Question

Sodium carbonate is often added to laundry detergents to soften hard water and make the detergent more effective. Suppose that a particular detergent mixture is designed to soften hard water that is 3.6×10−3M in Ca2+ and 1.3×10−3M in Mg2+ and that the average capacity of a washing machine is 20.0 gallons of water.

If 0.66 kg detergent is required per load of laundry, what percentage (by mass) of the detergent should be sodium carbonate in order to completely precipitate all of the calcium and magnesium ions in an average load of laundry water?

Answer 1

Na2CO3 +   Ca2+    ------------> CaCO3 (s) + 2 Na+

Na2CO3 +   Mg2+    ------------> MgCO3 (s) + 2 Na+

molar mass of Na2CO3 = 106 g/mol

1.00 gallon of water = 3.785 L

20.0 gallons of water = 20 x 3.785 = 75.7 L

mass of precipitate = (3.6 x 10^-3 + 1.3 x 10^-3) x 106 x 75.7

                               = 39.32 g

mass % of precipitate = (39.32 / 660 ) x 100

mass % of precipitate = 5.96 %