How to find equivalence point on titration curve excel

CHEM 2230 Quantitative Chemical Analysis Experiment

Acid-Base Equilibria and the pH Measurement

Required reading: To successfully complete this laboratory and the prelab quiz, you must read Chapter 7, Chapter 9 (9-2, 9-3), Chapter 11 (11-1, 11-2, 11-3, 11-5, 11-10) and section 15-5. INTRODUCTION

Acid-base reactions and equilibria are at the core of a plethora of phenomena being studied in many fields of science, ranging from chemistry, geology, food technology, molecular biology and chemical engineering, just to name a few. As a result, knowledge of the fundamental aspects of acid-base equilibria is important and these will be explored in detail in this laboratory experiment.

In a series of experiments you will study:

1. Weak base/acid titration curves (vs. theoretical models) 2. Fundamentals of a pH electrode and pH measurements 3. Accurate determination of the endpoint 4. Determination of the acid dissociation constant (Ka)

General theory1,2 According to the Brønsted-Lowry acid-base theory, the strength of an acid is related to its ability to donate protons. All acid-base reactions are then competitions between bases of various strengths of these protons. For example, the strong acid HCl reacts with water according to the Equation:

HCl + H2O  H3O+ + Cl- This is a strong acid and is completely dissociated, that is, 100 % dissociated in dilute solutions. Consequently, the concentration of H3O+, [H3O+], of a 0.1 M HCl solution is 0.1 M. HCl is a stronger acid than water and donates a proton to water to form H3O+. For the general weak acid HA the dissociation reaction and dissociation constant expression are:

HA(aq) + H2O(l)  H3O+(aq) + A-(aq) eq.1

𝐾𝐾𝑎𝑎 = [𝐻𝐻3𝑂𝑂+][𝐴𝐴−]

[𝐻𝐻𝐴𝐴] eq.2

The pH concept and titrations1 Concentrations of H3O+ in equilibrium reactions may range from relatively high values to many orders of magnitude smaller values, for example, 10 M to 10-12 M. To simplify the expression of

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these concentrations, a logarithmic (base 10) scale is used. In general, for some concentration X, the quantity pX is defined as

𝑝𝑝𝑝𝑝 = 𝑙𝑙𝑙𝑙𝑙𝑙10 1 𝑋𝑋

= − log𝑝𝑝 eq. 3

And so, for X = [H3O+], 𝑝𝑝𝑝𝑝 = − log[𝑝𝑝3𝑂𝑂+] eq.4 Solving eq. 2 for [H3O+] and using the definition of pH (eq. 4), one arrives* at the extremely useful Henderson-Hasselbalch equation: 𝑝𝑝𝑝𝑝 = 𝑝𝑝𝐾𝐾𝑎𝑎 + 𝑙𝑙𝑙𝑙𝑙𝑙

[𝐴𝐴−] [𝐻𝐻𝐴𝐴]

eq.5 where pKa is the –log Ka for the acid HA (*do you know how to do this derivation? You should!) By titrating a weak acid with a strong base and recording the pH versus the volume of base added, we can determine both the concentration of H3O+ and the ionization constant of the weak acid. Figure 1 shows a calculated titration curve of a weak acid with a strong base (Figure 11-2 in your textbook).

Figure 1. Calculated titration curve of a weak acid with a strong base (Figure 11-2 in your textbook). Finding the equivalence point and the Ka of the acid The equivalence point is where just enough base has been added to react completely with all of the weak acid present in solution. Graphically, this point corresponds to where the curve has its maximum slope or inflection point. Using this knowledge, one can pinpoint very accurately this position, that is, the volume of base at the equivalence point. Since the concentration of the base is also known, along with the volume of acid originally being titrated, the concentration of the unknown acid can be calculated (See Chapter 11 of your textbook). This can only work, however, if enough data points are collected during this section of the titration curve. Figure 1 also shows that at half this equivalence point, pH = pKa (why?...you should know that

too!). To accurately find the equivalence point (and thus the Ka of the weak acid), you will use two methods in this experiment: 1) the derivative method (first and second), and 2) the Gran Plot. Both of these methods are described in detail in section 11-5 of your textbook. Potentiometric measurement of the pH: the pH electrode (section 15-5 of your textbook)1 A pH meter consists of two electrodes: a glass electrode and a reference electrode. It measures the potential (i.e., voltage) difference across the glass membrane (so called because it is very thin and delicate!) between the unknown solution (e.g., your sample) and a constant H+ concentration inside the electrode. Schematically, the glass electrode and the Ag/AgCl reference electrodes are represented as follows:

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Modern pH electrodes combine these two electrodes into a single electrode casing, or pH combination electrode (Figure 2).

Figure 2. left: diagram of a glass combination electrode using silver-silver chloride reference electrode (Ag/AgCl) , right: ideal two-point calibration of a pH electrode using two standard buffer solutions of known pH’s. (both figures from Chapter 15, D.C. Harris textbook) The response of the glass electrode, that is, the potential (or voltage) output as a result of a H+ concentration difference across this glass membrane follows this equation:

E = constant – β (0.05916) pHoutside (at 25 oC) eq.6

Where β ≈1. The pH electrode is calibrated by using standard buffer solutions of known pH values. This process is shown on the right in Figure 2 (Figure 15-19 of your textbook). Based on eq. 6, what is the value of the slope of the calibration curve in Figure 2?

