Answer:
A mole of Mg = 1/24
These many moles of Mg is converted to Mg+ and Mg2+. The energy consumed for Mg to Mg+ and Mg2+ conversation is
740 + 1450 =2190.
Let us consider x grams of Mg+ ions and y grams of Mg2+ ions.
x + y =1 (Total mass in 1 gram)
Moles of Mg+ ions = x/24
Moles of Mg2+ ions = y/24
Energy absorbed for generating Mg+ ions = x/24 × 740
Energy absorbed for forming Mg2+ ions= y/24 × 2190
Total energy absorbed (E) = x/24 × 740 + y/24 × 2190
50 = x/24 × 740 + y/24 × 2190
1200 = 740x + 2190y
120 = 74x + 219y
since x + y =1
x = 1 – y
120 = 74(1 – y) + 219y
120 = 74 – 74y + 219y
120 = 145y + 74
46 = 145y
y = 0.3172
The mass of Mg2+ ions is 0.3172g
% of Mg2+ ions = 0.31721 × 100 = 31.72
Also, % of Mg+ ions =100 – 31.72 = 68.28.