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Difficulty: HardHydrogen: Preparation, Properties, Isotopes, and Water Hardness

A water treatment facility needs to soften 100 dm3100\text{ dm}^3 of well water containing 0.005 mol dm−30.005\text{ mol dm}^{-3} of dissolved calcium hydrogentrioxocarbonate(IV), Ca(HCO3)2\text{Ca(HCO}_3)_2, using Clark's process. What is the minimum mass of calcium hydroxide, Ca(OH)2\text{Ca(OH)}_2, required to completely precipitate the calcium ions responsible for this temporary hardness? [Ca=40, O=16, H=1][\text{Ca} = 40,\text{ O} = 16,\text{ H} = 1]

  1. 37.0 g37.0\text{ g}Answer
  2. B
    74.0 g74.0\text{ g}
  3. C
    18.5 g18.5\text{ g}
  4. D
    81.0 g81.0\text{ g}

Answer

The minimum mass of calcium hydroxide required is 37.0 g37.0\text{ g}.
The correct answer of 37.0 g37.0\text{ g} is obtained by finding the moles of dissolved Ca(HCO3)2\text{Ca(HCO}_3)_2 (0.005 mol dm−3×100 dm3=0.5 mol0.005\text{ mol dm}^{-3} \times 100\text{ dm}^3 = 0.5\text{ mol}) and applying the 1:11:1 stoichiometric ratio from the reaction equation Ca(HCO3)2+Ca(OH)2→2CaCO3+2H2O\text{Ca(HCO}_3)_2 + \text{Ca(OH)}_2 \rightarrow 2\text{CaCO}_3 + 2\text{H}_2\text{O}. Multiplying 0.5 mol0.5\text{ mol} by the molar mass of Ca(OH)2\text{Ca(OH)}_2 (74 g mol−174\text{ g mol}^{-1}) yields 37.0 g37.0\text{ g}.

Step-by-Step Solution

1
Calculate the amount in moles of dissolved calcium hydrogentrioxocarbonate(IV) in the water sample.
Moles of Ca(HCO3)2=Concentration×Volume=0.005 mol dm−3×100 dm3=0.5 mol\text{Moles of Ca(HCO}_3)_2 = \text{Concentration} \times \text{Volume} = 0.005\text{ mol dm}^{-3} \times 100\text{ dm}^3 = 0.5\text{ mol}.
Determining the exact molar quantity of solute is the first step in stoichiometric calculations.
2
Write the balanced chemical equation for Clark's process (slaked lime softening).
Ca(HCO3)2(aq)+Ca(OH)2(aq)→2CaCO3(s)+2H2O(l)\text{Ca(HCO}_3)_2\text{(aq)} + \text{Ca(OH)}_2\text{(aq)} \rightarrow 2\text{CaCO}_3\text{(s)} + 2\text{H}_2\text{O(l)}. The mole ratio of Ca(HCO3)2\text{Ca(HCO}_3)_2 to Ca(OH)2\text{Ca(OH)}_2 is 1:11:1.
Clark's process uses calculated amounts of calcium hydroxide to convert soluble hydrogentrioxocarbonates into insoluble trioxocarbonate(IV) precipitates.
3
Calculate the molar mass of calcium hydroxide, Ca(OH)2\text{Ca(OH)}_2.
Molar mass=40+2(16+1)=74 g mol−1\text{Molar mass} = 40 + 2(16 + 1) = 74\text{ g mol}^{-1}.
Molar mass is required to convert moles of reagent into mass in grams.
4
Determine the required mass of Ca(OH)2\text{Ca(OH)}_2.
Mass=Moles×Molar mass=0.5 mol×74 g mol−1=37.0 g\text{Mass} = \text{Moles} \times \text{Molar mass} = 0.5\text{ mol} \times 74\text{ g mol}^{-1} = 37.0\text{ g}.
Multiplying the required moles by molar mass gives the required mass of slaked lime.

Key Concept

Removal of temporary water hardness using Clark's process (addition of calculated lime).
Estimated Time:2m 0s
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Topics

Hydrogen: Preparation, Properties, Isotopes, and Water Hardness

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