Question

The Ohio River has a hardness of approximately 122 mg/L as CaCO₃. If 67% of the hardness is due to Ca²⁺ and the rest is due to Mg²⁺, what are the concentrations of Ca²⁺ and Mg²⁺ in terms of mg of the cation/L (e.g. mg Ca²⁺/L; mg Mg²⁺/L)? (MWs:   Ca²⁺ = 40 g/mole;   Mg²⁺ = 24.3 g/mole;   CaCO₃ = 100 g/mole)

Answer 1

Mass Concentration of CaCO3 = 122 mg/L x 1g/1000mg

= 0.122 g/L

Molar concentration of CaCO3 = mass/molecular weight

= (0.122g/L) / (100g/mol)

= 0.00122 mol/L

CaCO3 gives 1 mol of Ca2+

Molar concentration of Ca2+ = 0.00122 mol/L

Total concentration due to cations = ( 0.00122 mol/L) / 0.67

= 0.00182 mol/L

Molar concentration of Mg2+ = 0.00182 - 0.00122

= 0.00060 mol/L

Mass Concentration of Ca2+ = molar concentration x molecular weight

= 0.00122 mol/L x 40 g/mol

= 0.0488 g/L x 1000mg/g

= 48.8 mg/L

Mass Concentration of Mg2+ = molar concentration x molecular weight

= 0.00060 mol/L x 24.3 g/mol

= 0.01458 g/L x 1000mg/g

= 14.58 mg/L