Question

ionization energy is usually expressed in units of kj/ mole 1000 j = 1 Kj

use the bohr equation to calculate the ionization energy of hydrogen in K j/ mole ? show your work

Answer 1

To calculate the ionization energy of hydrogen in kJ/ mole use the Bohr equation as follows:

E = -Rh/n^2

Here E= energy,

Rh = Rydberg's Constant (2.18 * 10^-18)

n = energy level.
Delta E = E final - E initial

In the calculation of ionization energy the final energy state is infinity because in ionization electron is far apart from the atom.

First calculate the ionization energy for one atom than one mole:

The ionization energy of one hydrogen atom,

Delta E = E (infinity) - E (1).

Delta E = -Rh / infinity - ( -Rh / 1^2)

= 0 + 2.18 * 10^-18 J

= 2.18 * 10^-18 J per H atom.

Now calculate the ionization energy per mole multiply this number by Avogadro's number (6.022 * 10^23).

Delta E = 2.18 * 10^-18 J per H atom *6.022 * 10^23 atoms / mol

                = 13.1* 10^5 J / mol

Now convert the unit of energy from J to kJ:

1000 j = 1 Kj

13.1* 10^5 J *1 Kj / 1000 j =1310 kJ

Hence the ionization energy of hydrogen in K j/ mole is 1310.