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Difficulty: HardOxides of Carbon and Trioxocarbonate(IV) Salts

A water sample containing 0.010 mol0.010\text{ mol} of dissolved calcium hydrogentrioxocarbonate(IV), Ca(HCO3)2\text{Ca(HCO}_3)_2, responsible for temporary hardness, is boiled until complete precipitation of calcium trioxocarbonate(IV) occurs. The resulting solid residue is isolated and treated with an excess of dilute hydrochloric acid. What volume of carbon(IV) oxide gas, measured at room temperature and pressure (RTP, molar volume of gas =24.0 dm3 mol−1= 24.0\text{ dm}^3\text{ mol}^{-1}), is liberated during the acid treatment?

  1. 0.240 dm30.240\text{ dm}^3Answer
  2. B
    0.224 dm30.224\text{ dm}^3
  3. C
    0.480 dm30.480\text{ dm}^3
  4. D
    0.120 dm30.120\text{ dm}^3

Answer

The volume of carbon(IV) oxide gas liberated during the acid treatment is 0.240 dm30.240\text{ dm}^3.
Boiling 0.010 mol0.010\text{ mol} of Ca(HCO3)2\text{Ca(HCO}_3)_2 yields 0.010 mol0.010\text{ mol} of CaCO3\text{CaCO}_3 precipitate. Reacting this precipitate with excess dilute acid yields 0.010 mol0.010\text{ mol} of CO2\text{CO}_2 gas. At RTP, 0.010 mol×24.0 dm3 mol−1=0.240 dm30.010\text{ mol} \times 24.0\text{ dm}^3\text{ mol}^{-1} = 0.240\text{ dm}^3.

Step-by-Step Solution

1
Determine moles of CaCO3\text{CaCO}_3 precipitate formed during boiling.
The balanced thermal decomposition equation is Ca(HCO3)2(aq)→CaCO3(s)+H2O(l)+CO2(g)\text{Ca(HCO}_3)_2(aq) \rightarrow \text{CaCO}_3(s) + \text{H}_2\text{O}(l) + \text{CO}_2(g). Thus, 0.010 mol0.010\text{ mol} of Ca(HCO3)2\text{Ca(HCO}_3)_2 produces 0.010 mol0.010\text{ mol} of CaCO3\text{CaCO}_3.
Temporary hardness is removed by boiling, which decomposes hydrogentrioxocarbonate(IV) into insoluble trioxocarbonate(IV).
2
Determine moles of CO2\text{CO}_2 gas evolved from the reaction of CaCO3\text{CaCO}_3 with dilute HCl\text{HCl}.
The balanced chemical equation is CaCO3(s)+2HCl(aq)→CaCl2(aq)+H2O(l)+CO2(g)\text{CaCO}_3(s) + 2\text{HCl}(aq) \rightarrow \text{CaCl}_2(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g). 0.010 mol0.010\text{ mol} of CaCO3\text{CaCO}_3 reacts to release 0.010 mol0.010\text{ mol} of CO2\text{CO}_2.
Trioxocarbonate(IV) salts react with acids in a 1:1 mole ratio with respect to carbon(IV) oxide gas produced.
3
Calculate the volume of CO2\text{CO}_2 gas evolved at RTP.
\text{Volume} = 0.010\text{ mol} \times 24.0\text{ dm}^3\text{ mol}^{-1} = 0.240\text{ dm}^3$.
At room temperature and pressure, one mole of any gas occupies 24.0 dm324.0\text{ dm}^3.

Key Concept

Thermal decomposition of temporary water hardness salts and acid reactions of trioxocarbonate(IV) salts
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Topics

Oxides of Carbon and Trioxocarbonate(IV) Salts

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