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EXPERIMENTAL PROCEDURE2 Day 1: NaOH solution standardization, preparation and titration of unknown solutions NOTE: ALL titrations and data collection must be completed on Day 1 of the experiment. Day 2: Calculations in the computer laboratory. No titrations will be allowed on Day 2 of the experiment. Equipment and reagents Buret, buret stand, pH meter, std. buffer solutions, solid KHP, solid NaOH, vinegar solution. Day 1: Procedure 1. Prepare approximately 0.5 L of 0.5 M NaOH. Standardize this solution against weighed

portions of dried primary standard grade potassium hydrogen phthalate (HO2C)C6H4CO2K (KHP; FW 204.221). Determine the quantity of KHP needed to make 25 mL of a 0.5 M solution. Exactly about weigh this amount of KHP and add it to a 250 mL Erlenmeyer flask. Add enough distilled water to the KHP to make ~ 25 mL of solution. Add a few drops of phenolphthalein and titrate with the NaOH solution to a light pink end point. Perform two more trials of this titration. Compute the average concentration of the standardized base.

2. Calibrate the pH electrode with the provided buffer solutions according to the instructions given by your TA for the particular model of pH meter you are using.

3. Refill the buret with the standardized 0.5 M NaOH solution and record the initial volume of NaOH in your notebook (note: this should NOT be 0.00 mL!). Using a carefully cleaned and rinsed transfer pipet, dispense a 10.00 mL aliquot of unknown weak acid solution into a clean, dry 150 or 250 mL beaker. Dilute with about 75 mL of distilled water. Add 3 drops of phenolphthalein.

4. Setup the titration by adding a magnetic stirring bar to the vinegar solution, taking extreme care not to hit the pH electrode. Secure the pH electrode with a clamp. Take the initial pH reading (at zero volume of base added). Titrate the vinegar solution by initially adding 1-2 mL of NaOH, carefully not splashing any liquid out of the beaker. Rinse any splash from the internal walls of the beaker. Record down the added volume of NaOH and the resulting pH (allow 10-20 sec for mixing to occur and the reading to stabilize). Continue to add base and recording both the volume added and the pH of the solution. You should be careful as you get close to the equivalence point (pH > ~5-6) as the pH will change very rapidly for small volumes of base. Remember, this is the region where you want to collect more data points in order to accurately determine the endpoint (see step #5 of “Standard 0.1 NaOH” on page 235 of your textbook on how to deliver 1 drop at a time when near the equivalent point).

5. Titrate past the equivalence point, at a point where the pH does not change with volume of base added (pH > ~12).

6. Repeat steps 3-5 for at least 2 more samples of “unknown acid”.

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Day 2: Calculation of equivalence point, Ka and comparison with a theoretical titration curve 1. In a spreadsheet, plot the data for all of your titrations (you can do this ahead of time before

coming to Day 2 lab period). Print a plot for each titration making sure all axis are properly labelled (parameter and units! As in Figure 1 of this manual).

2. Use the derivatives method (outlined in detailed on p. 243-244 of your textbook) to find the end point for each titration curve. Generate and print a graph for the second derivatives of each of your titrations similar to the plots in Figure 11-7 (p. 245) in your textbook. Make sure you “zoom-in” the x-axis in order to clearly estimate the equivalence volume. Again, make sure your plots and axis are clearly labelled.

3. Compute the concentration of the unknown acid for each titration and report, in a table format, each value and their combined average and standard deviation (with proper number of significant figures…always use the real rule for significant figures, p. 54 in textbook).

4. Compute the value of Ka for each titration and report, in a table format, each value and their combined average and standard deviation.

5. Use the Gran plot method (outlined on p. 245-246 in your textbook) to find both the concentration of unknown weak acid and the Ka. Construct a graph of the Gran Plot for each titration curve. On each of the graphs, indicate the equivalence point and the slope of the line. Report in a table format values for the concentration and Ka obtained from each titration curve/Gran Plot calculation along with their average and standard deviation.

6. See section 11-10 in DCH textbook before proceeding with this calculation. In this section you will use a spreadsheet to generate calculated (i.e., theoretical) titration curves. You will generate a calculated titration curve and then compare it with one of your experimental titration curves. Based on the values for the concentration of your standard NaOH solution (Cb), experimentally determined acid concentration (Ca), dissociation constant (Ka) and volume of unknown acid (Va), compute the titration curve. Submit a print out of the top portion of the Excel spreadsheet titration curve calculation as shown in Figure 11-13 of your textbook (do not print the entire spreadsheet!). Plot the calculated titration curve along with one of your experimental curves on the same graph (plot each curve in different colors and indicate which one is the calculated and the experimental).

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RESULTS AND DISCUSSION 1. Submit all plots and tables and clearly indicate its section number above. Failure to report

your results in the requested format (tables) will result in no credit. 2. Repeat the same calculation as in #6, assuming that the acid has a pKa = 4.76 (i.e., acetic

acid; this should only take a few clicks to enter the new number and re-calculate). Plot the calculated titration curve along with the same experimental curve used in #6 on the same graph (plot each curve in different colors).

3. Based on your graph in section #6 above, discuss if your experimental results match the theoretical curve.

4. Email your spreadsheet with all of the calculations to basile@uwyo.edu with the subject line: “CHEM2230 2017 exp #3” by noon on the day your report is due (i.e., the next lab session).

A word of caution about plagiarism: Preparation of the report including data analysis, interpretation, spreadsheet setup/calculations and discussion must be prepared by the individual student submitting the report. A grade of zero for this report will be given to all parties involved. REFERENCES

1. Harris, D. C. Quantitative Chemical Analysis, 8th edition; W. H. Freeman and Company: New York, 2010.

2. Nelson, J. H., Kemp, K. C., Laboratory Experiments for “Brown & LeMay Chemistry The Central Science”, 4th edition, Prentice Hall, NJ 1988.

Acid-Base Equilibria and the pH Measurement