Calculate the total ionization energy for the formation of C4+ from a gaseous C atom.

Calculate the total ionization energy for the formation of C⁴⁺ from a gaseous C atom.

Expert Solution

Ionization energy for formation of C4+ ion from gaseous C atom = ionization energy to remove the 1st electron + ionization energy required to remove second electron

So,

ionization energy required to remove the 1st electron from gaseous C atom to form C5+ ion (IE1) is given as

deltaE = - 2.18 x 10^-18 * Z^2 [ 1/nf^2 - 1/ni^2 ] for 1st ionization energy nf = infinity and ni = 1

deltaE = - 2.18 x 10^-18 * (6)^2 * [ 1/(infinity)^2 - 1/1]

deltaE = -2.18 x 10^-18 * 36 * (-1) Since 1 / infinity = 0

deltaE = 7.85 x 10^-17 J

Energy per mol = 6.022 x 10^23 mol^-1 * 7.85 x 10^-17 J = 4.727 x 10^5 J/mol = 472.7 kJ/mol

Ionization energy required to remove the 1st electron from gaseous C atom to form C4+ ion (IE2) is given as

deltaE = - 2.18 x 10^-18 * Z^2 * [1/nf^2 - 1/ni^2 ]

deltaE = - 2.18 x 10^-18 * 36 * [ 0 - 1/4] ( ni = 2 and nf = infinity)

deltaE = 1.962 x 10^-17 J

Energy per mol = 6.022 x 10^23 * 1.962 x 10^-17 J/mol = 1.182 x 10^5 J/mol = 118.2 kJ/mol

So total ionization energy = IE1 + IE2 = (472.7 + 118.2) kJ/mol = 590.9 kJ/mol

queen_honey_blossom answered 2 months ago

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