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JEE Advanced levelNumerical answerDifficulty 3 of 3el055

A hard water contains of and of per litre. Each divalent ion precipitates two stearate ions as the insoluble stearate. Use atomic masses Ca = 40, Mg = 24 and a molar mass of sodium stearate of . Calculate the mass of sodium stearate wasted as scum in treating of this water. Give the answer in grams, to the nearest integer.

Numerical answer type, answer in g, tolerance 0.5.

Answer: 551 g

Moles per litre: Ca2+ = 0.096/40 = 0.0024 mol and Mg2+ = 0.0288/24 = 0.0012 mol, total 0.0036 mol of divalent ions. Stearate needed = 2 x 0.0036 = 0.00720 mol per litre. For 250 L the mass is 0.00720 x 250 x 306 = 550.8 g, about 551 g.
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