38 Acid base titration: Polyprotic acids, determination of the molar concentration of phosphoric acid in cola

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1 Chemistry Sensors: Loggers: ph, Drop / Bubble counter Any EASYSENSE Logging time: EasyLog Teacher s notes 38 Acid base titration: Polyprotic acids, determination of the molar concentration of phosphoric acid in cola Read This investigation continues and applies the work from the investigation into polyprotic acids (phosphoric acid), which does not have to be conducted for this work. Many of the common acids such as hydrochloric acid and ethanoic acid have only one hydrogen, which is easily transferred to water to form H 3 O +. These acids are called monoprotic acids. Acids such as carbonic acid and phosphoric acid have more than one ionisable proton. These acids are called polyprotic and they show the release of protons in step wise manner. Ka 1 H 3 PO 4 + H 2 O (l) H 3 O + + H 2 PO 4 Ka 2 H 2 PO 4 + H 2 O (l) H 3 O + + HPO 4 Ka 3 HPO 4 + H 2 O (l) H 3 O + + PO 4 3 Reaction Ka 2 will not take place until reaction Ka 1 has finished. HPO Ka 1= = [ HPO] 3 4 HPO Ka 2= = 6.2 HPO PO Ka 3= = 4.8 HPO Ka 1 is much larger than Ka 2 which in turn is much larger than Ka 3. This tells us that the first proton is more easily lost from the phosphoric acid than the second and third protons. It can be assumed therefore that the majority of protons donated come from the first ionisation. The Ka values listed after each calculation above are the acid ionisation constants. They indicate the relative ease with which each reaction takes place. A small Ka value indicates a reaction that will not take place easily. T38 1(V2)

2 When the moles of acid and base are the same, further additions of the titrant will cause massive changes in the ph until the ph eventually stabilises. The pka 1 of phosphoric acid will indicate the equivalence point of the first ionisation. This will (if ph against volume has been recorded) give the volume of titrant added, which in turn will give the moles of base that are equal to the moles of acid (in this case phosphoric acid). Apparatus 1. An EASYSENSE logger. 2. A Smart Q ph sensor. 3. A Smart Q Drop / Bubble counter set to the correct volume range (see calibrating the Drop counter) with alignment adapter fitted 4. The drop counter reagent reservoir fitted with two stopcocks and tip x 200 ml beakers. 6. Magnetic stirrer and follower cm 3 of 0.1 mol dm 3 Sodium hydroxide (NaOH). 8. Measuring cylinder (50 ml capacity). 9. A 50 cm 3 sample of Cola that has been boiled for minutes to remove the carbon dioxide and associated carbonic acid. Set up of the software and logger The time for the experiment will depend upon the drop rate. To account for variation of this in individual experiments use EasyLog which is open ended. When testing the experiment with the solutions suggested the titration was complete in 20 minutes. Notes Hazard information Sodium Hydroxide Precautions Corrosive 0.5 M or higher Irritant Goggles and gloves should be worn The solid hydroxide should not be allowed to come into contact with skin, if it does it should be washed away with plenty of running cold water The Cola sample needs to be boiled for minutes to remove the acid from the dissolved carbon dioxide in the Cola. This can present one source of error, evaporation will concentrate the sample. The Cola does not have to be diet, regular or max but it is best to avoid flavoured colas especially the lemon varieties. Published values of phosphoric acid are in the range mg L 1 for Coke, other brands will have different values and it is suggested that regional variations exist. T38 2(V2)

