Hard water often contains dissolved ca2+ and mg2+ ions. one way to soften water is to add phosphates. the phosphate ion forms insoluble precipitates with calcium and magnesium ions, removing them from solution. suppose that a solution is 5.0×10−2 m in calcium chloride and 8.5×10−2 m in magnesium nitrate. what mass of sodium phosphate would have to be added to 2.0 l of this solution to completely eliminate the hard water ions? assume complete reaction.

30 g

Explanation:

For CaCl₂

3CaCl₂ + 2Na₃PO₄ ⟶ Ca₃(PO₄)₂ + 6NaCl

Moles of CaCl₂ = c×V = 5.0 × 10⁻² × 2.0 = 0.100 mol

Moles of Na₃PO₄ = 0.100 × 2/3 = 0.0667 mol

Mass of Na₃PO₄ = 0.0667 × 163.94 = 10.9 g

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For Mg(NO₃)₂

3Mg(NO₃)₂  + 2Na₃PO₄ ⟶ Mg₃(PO₄)₂ + 6NaCl

Moles of Mg(NO₃)₃ = c×V = 8.5 × 10⁻² × 2.0 = 0.170 mol

Moles of Na₃PO₄ = 0.170 × 2/3 = 0.113 mol

Mass of Na₃PO₄ = 0.113 × 163.94 = 1 g

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Total mass of Na₃PO₄ = 10.9 + 18.6 = 29.5 g

To two significant figures, mass = 30 g

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).