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

A 10 dm310\text{ dm}^3 sample of well water contains 0.002 mol dm−30.002\text{ mol dm}^{-3} of dissolved calcium hydrogentrioxocarbonate(IV), Ca(HCO3)2\text{Ca(HCO}_3)_2, and 0.003 mol dm−30.003\text{ mol dm}^{-3} of dissolved calcium tetraoxosulfate(VI), CaSO4\text{CaSO}_4. A student boils the water sample thoroughly to soften it and filters off any precipitate formed. What is the molar concentration of Ca2+\text{Ca}^{2+} ions remaining in the filtered solution?

  1. 0.003 mol dm−30.003\text{ mol dm}^{-3}Answer
  2. B
    0.000 mol dm−30.000\text{ mol dm}^{-3}
  3. C
    0.002 mol dm−30.002\text{ mol dm}^{-3}
  4. D
    0.005 mol dm−30.005\text{ mol dm}^{-3}

Answer

0.003 mol dm−30.003\text{ mol dm}^{-3}
Boiling converts soluble Ca(HCO3)2\text{Ca(HCO}_3)_2 into insoluble CaCO3\text{CaCO}_3, which is removed by filtration. Since CaSO4\text{CaSO}_4 causes permanent hardness and does not decompose upon boiling, its concentration of 0.003 mol dm−30.003\text{ mol dm}^{-3} remains dissolved in the filtered water.

Step-by-Step Solution

1
Identify the types of water hardness present in the sample.
Dissolved Ca(HCO3)2\text{Ca(HCO}_3)_2 causes temporary hardness, while dissolved CaSO4\text{CaSO}_4 causes permanent hardness.
Hydrogentrioxocarbonates of calcium and magnesium cause temporary hardness, whereas tetraoxosulfates and chlorides cause permanent hardness.
2
Determine the chemical effect of boiling on temporary hardness.
Thermal decomposition occurs: Ca(HCO3)2(aq)→ΔCaCO3(s)+H2O(l)+CO2(g)\text{Ca(HCO}_3)_2\text{(aq)} \xrightarrow{\Delta} \text{CaCO}_3\text{(s)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)}.
Soluble calcium hydrogentrioxocarbonate(IV) decomposes on heating into insoluble calcium trioxocarbonate(IV), which precipitates out of solution.
3
Determine the chemical effect of boiling on permanent hardness.
CaSO4\text{CaSO}_4 remains dissolved and unaffected by boiling.
Permanent hardness cannot be removed by boiling because calcium tetraoxosulfate(VI) does not undergo thermal decomposition at 100∘C100^\circ\text{C}.
4
Calculate the residual concentration of Ca2+\text{Ca}^{2+} ions after filtration.
[Ca2+]=0.003 mol dm−3[\text{Ca}^{2+}] = 0.003\text{ mol dm}^{-3}.
All 0.002 mol dm−30.002\text{ mol dm}^{-3} of Ca2+\text{Ca}^{2+} from temporary hardness is precipitated and filtered out, leaving only the 0.003 mol dm−30.003\text{ mol dm}^{-3} of Ca2+\text{Ca}^{2+} contributed by CaSO4\text{CaSO}_4.

Key Concept

Distinction between temporary and permanent water hardness and their behavior upon thermal treatment (boiling).
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Topics

Hydrogen: Preparation, Properties, Isotopes, and Water Hardness

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