(Solved): Sodium carbonate is often added to laundry detergents to soften hard water and make the detergent ...

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 \( 3.8 \times 10^{-3} M \) in \( \mathrm{Ca}^{2+} \) and \( 1.1 \times 10^{-3} M \) in \( \mathrm{Mg}^{2+} \) and that the average capacity of a washing machine is \( 17.5 \) gallons of water. 1 gallon \( =3.785 \mathrm{~L} \) Part A If the detergent requires using \( 0.68 \mathrm{~kg} \) 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.