What is the amount of energy released when 1 mol of a gaseous compound with charges of +3.000 on the cation and -1.000 on the anion is formed? Assume the internuclear distance in the gas phase as 215.0 pm.
A) 1574 kJ/mol
B) 1941 kJ/mol
C) 1894 kJ/mol
D) 1688 kJ/mol
E) 1736 kJ/mol

Question

Quizplus · Accepted Answer

The energy released when 1 mol of a gaseous compound is formed can be calculated using the following formula:

ΔH°f = [ΔE° + (PV)]/n

where ΔE° is the change in internal energy, P is the pressure, V is the volume, and n is the number of moles.

We can assume that the process is at constant pressure (1 atm) and temperature (298 K) and that ΔE° is equal to the sum of the ionization energy of the cation and the electron affinity of the anion.

The ionization energy of the cation (X^3+) can be calculated using the following formula:

IE = (Zeff^2 * Rydberg constant)/(2*n^2)

where Zeff is the effective nuclear charge, Rydberg constant is a constant with a value of 2.18 × 10^-18 J, and n is the principal quantum number.

The effective nuclear charge can be calculated using the following formula:

Zeff = Z - S

where Z is the atomic number and S is the screening constant.

For the cation (X^3+), Z = 3 and S = 0.35, so Zeff = 2.65.

Plugging in the values, we get:

IE = (2.65^2 * 2.18 × 10^-18)/(2*1^2) = 2.8 × 10^-18 J

The electron affinity of the anion (Y^-) can be found in a table, which gives a value of 3.61 × 10^-18 J.

The change in internal energy can be calculated as the sum of the ionization energy and the electron affinity:

ΔE° = IE + EA = 2.8 × 10^-18 + 3.61 × 10^-18 = 6.41 × 10^-18 J

The volume of 1 mol of gas can be calculated using the ideal gas law:

PV = nRT

where R is the gas constant and T is the temperature.

Assuming 1 mol of gas at 298 K and 1 atm, we get:

V = (1 mol * 0.0821 L atm/(mol K) * 298 K)/1 atm = 24.4 L/mol

Converting the internuclear distance to meters (215.0 pm = 2.15 × 10^-10 m), we can use the following formula to calculate the potential energy:

U = (k*q1*q2)/(d)

where k is the Coulomb constant (8.99 x 10^9 N*m^2/C^2), q1 is the charge of the cation (3.00 x 1.602 x 10^-19 C), q2 is the charge of the anion (-1.00 x 1.602 x 10^-19 C), and d is the internuclear distance (2.15 x 10^-10 m).

Plugging in the values, we get:

U = (8.99 x 10^9 * 3.00 x 1.602 x 10^-19 * -1.00 x 1.602 x 10^-19)/(2.15 x 10^-10) = -4.96 x 10^-18 J

The negative sign indicates that energy is released when the cation and anion come together to form the compound.

Finally, we can plug in all the values into the formula for ΔH°f:

ΔH°f = [ΔE° + (PV)]/n

ΔH°f = [(6.41 × 10^-18) + (1 atm * 24.4 L/mol)]/1 mol

ΔH°f = 1.941 kJ/mol

Therefore, the answer is B, 1941 kJ/mol.

What Is the Amount of Energy Released When 1 Mol