Question

The energy required to convert all atoms presents in $1.2g$ magnesium to ${Mg}^{2+}$ ions if $IE$. and ${IE}_2$ of magnesium are $120$ kJ ${mol}^{-1}$ and $240$ kJ ${mol}^{-1}$ respectively:

• A. $18$ kJ
• B. $36$ kJ
• C. $360$ kJ
• D. $24$ kJ

Answer 1

The correct option is A $18$ kJ

Solution:- (A) 18 KJ

Molar mass of magnesium = 24

$\therefore$ No. of atoms present in 24 g Magnesium $=6.022\times {10}^{23}=N_A$

$\Rightarrow$ No. of atoms present in 1.2 g Magnesium $=\frac{N_A}{24}\times 1.2=\frac{N_A}{20}$

Total energy required to convert $N_A$ no. of atoms of magnesium to ${Mg}^{+2}={I.E.}_1+{I.E.}_2=120+240=360KJ{mol}^{-1}$

$\therefore$ Total energy required to convert $\frac{N_A}{20}$ no. of atoms of magnesium to ${Mg}^{+2}=\frac{360}{N_A}\times \frac{N_A}{20}=18KJ$

Hence, the energy required to convert all atoms present in 1.2g magnesium to ${Mg}^{2+}$ ions is 18KJ.