Sodium carbonate is often added to laundry detergents to soften hard water and m

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 3.8×10^3 M in Ca2+ and 1.0×10^3 M in Mg2+ and that the average capacity of a washing machine is 20.0 gallons of water.If 0.63 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?

Explanation / Answer

20 gallons = 75.71 L

moles of Mg2+ in 20 gallons water = molarity x volume = 1.0 x 10^-3 x 75.71 = 0.076 mols

moles of Ca2+ in 20 gallons water = 3.8 x 10-3 x 75.71 = 0.30 mols

Total moles of Mg2+ + Ca2+ = 0.076 + 0.30 = 0.376 mols

So moles of Na2CO3 required = 0.376 moles

mass of Na2CO3 required = 0.376 x 105.99 = 39.85 g

weight of detergent = 0.63 kg = 630 g

So, percentage of Na2CO3 required for complete precipitation of both ions = (39.85/630) x 100 = 6.32%

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