# Titrations. x C A V B V A. n A n B. x C B C A C B. Acid-base titrations:

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1 Acid-base titrations: Titrations n A A + n B B products Where: n A moles of acid (A) are neutralised by n B moles of base (B). If we have a solution of known acid but of unknown concentration then we can determine its concentration by titrating it against a solution of a base of known concentration (standard solution), such as NaOH(aq) or Na 2 CO 3 (aq). Similarly, a solution of a base of unknown strength can be titrated against a standard solution of acid of known strength. We can then calculate the concentration of the unknown by neutralising it exactly (using an indicator to show us when the solution is neutral). We can calculate the concentration of the unknown using the following formula: V A x C A V B x C B = n A n B Where: V A and V B are the concentrations of the acid and base, respectively; and C A and C B are the concentrations of the acid and base, respectively. We will need to obtain either C A or C B, whichever is the unknown, by rearranging the formula: C A = n A n B x V B x C B V A C B = n B n A x V A x C A V B Note that the original formula is derived from: Concentration = number moles / volume So, number moles = concentration x volume

2 Worked example: A 2.65 g sample of anhydrous sodium carbonate was dissolved in water and the solution made up to 250 cm 3. In a titration, 25.0 cm 3 of this standard solution required 22.5 cm 3 of hydrochloric acid at the end-point with methyl orange as the indicator. Calculate the concentration of the acid. (Note that in this case the standard solution was placed in the flask with a pipette and the acid was placed in the burette; 22.5 cm 3 is the mean titre). Always start by writing the equation for the reaction carbonate + acid salt + water + carbon dioxide Na 2 CO 3 (aq) + 2HCl(aq) 2NaCl(aq) + H 2 O(l) + CO 2 (g) Remember to convert volumes in cm 3 to volumes in dm 3 by dividing by g of Na 2 CO 3 (s) was dissolved in 250 cm 3 = dm 3 water Volume of Na 2 CO 3 used in reaction = 25 cm 3 = dm 3 Volume of HCl required = 22.5 cm 3 = dm 3 Convert masses into moles: Molar mass(na 2 CO 3 ) = 106 g/mol Number of moles = mass (g) / molar mass (g/mol) Number of moles (Na 2 CO 3 ) = 2.65 / 106 = mol. (Note: we used 1/10 of this (25.0 cm 3 ) in the titration = mol). Work out concentration of standard solution (unless given, as it often is!): Concentration (mol/dm 3 ) = number moles / volume (dm 3 ) Concentration (Na 2 CO 3 ) = / = 0.1 mol/dm 3 (0.1M)

3 To work out the unknown solution, in this case the acid, there are two methods: 1. using the formula (rearrange it!): C A = [n A (V B x C B ) ] / [n B x V A ] = (N A /N B ) x (V B x C B ) / V A From the equation: N A /N B = 2. So, C A = 2 x (V B x C B ) / V A = 2 x (0.025 x 0.1) / = 0.22 mol dm -3 (2 d.p.). 2. By application of basic mole principles: From the equation: 2 moles of HCl will exactly neutralise 1 mole of Na 2 CO 3. Thus, at the end-point there will be twice as many moles of HCl as Na 2 CO 3 in the reaction flask. We know that the number moles Na 2 CO 3 in the flask = mol (NOT mol, the volume we made-up to start with!). So we used 2 x = mol of HCl to neutralise the Na 2 CO 3. Thus, there were mol HCl in our titre of dm 3, Concentration (mol/dm 3 ) = number moles / volume (dm 3 ) So, the concentration of our acid was = / dm 3 = 0.22 mol dm -3 (2 d.p.). We have achieved our goal of calculating the concentration of the unknnown HCl solution! Q.1 In a titration, cm 3 of a solution of hydrochloric acid exactly neutralised 25.0 cm 3 of standard 0.1 M NaOH solution. What is the concentration of the hydrochloric acid? Q.2 In a titration, cm 3 of a solution of sodium hydroxide exactly neutralised 25.0 cm 3 of 0.1 M sulphuric acid. What is the concentration of the sodium hydroxide solution?

