Step 1

**$\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{}\overline{)\mathbf{ga}}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{3}\mathbf{.}\mathbf{785}\mathbf{}\mathbf{L}}{\mathbf{1}\mathbf{}\overline{)\mathbf{ga}}}$= 75.7 L**

Step 2

$\mathbf{75}\mathbf{.}\mathbf{7}\mathbf{}\mathbf{L}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{3}\mathbf{.}\mathbf{6}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\overline{)\mathbf{mol}\mathbf{}{\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}}}{\mathbf{1}\mathbf{}\overline{)\mathbf{L}}}$** = 0.27252 mol Ca ^{2+}**

$\mathbf{75}\mathbf{.}\mathbf{7}\mathbf{}\mathbf{L}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\overline{)\mathbf{mol}\mathbf{}{\mathbf{Mg}}^{\mathbf{2}\mathbf{+}}}}{\mathbf{1}\mathbf{}\overline{)\mathbf{L}}}$** = 0.09084 mol Mg ^{2+}**

**Total mol = 0.27252 mol + 0.09084 mol = 0.36336 mol**

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 3.6×10^{−3} M in Ca^{2 + } and 1.2×10^{−3} M in Mg^{2 + } and that the average capacity of a washing machine is 20.0 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.

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