2.3.5 Acid-Base Titrations with Indicators

• Acid-base titrations are used to find the unknown concentrations of solutions of acids and bases
• Acid-base indicators give information about the change in chemical environment
• They change colour reversibly depending on the concentration of H⁺ ions in the solution
• Indicators are weak acids and bases where the conjugate bases and acids have a different colour
• Many acid-base indicators are derived from plants, such as litmus

Common Indicators Table

• A good indicator gives a very sharp colour change at the equivalence point
• In titrations is it not always possible to use two colour indicators because of this limitation, so for example litmus cannot be used successfully in a titration
• When phenolphthalein is used, it is usually better to have the base in the burette because it is easier to see the sudden and permanent appearance of a colour (pink in this case) than the change from a coloured solution to a colourless one

Volumes & concentrations of solutions

• The concentration of a solution is the amount of solute dissolved in a solvent to make 1 dm³ of  solution
  • The solute is the substance that dissolves in a solvent to form a solution
  • The solvent is often water

Concentration (mol dm³) = 

• A concentrated solution is a solution that has a high concentration of solute
• A dilute solution is a solution with a low concentration of solute
• When carrying out calculations involve concentrations in mol dm^-3 the following points need to be considered:
  • Change mass in grams to moles
  • Change cm³ to dm³ 

• To calculate the mass of a substance present in solution of known concentration and volume:
  • Rearrange the concentration equation

number of moles (mol) = concentration (mol dm^-3) x volume (dm³)

• • Multiply the moles of solute by its molar mass

mass of solute (g) = number of moles (mol) x molar mass (g mol^-1)

Answer

Step 1: Write the balanced symbol equation

Na₂CO₃  +  2HCl  →  2NaCl  +  H₂O  +  CO₂

Step 2: Calculate the amount, in moles, of sodium carbonate reacted by rearranging the equation for amount of substance (mol) and dividing the volume by 1000 to convert cm³ to dm³

amount (Na₂CO₃) = 0.025 dm³ x 0.050 mol dm^-3 = 0.00125 mol

Step 3: Calculate the moles of hydrochloric acid required using the reaction’s stoichiometry

1 mol of Na₂CO₃ reacts with 2 mol of HCl, so the molar ratio is 1 : 2

Therefore 0.00125 moles of Na₂CO₃ react with 0.00250 moles of HCl

Step 4: Calculate the concentration, in mol dm^-3, of hydrochloric acid

concentration (HCl) (mol dm^-3) = 0.125 mol dm^-3

Answer:

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Percentage Uncertainties

• Percentage uncertainties are a way to compare the significance of an absolute uncertainty on a measurement
• This is not to be confused with percentage error, which is a comparison of a result to a literature value
• The formula for calculating percentage uncertainty is as follows:

Adding or subtracting measurements

• When you are adding or subtracting two measurements then you add together the absolute measurement uncertainties
• For example,
  • Using a balance to measure the initial and final mass of a container
  • Using a thermometer for the measurement of the temperature at the start and the end
  • Using a burette to find the initial reading and final reading

• In all of these examples, you have to read the instrument twice to obtain the quantity
• If each time you read the instrument the measurement is ‘out’ by the stated uncertainty, then your final quantity is potentially ‘out’ by twice the uncertainty

Total experimental uncertainty

• Some experiments use multiple pieces of equipment, which each have a measure of uncertainty in their use
• For example, a titration against a standard solution will have the following uncertainties:
  • Using a balance to measure the mass of the solid used to make the standard solution
  • Using a volumetric flask to make the standard solution
  • Using a volumetric pipette to measure the sample that is being titrated against
  • Using a burette to find the initial reading and final reading that determine the titre volume

• If each piece of equipment used in the experiment has its own associated uncertainty, you can determine the total experimental uncertainty by adding the total individual uncertainties

• For example, a titration against a standard solution may have:
  • An uncertainty of ±0.5% for the use of the balance
  • An uncertainty of ±0.1% for the use of the volumetric flask
  • An uncertainty of ±0.2% for the use of the volumetric pipette
  • An uncertainty of ±0.4% for the use of the burette
  • Therefore, the total experimental uncertainty would be 0.5 + 0.1 + 0.2 + 0.4 = ±1.2%