Descaler by Vinegar: How Much Is Enough, and How Do You Know?
The tap water in a Nagano household is hard, and boiling it leaves a white crust inside the kettle. The crust is 2.0 g of almost pure calcium carbonate, CaCO₃. To remove it, a student plans to fill the kettle with 200 mL of household vinegar, which is 5.0% ethanoic (acetic) acid by mass with a density of 1.0 g/mL, and leave it overnight. The reaction is:
CaCO₃ + 2CH₃COOH → Ca(CH₃COO)₂ + H₂O + CO₂
Molar masses: CaCO₃ = 100 g/mol, CH₃COOH = 60 g/mol, CO₂ = 44 g/mol. A parent warns that vinegar attacks metal and that the kettle should not be left full overnight. After ten minutes the fizzing slows and stops, and the liquid still smells strongly of vinegar, although a ring of crust is still visible just above the liquid surface.
1. Calculate the minimum volume of vinegar needed to dissolve all 2.0 g of calcium carbonate, and judge whether 200 mL is a sensible amount.
Read the worked answer
Amount of CaCO₃ = 2.0 g ÷ 100 g/mol = 0.020 mol.
From the equation, 1 mol CaCO₃ needs 2 mol acid, so acid needed = 0.040 mol. Mass of acid = 0.040 × 60 = 2.4 g.
Vinegar is 5.0% acid by mass and has density 1.0 g/mL, so 1 mL contains 0.050 g of acid. Volume needed = 2.4 ÷ 0.050 = 48 mL (or: 0.040 mol ÷ 0.83 mol/L ≈ 0.048 L).
200 mL is roughly four times the minimum. That is not automatically wrong - excess acid makes the reaction finish and the bubbling stirs the liquid - but the excess is the reason the liquid still smells strongly of vinegar, and it is the reason the parent's warning matters: with nothing left to neutralise it, the remaining acid can attack exposed metal (especially aluminium or a chipped enamel patch) overnight.
2. The fizzing has stopped but a ring of crust remains above the liquid line. Explain what this shows about which reactant is in excess, and describe one quick test to confirm your explanation.
Read the worked answer
The reaction can only proceed where acid touches carbonate. The remaining crust is above the liquid surface, so the acid never reached it - it is not evidence that the acid ran out.
At the same time, the smell of vinegar and the fact that 200 mL contained about four times the acid needed both point to acid being in excess; the carbonate below the liquid line was the limiting reactant.
Test: add a small pinch of sodium hydrogencarbonate (baking soda) to the clear liquid. If it fizzes, acid is still present (CO₂ is produced); if nothing happens, the acid has been used up. Universal indicator paper turning red/orange (pH below about 3) gives the same information more quickly.
To clear the ring, the practical fix is mechanical - the liquid must be brought into contact with the crust, for example by filling the kettle above the ring or by repeated warm (not boiling) soaking, not simply by adding more acid.
3. Describe a test using a named solution that shows the clear liquid contains calcium ions, write the ionic equation, and explain why the test would fail if it were done before the fizzing stopped.
Read the worked answer
Test: add a few drops of sodium carbonate solution to a sample of the clear liquid. A white precipitate forms.
Ionic equation: Ca²⁺(aq) + CO₃²⁻(aq) → CaCO₃(s)
Reasoning: the calcium ion is a cation and needs a source of carbonate ions to re-form the insoluble solid; sodium carbonate supplies CO₃²⁻ and the sodium ions stay dissolved as spectator ions. A flame test on a clean wire would also give an orange-red colour, but the precipitation test is more specific here.
Why it fails before the fizzing stops: while acid is in excess and CO₂ is still being produced, the solution is strongly acidic. Any carbonate ions added are converted to CO₂ and water (CO₃²⁻ + 2H⁺ → H₂O + CO₂), so the carbonate concentration stays far too low for CaCO₃ to precipitate and no white solid appears even though Ca²⁺ is present. The gas must be allowed to escape and the excess acid used up first, or the solution partly neutralised.