First, let's balance the chemical equation:
Mg(OH)2(aq) + 2 HCl(aq) → MgCl2(s) + 2 H2O(l)
Now, let's calculate the molar masses of the compounds involved using the average atomic masses from the periodic table:
Molar mass of Mg(OH)2 = (1 x atomic mass of Mg) + (2 x atomic mass of O) + (2 x atomic mass of H)
= (1 x 24.31 g/mol) + (2 x 15.999 g/mol) + (2 x 1.008 g/mol)
= 58.33 g/mol
Molar mass of HCl = (1 x atomic mass of H) + (1 x atomic mass of Cl)
= (1 x 1.008 g/mol) + (1 x 35.453 g/mol)
= 36.46 g/mol
Molar mass of MgCl2 = (1 x atomic mass of Mg) + (2 x atomic mass of Cl)
= (1 x 24.31 g/mol) + (2 x 35.453 g/mol)
= 95.21 g/mol
Molar mass of H2O = (2 x atomic mass of H) + (1 x atomic mass of O)
= (2 x 1.008 g/mol) + (1 x 15.999 g/mol)
= 18.02 g/mol
Now, let's calculate the total mass on both sides of the equation:
Left side:
Mg(OH)2(aq) + 2 HCl(aq)
Molar mass of Mg(OH)2 = 58.33 g/mol
Molar mass of HCl = 2 x 36.46 g/mol = 72.92 g/mol
Total mass on left side = 58.33 g/mol + 72.92 g/mol = 131.25 g/mol
Right side:
MgCl2(s) + 2 H2O(l)
Molar mass of MgCl2 = 95.21 g/mol
Molar mass of H2O = 2 x 18.02 g/mol = 36.04 g/mol
Total mass on right side = 95.21 g/mol + 36.04 g/mol = 131.25 g/mol
As we can see, the total mass on both sides of the equation is equal (131.25 g/mol), which demonstrates that both sides of the equation have equal masses, satisfying the law of conservation of mass.