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Chemistry problem with molarity and ions

  1. Oct 16, 2010 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

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

    3. 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 heres 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.
     
  2. jcsd
  3. Oct 16, 2010 #2

    Borek

    User Avatar

    Staff: Mentor

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

    I guess you mean moles, not grams.

    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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