Determining Calcium Ion Concentration in Water by Complexometric Titration Chemistry Tutorial

Key Concepts

• Calcium and magnesium ions dissolved in water cause water hardness.
• Ethylenediaminetetraacetic acid (EDTA), shown on the right in its deprotonated form, is commonly used in a titration to determine the concentration of Ca²⁺ and Mg²⁺ ions in water because both ions form complexes with EDTA.
• In order to determine the concentration of Ca²⁺ in water, the Mg²⁺ must be removed first, usually by precipitation.
• The titration with EDTA then determines the concentration of Ca²⁺ remaining in the water.
• The complex formed between Ca²⁺ and EDTA is colourless and soluble, so a suitable indicator must be used to show the endpoint of the titration.
• The concentration of Ca²⁺ in water can then be calculated.

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Precipitating the Magnesium Ions.

Ksp magnesium calcium carbonate 3.5 x 10-8 2.8 x 10-9 oxalate 1.0 x 10-8 4.0 x 10-9 fluoride 6.5 x 10-9 4.0 x 10-11 hydroxide 1.8 x 10-11 5.0 x 10-6 Magnesium carbonate, oxalate and fluoride are all more soluble than calcium carbonate, oxalate and fluoride. Magnesium hydroxide, however, is less soluble than calcium hydroxide. It should be possible to precipitate magnesium hydroxide out of the water without precipitating out all the calcium as calcium hydroxide.

Mg(OH)2 Mg2+(aq) + 2OH-(aq) Ksp(Mg(OH)2) =[Mg2+][OH-]2 1.8 x 10-11 = [Mg2+][OH-]2 Let y = [Mg2+] at equilibrium Then [OH-] = 2y at equilibrium So 1.8 x 10-11 = y x (2y)2 1.8 x 10-11 = y x 4y2 1.8 x 10-11 = 4y3 4.5 x 10-12 = y3 y = 1.65 x 10-4 [Mg2+] = 1.65 x 10-4 mol L-1 [OH-] = 2 x 1.65 x 10-4 = 3.30 x 10-4 mol L-1 Ca(OH)2 Ca2+(aq) + 2OH-(aq) Ksp(Ca(OH)2) =[Ca2+][OH-]2 5.0 x 10-6 = [Ca2+][OH-]2 Let y = [Ca2+] at equilibrium Then [OH-] = 2y at equilibrium So 5.0 x 10-6 = y x (2y)2 5.0 x 10-6 = y x 4y2 5.0 x 10-6 = 4y3 1.25 x 10-6 = y3 y = 1.08 x 10-2 [Ca2+] = 1.08 x 10-2 mol L-1 [OH-] = 2 x 1.08 x 10-2 = 2.16 x 10-2 mol L-1 Under the same conditions, the concentration of hydroxide ions in the calcium hydroxide solution is about 100 times more than the concentration of hydroxide ions in the magnesium hydroxide solution. Calcium hydroxide is more soluble than magnesium hydroxide under the same conditions.

An aqueous solution of sodium hydroxide can be used to precipitate out the magnesium hydroxide.

The Titration

• The burettte is filled with an EDTA solution of known concentration.

  Concentrations of 0.010 mol L^-1 are commonly used.

• A suitable aliquot of hard water is placed in the conical flask.

  For example, a 50.0 mL transfer pipette can be used to put the water sample into the flask.

• A drop of a suitable indicator is added to the water sample.

  For example, Patton and Reeder's Indicator (also abbreviated to HHSNNA)
  Patton and Reeder's Indicator will be red in the hard water sample and blue when excess EDTA has been added.

• EDTA is added from the burette to the conical flask until the indicator changes colour, indicating that the endpoint has been reached.
• The volume of EDTA used is recorded.
• The steps above are repeated until three concordant titres are obtained, that is, three volumes of EDTA that agree to within a drop, or 0.05 mL, of each other.
• The average of these concordant titres is then used to calculate the concentration of calcium ions in the hard water.

The Calculations

Ca²⁺ + H₂EDTA^2- → CaEDTA^2- + 2H⁺

The stoichiometric (mole) ratio of Ca²⁺ : EDTA is 1 : 1

That is, at the equivalence point, the moles of EDTA added to the water equals the moles of Ca²⁺ originally present in the water
At the equivalence point: moles Ca²⁺ = moles EDTA

moles of EDTA = EDTA concentration (mol L^-1) x volume EDTA used (L)

volume used = average of the concordant titres (L)

moles Ca²⁺ in hard water sample = moles EDTA used = EDTA concentration (mol L^-1) x volume EDTA used (L)

concentration (molarity) of Ca²⁺ in hard water = moles Ca²⁺ ÷ volume of water sample used (L)

[Ca²⁺] = (EDTA concentration (mol L^-1) x volume EDTA used (L)) ÷ volume water sample (L)

Worked Example

Calculate the concentration of calcium ions in the hard water sample.

• Calculate the average titre of EDTA:

  average titre = (8.76 + 8.80 + 8.78) ÷ 3 = 8.78 mL = 8.78 x 10^-3 L

• Calculate the moles of EDTA in the average titre:

  moles(EDTA) = concentration (mol L^-1) x volume (L) = 0.010 x 8.78 x 10^-3 = 8.78 x 10^-5 mol

• Calculate moles of Ca²⁺ present in the 50.0 mL water sample:

  Ca²⁺ + H₂EDTA^2- → CaEDTA^2- + 2H⁺
  moles Ca²⁺ = moles EDTA = 8.78 x 10^-5 mol

• Calculate concentration (molarity) of calcium ions in the water:

  molarity(Ca²⁺) = moles ÷ volume (L) = 8.78 x 10^-5 ÷ 50.0 x 10^-3 = 1.76 x 10^-3 mol L^-1

• Convert the concentration in mol L^-1 to a concentration in mg L^-1:

  1 L of water contains 1.76 x 10^-3 moles Ca²⁺
  mass Ca²⁺ = moles x molar mass = 1.76 x 10^-3 x 40.08 = 7.05 x 10^-2 g
  convert mass in grams to mass in mg by multiplying by 1000:
  7.05 x 10^-2 g = 7.05 x 10^-2 x 1000 mg/g = 70.5 mg
  concentration of Ca²⁺ = 70.5 mg L^-1