5. Titration

• Titration


  A quantitative procedure based on measuring the amount of a reagent of known concentration that is consumed by an analyte in a chemical or electrochemical reaction
• Types of titration

  • Volumetric titration
  • Gravimetric titration
  • Coulometric titration
• Standard solution (or standard titrant)


  A reagent of known concentration that is used to carry out a volumetric titration
• Volumetric titration process

  1. Slowly adding a standard solution from a buret or other liquid-dispensing device to a solution of the analyte

  2. Determining the volume or mass of reagent needed to complete the titration from the difference between the initial and final readings
• Back-titration


  A process in which the excess of a standard solution used to consume an analyte is determined by titration with a second standard solution
• Equivalence point


  The theoretical point reached when the amount of added titrant is chemically equivalent to the amount of analyte in the sample
• End point


  The point in a titration when a physical change occurs that is associated with the condition of chemical equivalence
• Titration error


  The difference in volume or mass between the equivalence point and the end point
• Indicators used in titrations

  • Appearance or disappearance of a color
  • Change in color
  • Appearance or disappearance of turbidity
• Instruments used to detect end points

  • Respond to properties of the solution that change in a characteristic way during the titration
  • Examples: colorimeters, turbidimeters, spectrophotometers, temperature monitors, refractometers, voltmeters, current meters, conductivity meters
• Typical titration setup and process

  1. Buret filled with titrant solution

  2. Solution to be titrated placed in flask with indicator added

  3. Titrant added to flask with swirling until indicator color persists

  4. Smaller portions added as end point approached

  5. End point reached when less than half a drop causes indicator color change
• Titration

  1. Add titrant to flask with swirling until indicator color persists

  2. In initial region, titrant may be added rapidly

  3. As end point is approached, add increasingly smaller portions

  4. At end point, less than half a drop of titrant should cause indicator to change color
• End point


  Achieved when the barely perceptible pink color of phenolphthalein persists
• Titration color changes

  • Red prior to end point due to Mg2+ indicator complex
  • Purple at end point
  • Blue after end point due to uncomplexed indicator
• Primary standard

  Ultrapure compound that serves as reference material for titration or quantitative analysis
• Secondary standard


  Compound whose purity has been determined by chemical analysis, used as working standard material
• Requirements for primary standard

  • High purity with established purity confirmation methods
  • Atmospheric stability
  • Absence of hydrate water
  • Modest cost
  • Reasonable solubility in titration medium
  • Reasonably large molar mass
• Requirements for ideal standard solution

  • Sufficiently stable so concentration only needs to be determined once
  • Reacts rapidly with analyte
  • Reacts more or less completely with analyte
  • Undergoes selective reaction with analyte
• Titration curve

  Plot of some function of analyte or titrant concentration vs titrant volume, defines indicator/instrument properties and allows estimating titration error
• Types of titration curves

  • Sigmoidal curve (important observations confined to small region around equivalence point)
  • Linear segment curve (measurements made on both sides of, but well away from, equivalence point)
• Instrument signal is proportional to concentration of analyte or titrant
• Equivalence point


  Point where stoichiometric amounts of titrant and analyte have reacted
• Molar concentration


  Number of moles of reagent per liter of solution
• Normal concentration


  Number of equivalents of reagent per liter of solution
• Calculating moles and concentrations

  1. Amount (mol) = mass (g) / molar mass (g/mol)

  2. Amount (mmol) = mass (mg) / millimolar mass (mg/mmol)

  3. Amount (mol) = volume (L) * concentration (mol/L)

  4. Amount (mmol) = volume (mL) * concentration (mmol/L)
• AgNO3

  Silver nitrate
• To obtain the mass of AgNO3

  1. Rearrange Equation 13-2

  2. Multiply 0.1000 mol AgNO3 by 169.87 g AgNO3/mol AgNO3

  3. Result is 16.987 g AgNO3
• The solution should be prepared by dissolving 16.987 g of AgNO3 in water and diluting to the mark in a 2.000 L volumetric flask
• Standard 0.0100 M solution of Na+

  Required to calibrate an ion-selective electrode method to determine sodium
• Prepare 500 mL of 0.0100 M Na+ solution from primary standard Na2CO3

  1. Compute the mass of Na2CO3 needed to produce 0.0100 mmol Na+

  2. Since Na2CO3 dissociates to give two Na+ ions, the mmol of Na2CO3 needed is 0.0100 mmol Na+ / 2
• Prepare 50.0-mL portions of 0.00500 M, 0.00200 M, and 0.00100 M Na+ solutions


  The number of millimoles of Na+ taken from the concentrated solution must equal the number in the dilute solutions
• Titrate 50.00-mL of HCl solution with 0.01963 M Ba(OH)2

  1. 1 mmol of Ba(OH)2 reacts with 2 mmol of HCl

  2. Calculate the molar concentration of the HCl
• Titrate 0.2121 g of pure Na2C2O4 with KMnO4


  1. 2 mmol of KMnO4 react with 5 mmol of C2O4^2-

  2. Calculate the molar concentration of the KMnO4 solution
• Titrate Fe2+ from a 0.8040-g iron ore sample with 0.02242 M KMnO4

  1. 5 mmol of Fe2+ react with 1 mmol of KMnO4

  2. Calculate the % Fe and % Fe3O4 in the sample
• Precipitate PO4^3- from a 4.258-g plant food sample as Ag3PO4 using 50.00 mL of 0.0820 M AgNO3


  1. Back-titrate the excess AgNO3 with 0.0625 M KSCN

  2. Express the results in terms of % P2O5
• Convert CO in a 20.3-L gas sample to CO2 using I2O5


  1. Collect the I2 produced in 8.25 mL of 0.01101 M Na2S2O3

  2. Back-titrate the excess Na2S2O3 with 0.00947 M I2

  3. Calculate the concentration of CO in mg/L
• How to calculate millimoles of solute in various volumes and concentrations
• Titrate 0.4723 g of Na2CO3 with H2SO4

  1. CO3^2- + 2H+ → H2O + CO2

  2. Calculate the molar concentration of the H2SO4
• Titrate 0.5002 g of 96.4% Na2SO4 with BaCl2

  Calculate the molar concentration of the BaCl2 solution
• Titrate I2 produced from 0.1142 g of KIO3 with Na2S2O3

  IO3- + 5I2 + 6H+ → 3I2 + 3H2O

  I2 + 2S2O3^2- → 2I- + S4O6^2-

  Calculate the concentration of the Na2S2O3