3 The urban legends surrounding Cola are worth considering as an example of how knowledge can be misinterpreted or taken out of context (bad science). In researching this investigation there was even a suggestion that Cola was responsible for the spread of AIDS!! The concentration of the sodium hydroxide will affect the time of the titration; the suggested 0.1 molar is a compromise between accuracy of results and the time for the titration. Using 0.02 mol dm 3 resulted in a titration that took over an hour to complete. Calibrating the Drop counter This investigation uses the Drop counter with one of its preset calibrated ranges e.g. 27 drops/cm 3 so the drops counted are automatically converted and displayed as volume in cm 3. If accuracy is not critical and you are using the reagent reservoir and tip supplied with a low viscosity liquid (like water) and the flow rate set to: Fast e.g. 10 plus drops per second, use the 24 drops/cm 3 range. Medium e.g. between 5 10 drops per second, use the 25 drops/cm 3 range. Slow e.g. between drops per second, use the 26 drops/cm 3 range. Very Slow e.g. less than 1.5 drops per second, use the 27 drops/cm 3 range When used with a ph Sensor, the flow rate is best set very slow (less than 1.5 drops per second) to allow the ph Sensor time to settle to a new reading after addition of the titrant. To calculate the number of drops in a cm 3 1. Set up the reagent reservoir in the alignment adapter of the Drop / Bubble Counter. Close both stopcocks and fill the reservoir with the type of solution being used. 2. The first step is to adjust the flow rate. Place a beaker under the stopcock to catch the drops. Fully open the lower stopcock. Slowly turn the top stopcock round until it begins to produce drops and then finely adjust the drop rate. When the correct flow rate of drops is achieved close the lower stopcock to stop the flow. Now the flow rate is set, do not adjust the top stopcock leave in this position. Use the lower stopcock to turn the drops on and off. 3. Top up the reservoir. Place an accurate measuring container e.g. volumetric flask (10 ml or less) under the dropping tip. Open the lower stopcock fully and count the number of drops required to fill up to the volume mark on the measuring container. You can use the Drop / Bubble Counter to count the total number of drops (set to the Drop / bubble count range). Make sure you zero the Sensor before each run. Close the lower stopcock to stop the drops. 4. Divide the number of drops by the volume (in cm 3 ) to get the drops per cm 3 value e.g. 272 drops fill a capacity of 10 ml = 27.2 drops/cm 3. Top up the reservoir and repeat three times to get an average value. Results and analysis The data will be displayed a Volume and ph vs. Time graph. To alter the display to a ph vs. volume graph select Options from the toolbar, select the XAxis tab and click on Channel. If necessary, click outside the graph area to alter the data channel displayed so that ph is on the yaxis (vertical) and Volume is on the xaxis (horizontal). Use Values to find the end point (or point of neutralization), which is the maximum rate of ph change. Advanced The a dx/dt function can be applied to the ph data to produce a first derivative curve. From the Tools menu select Postlog Function. Choose the formula function a dx/dt and set the following parameters, x = ph sensor T38 3(V2)

4 a = 10 (this value may need to be altered, it corrects for the smallness of the decimal produced) Number of decimals = 4 (the derivative can produce very small numbers; with a few decimals the detail of the number is lost. Max = 10 Min = 0 Name = Rate of change Note: the value of a may need altering according to the quality of the results, a value of 10 is a good starting point, if the peaks on the graph are too small increase the value and vice versa. Plot rate of change vs. ph, which will produce a graph with peaks at the equivalence points. Note: If the acid is titrated into the alkali the a value in the function wizard should be a negative value. Setting a to 10 makes the peaks produced large enough to be seen without having to reset the sensor axis limits. Rate of change (ph) m 20s Time 2m 40s Graph of sodium hydroxide titration against cola showing the first derivative plot. For the calculations, the highest part of each peak of the derivative curve was used. The derivative is best if the ph data is smoothed before the application of the a dx/dt function. Small variations in the rate of ph change are magnified by the derivative calculation. Additional smoothing of the derivative curve may be needed. Calculating the Phosphate content of the Cola The equivalence point of the first ionization point is required. This will (if ph against volume has been recorded) give the volume of titrant added, which in turn will give the moles of base that are equal to the moles of acid (in this case phosphoric acid). Find the volume of sodium hydroxide used to reach the equivalence point and calculate the number of moles of sodium hydroxide. The number moles of sodium hydroxide used are equal to the number of moles of phosphoric acid. Calculate the molecular weight of phosphoric acid and use this to find the mass of phosphoric acid present in the sample. T38 4(V2)

5 Make the mass value for the sample into a mass value for a litre and express the final answer as milligrams of phosphoric acid per litre of Cola. Find a reference value to the phosphoric acid of a Cola based drink. This information may be on the original container of the drink or on the web. Sample calculation In a titration using 0.02 mol dm 3 sodium hydroxide it was found that 1.5 cm 3 of sodium hydroxide was needed to reach the first equivalence point. Calculating the number of moles of sodium hydroxide as volume of base used x concentration of base Correcting for the volume used (1.51 x 0.02) / 1000 = moles x (30 cm 3 of cola were used) = moles Mass of phosphoric acid is the number of moles x the MW of phosphoric acid. Mw = x 98.5 = g or mg L 1 Extension 1. Repeat using colas from different companies or the same company but different batches. 2. Try the following titration and compare the results, 0.1 mol dm 3 sodium hydroxide solution vs. 0.1 mol dm 3 sulphuric acid. T38 5(V2)