Chemistry problem with molarity and ions

[ahhppull]

Homework Statement

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 1.1×10^−3 M in Mg2+ and that the average capacity of a washing machine is 19.0 gallons of water.

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.

Homework Equations

Molarity = moles/L
MM Ca = 40.08g
MM Mg = 24.31g
1 kg = .001 g
1 gal = 3.785L

The Attempt at a Solution

I was confused about this problem, but I used 2 of my tries and have 1 try left over. My first answer was 46& and my second answer was 98% (both of these are wrong)

My method's probably wrong, but here's what I did. I started by multiplying 19 gallons by 3.785 to get 71.915 liters. Then I multiplied the molarity of Ca and Mg each by 71.915 liters to get the grams of each. Then I multiplied the moles by the MM of each of the element. Then I added these two up and added it to .63Kkg (630g) and dived 630g by the total mass.

 

[Borek]

My method's probably wrong, but here's what I did. I started by multiplying 19 gallons by 3.785 to get 71.915 liters.

No idea if conversion factor is correct, but the idea is OK.

Then I multiplied the molarity of Ca and Mg each by 71.915 liters to get the grams of each.

I guess you mean moles, not grams.

Then I multiplied the moles by the MM of each of the element. Then I added these two up and added it to .63Kkg (630g) and dived 630g by the total mass.

You calculated total mass of calcium and magnesium dissolved. That's not what you are looking for - you need to add enough sodium carbonate to precipitate both metals.

I guess you are to ignore solubility product and assume reaction goes simply to completion. What reaction? That's what you need to solve the question.

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