4 Making up standard solutions: Clearly, if a standard solution is to be used to determine the concentration of an unknown, then the standard solution better be as accurate as we can get it! Procedure for making up a standard solution: Take a watch glass or weighing boat and place it on the balance. Tare the balance (set it to zero). Carefully weigh out the required mass of substance. Transfer this amount to a beaker. Add water from a wash bottle to dissolve it. Use some of the water to rinse all the substance off the watch glass. Do this at least twice. Stir with a glass rod until all the solid is dissolved, then transfer the solution to the volumetric flask. Use more water from the wash bottle to rinse out the beaker and the glass rod. Do this at least twice. Add water to just below the line on the volumetric flask. Add the final drops with a teat pipette to ensure that the bottom of the meniscus is on the line. Put the stopper on the flask and turn the flask over a couple of times to mix the solution. Label your solution with your name, the date, and the contents, e.g. 2.0M NaCl. Then tidy up! Q.3 What mass of sodium carbonate must be used to make up 1.00 dm 3 of a O.2M standard solution? Q.4 A silver nitrate solution, AgNO 3 (aq), of unknown concentration, can be titrated against a standard solution of NaCl(aq). A potassium chromate (K 2 CrO 4 ) indicator can be used (which forms a bright red precipitate of silver chromate with even a slight excess of AgNO 3 : Ag + (aq) + CrO 4 2 (aq) AgCrO 4 (s) ). (i) Write a balanced equation for the reaction between AgNO 3 and silver chloride. (ii) What is the concentration of a standard solution of sodium chloride, prepared by dissolving 15.50g of sodium chloride in cm3 of water? (iii) What mass of solid sodium chloride would you require to make-up cm 3 of a standard solution of concentration 0.1M? (iv) How would you carry out this titration?

6 Calculating percentage errors Suppose we measure a temperature T. The measurement will not be exact, even if we eliminated human error, then the thermometer we use will itself have an inherent error. Supposing we measured the temperature of a solution as 34 o C (add 273 to convert to degrees Kelvin, so 34 o C = 307K) and we eliminate human error by reading very carefully. The reading will still be in error since the thermometer may only be accurate to the nearest 0.1 of a degree. This means that it might be 0.05 of a degree out on either side, so we could write the error as ±0.05 o C and we ought to record our measured value as 34 ± 0.05 o C. Calculating percentage errors: The percentage error is given by the following formula: percentage error in X = (error in X)/X x 100 In our example, percentage error = ± 0.05/34 x 100 = ±0.147%, so our reading is pretty accurate! Q.1 The accuracy of a (class B) pipette is ±0.10 cm 3. What is the percentage error in a reading of cm 3? Q.2 The error in a (class A) burette is 0.05 cm 3. What is the percentage error in a measured titre of cm 3?

7 Redox Titrations Example: the determination of bleach (Bleach is essentially a solution of sodium hypochlorite (sodium chlorate(i)). Bleach can be analysed using an iodine-thiosulphate titration: This is a redox reaction. Procedure: I 2 (aq) + 2S 2 O 3 2 (aq) 2I (aq) + S 4 O 6 2 (aq) 1 Add acid to the bleach to extract the chlorine from the hypochlorite (chlorate(i)): OCl (aq) + 2H + (aq) Ý Cl 2 (aq) + H 2 O(l) (a redox reaction) 2. The chlorine then oxidises iodide (in KI(aq)) to iodine: Cl 2 (aq) + 2I (aq) 2Cl (aq) + I 2 (aq) 3. The iodine remains in solution as a yellow-brown colour. Titrate this iodine with thiosulphate to convert the iodine back to colourless iodide. the iodine solution decolourises. 4. When you are near to the end-point, add a few drops of starch solution (turns blue/back in the presence of iodine) to assist in visualising the end-point. Q cm 3 of bleach (measured from a burette or 5 cm 3 volumetric pipette) was placed in a flask and diluted with distilled water. Excess potassium iodide was dissolved in the solution which was then acidified (using dilute ethanoic acid, but hydrochloric acid will also work in this case). The iodine formed was titrated against a 0.05 M standard solution of sodium thiosulphate (from a burette). The volume of sodium thiosulphate needed to decolourise the blue iodine-starch solution at the end-point was cm 3. Calculate the concentration of available chlorine in the bleach. Q.6 How would you modify this method to satndardise sodium hypoiodite (sodium iodate(1))?

8 Other examples of redox titrations: 1. Iron determination using dichromate: Cr 2 O 2 7 (aq) + 14H + (aq) + 6e 2Cr 3+ (aq) + 7H 2 O(l) 6Fe 2+ (aq) 6Fe 3+ (aq) + 6e Cr 2 O H + + 6Fe 2+ (aq) 2Cr 3+ (aq) + 7H 2 O(l) 2. Iron determination using permanganate (manganate(vii)): MnO 4 (aq) + 8H + (aq) + 5e Mn 2+ (aq) + 4H 2 O(l) 5Fe 2+ (aq) 5Fe 3+ (aq) + 5e Cr 2 O H Fe 2+ (aq) 2 Cr 3+ (aq) + 7 H 2 O(l) Dichromate is the preferred method since it is hard to standardise a manganate (VII) solution, a sit will always contain some Mn(IV) impurity (as brown MnO 2 ) and so must be standardised itself by titrating with another standard (typically oxalic acid, H 2 C 2 O 4, also known as ethanedioic acid)! Note: to aciidify permanganate, we should not use hydrochloric acid since permanganate oxidises this to Cl 2! Nitric acid is also inappropriate since it is an oxidising agent!

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