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 3.8×103 M in Ca2+ and 1.1×103 M in Mg2+ and that the average capacity of a washing machine is 19.0 gallons of water.

If the detergent requires using 0.66 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.

Explanation / Answer

M = 3.8*10^-3 Ca+2

M = 1.1*10^-3 Mg+2

Ca2+ CO3-2 --> CaCO3(s)

Mg+2 + CO3-2 --> MgCO3(s)

V = 19 gallons = 71.92 liters (per load)

m = 0.66 kg of detergent per load

a) % of Na2CO3 in order to precipitate all Ca+2 and MG+2

the total amount of CO3-2 needed is:

mol of X+2 = M1*V + M2*V = (3.8*10^-3 + 1.1*10^-3)71.92 = 0.352 mol of X+2

Since ratio is

1 X+2 : 1 CO3-2 then

we need 0.352 mol of CO3-2

that is

1 mol of Na2CO3 : 1 mol of CO3-2

0.352 mol of Na2CO3 are needed

mass = Mol*MW = 105.9888*0.352 = 37.31 grams of Na2CO3 needed

% mass = 37.31 grams / 660 grams of detergnet *100% = 5.65% is needed

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