -k * (Z+ * Z-) / d
Where:
k = proportionality constant
Z+ = charge on the cation (magnesium = 2)
Z- = charge on the anion (selenium = -2)
d = distance between the ions
In this case, k = 2.31 × 10^-19 J*m and d = the sum of the ionic radii (0.65 + 1.98) × 10^-10 m.
Substituting the values:
ΔH°LE = -2.31 × 10^-19 J*m * (2 * (-2)) / ((0.65 + 1.98) × 10^-10 m)
= -5.64 × 10^-19 J
5. Calculate the enthalpy of formation (ΔH°f):
Finally, we can calculate the enthalpy of formation using the equation mentioned earlier.
ΔH°f = ΔH°sub + ΔH°ion + ΔH°ea + ΔH°LE
ΔH°f = 4.92 × 10^-18 J + 737 kJ/mol + (-195 kJ/mol) + (-5.64 × 10^-19 J)
Now, we need to convert kJ to J:
1 kJ = 1000 J
Converting the units and adding the values:
ΔH°f = (4.92 × 10^-18 J) + (737 × 10^3 J/mol) + (-195 × 10^3 J/mol) + (-5.64 × 10^-19 J)
= 3.78 × 10^5 J/mol
Therefore, the amount of energy required for the formation of one mole of MgSe bonds is 3.78 × 10^5 J/mol.