# 100 liters of water for softening needed 15.9 grams of Na_2CO_3. What was the hardness of water?

15.9 gr of $N {a}_{2} C {O}_{3}$ are 0.15 moles, therefore the 100 liters softened water contain 0.15 moles of $C a C {O}_{3}$, i.e. 1.5 millimolar Calcium ion, corresponding to 15 french degrees (moderately hard water)