determine what percentage (by mass) of the detergent should be sodium carbonate in order to completely...?

Question

If the detergent requires using 0.63 kg detergent per load of laundry, determine 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.
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 3.3×10^−3 in Ca+2 and 1.0×10^-3 M in Mg 2+ and that the average capacity of a washing machine is 20.0 gallons of water.

Answer 1

Na2CO3 ≈ 2*23 + 12 + 3*16 ≈ 106 g/mol
(4.3*10^-3 M)(106 g/mol) ≈ 0.4558 g/L
(100)(0.4558 g/L)(20 gal)(3.7854118 L/gal)/(630 g) ≈ 5.5%

Answer 2

Horrible problem with mixed units. You deserve better. But here's how, and why. You want to remove all the calcium ions and magnesium ions. So you need to find out how much of them you have, total moles. You need to know how many carbonates react with each calcium or magnesium ion (1, of course, in this case, but always ask yourself this question when going from one substance to another) You can then work out how many moles of carbonate you need, then how many grams, and what percentage that is of the total load (0.66 kg? That's almost 1 1/2 lb!) So, first convert 20.0 gallons to liters. Then use volume (L) x conc(M) = amount(moles) to find moles of Ca2+ and Mg2+ Then add up moles Ca2+ and Mg2+ Then use 1 mole M2+ = 1 mole Na2CO3 1 mole na2CO3 = [you work it out] g Na2CO3 g Na2CO3/(660 g detergent) x 100% = [your answer] And finally round down your answer to 2 sig figs, in case your teacher bothers with that sort of thing (I never did)