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 3.8×10−3M in Ca2+ and 1.1×10−3M in Mg2+ and that the average capacity of a washing machine is 24.5 gallons of water. 1gallon=3.785L If the detergent requires using 0.61 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.Express your answer in percent to two significant figures.

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Asked Oct 17, 2019
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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 3.8×10−3M in Ca2+ and 1.1×10−3M in Mg2+ and that the average capacity of a washing machine is 24.5 gallons of water. 1gallon=3.785L
 
If the detergent requires using 0.61 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.
Express your answer in percent to two significant figures.
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Expert Answer

Step 1

Given,

Concentration of Ca2+ = 3.8×10−3 M = 3.8×10−3 mol/L

Concentration of Mg2+ = 1.1×10−3 M = 1.1×10−3 mol/L

1gallon = 3.785L

The average capacity of a washing machine = 24.5 gallons

                                                                                                  = 24.5 × 3.785 L = 92.7325 L

Mass of detergent = 0.61 kg

                                          = 0.61 × 1000 g = 610 g

Step 2

Moles of Ca2+ and Mg2+ can be calculated as:

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Moles Molarity Volume in litre Moles Molarity x Volume in litre Moles of Ca2 = 3.8x10-3 mol/L x 92.7325 L = 0.3524 mol Moles of Ca2 = 1.1x103 mol/L x 92.7325 L = 0.1020 mol

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Step 3

The reaction of sodium carbonate with calcium and magnesium ions to give precipitate can be written as:

 Na2CO3 + Ca2+ → CaCO3 (s) + Na+

 Na2CO3 + Mg2+ → MgCO3 (s) + Na+

1 mole of Ca2+ is required to precipitate 1 mole of Na2CO3

1 mole of Mg2+ is required to precipita...

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Moles of sodium carbonate = 0.3524 mol 0.1020 mol Moles of sodium carbonate = 0.4544 mol

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