Question

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.

Answer 1

Here is the full 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 3.8×10−3M 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.

Answer:

7.90%

Explanation:

The equation for the reaction can be written as:

$Na_2CO_3+Ca^{2+} ---------> CaCO_3(s) +2Na^+$

$Na_2CO_3+Mg^{2+} ---------> MgCO_3(s) +2Na^+$

Molar mass of $Na_2CO_3$ = 106 g/mol

1.00 gallon of water = 3.785 L

∴ 24.5 gallons of water = 24.5 × 3.785

= 92.7325 L

mass precipitate = $[(3.8*10^{-3})+(1.1*10^{-3})]\frac{mol}{L} *92.7325*\frac{106g}{mol}$

mass precipitate = 48.162605

mass precipitate = 48.2 g

mass % = $\frac{mass ofprecipitate}{mass of detergent} *100%$%

mass % = $\frac{48.2g}{0.61kg}*\frac{1kg}{1000g}*100$%

mass % = 7.901639344

mass % = 7.90 %