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 3.4×103 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.f 0.67 kg detergent is required per load of laundry, 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 using two significant figures.

Explanation / Answer

The reactions between sodium carbonate, Na2CO3, and Ca^2+ and Mg^2+ are:
Na2CO3 + Ca(2+) ==> CaCO3(s) + 2Na+
Na2CO3 + Mg(2+) ==> MgCO3(s) + 2Na+

Now calculate the number of moles of Ca2+ and Mg2+:

Volume of water :

1 gallon = 3.78541 L

19.0 Gallons = 71.92 L

Moles of Ca 2+ = molarity * volume in L

=3.4×103 M * 71.92 l

= 0.245 mol

Moles of Mg 2+ = molarity * volume in L

=1.1×103 M * 71.92 l

= 0.079 mol

Total number of moles of sodium carbonate :

0.079+0.245= 0.324 mol sodium carbonate

Now calculate the amount sodium carbonate:

The molar mass of Na2CO3 is: 105.99 g/mol,

0.324 mol sodium carbonate*105.99 g/mol

= 35.6 g

Amount of detergent = 0.67 kg or 670 g

Percentage of sodium carbonate = 35.6 g/670 g*100

= 5.31% sodium carbonate

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