Question

Use coulomb's law to calculate the ionization energy in kj/mol of an atom composed of a proton and an electron separated by 185.00 pm .

Answer 1

Answer:

Energy = 752.88 kJ/mol

Explanation:

The force of attraction can be written as:

$F=\frac {K\times |Z_{cation}|e\times |Z_{anion}|e}{r^2}$

Integrating to find the expression for energy. We get that:-

$E=\frac {K\times |Z_{cation}|e\times |Z_{anion}|e}{r}$

Where,  

K is the Coulomb's constant having value 9×10⁹ N. m²/C²

$Z_{cation}$  is the charge on the cation

$Z_{anion}$  is the charge on the anion

e is electronic charge = Charge of the electron = Charge on proton $1.602\times 10^{-19}\ C$

r is the distance between the cation and anion  = 185.00 pm

Also, 1 pm = 10⁻¹² m

So, r = 185×10⁻¹² m

$Z_{cation}=Z_{anion}=1$

Applying in the equation,  

$E=\frac{9\times 10^9\times 1.6\times 10^{-19}\times 1.6\times 10^{-19}}{185\times 10^{-12}}=1.25\times 10^{-18}\ J/atom$

Also,

1 atom = $6.023\times 10^{23}\ mole^{-1}$

So,

Energy = $1.25\times 10^{-18}\times 6.023\times 10^{23}\ J/mole=752875\ J/mole$

Also, 1 J = 0.001 kJ

So, Energy = 752.88 kJ/mol

Answer 2

Coulomb's law mathematically is:
F = kQ₁Q₂/r²
we integrate this with respect to distance to obtain the expression for energy:
E = kQ₁Q₂/r; where k is the Coulomb's constant = 9 x 10⁹; Q are the charges, r is the seperation
Charge on proton = charge on electron = 1.6 x 10⁻¹⁹ C
E = (9 x 10⁹ x 1.6 x 10⁻¹⁹ x 1.6 x 10⁻¹⁹) / (185 x 10⁻¹²)
E = 1.24 x 10⁻¹⁸ Joules per proton/electron pair
Number of pairs in one mole = 6.02 x 10²³
Energy = 6.02 x 10²³ x 1.24 x 10⁻¹⁸
= 746.5 kJ