Case
You will accomplish several acid-base titration exercises to complete this Case Assignment at the following Virtual Laboratory website:
Strong acid versus strong base titration and weak acid versus strong base titration
https://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flashfiles/stoichiometry/a_b_phtitr.html
First read the following article about pH indicators:
https://chemwiki.ucdavis.edu/Physical_Chemistry/Acids_and_Bases/Case_Studies/Acid_and_Base_Indicators
In this experiment you will be analyzing the neutralization between a strong acid and a strong base. According to the Arrhenius Acid-base Theory, when dissolved in water, an acid raises the concentration of hydrogen ion, H+ while a base increases the hydroxide ion, OH- concentration. When reacted together the acid and base will neutralize each other according to the net ionic equation (1).
H+(aq) + OH- (aq) → H2O(l) (1)
An acid is considered to be strong if it completely ionizes in water. In this lab, you will be using the strong acid, hydrochloric acid, HCl, to neutralize the strong base, sodium hydroxide, NaOH, according to the neutralization reaction below.
HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l) (2)
The progression of the reaction will be observed using a pH meter and a titration curve will be created using the experimental data. You will start with a sample containing only the acid and indicator and slowly add your standardized base. A titration curve is simply a plot of the pH of an acid versus the volume of base added, or vice versa. The titration curve gives a good description of how an acid-base reaction proceeds. The pH will start out low and acidic, then increase as it approaches the equivalence point, where the concentration of acid equals that of the base. Then as the solution becomes more basic, it will slowly rise and level off as an excess amount of base is added. Note that the equivalence point is slightly different from the endpoint of a titration. The endpoint is when the indicator changes color. This does not always correspond to the equivalence point.
As pre-laboratory preparation it is critical that you review the ideas on strong acid-strong base titration presented in your class readings.
Strong acid versus strong base
1. With your first sample, select an indicator from the two options and do a quick titration by adding 1 mL increments until you reach pH 2.5; then dropwise increments until you reach pH 10.7; after that add 1 mL increments until pH 11.5. Record your buret readings after the addition of each increment. Allow time for the reaction vessel to become equilibrated and for the pH reading to become stabilized and then record the pH value in your notebook alongside the buret reading. Leave an empty column between the buret reading and the pH in which to place the volume of NaOH added (difference between present buret reading and initial buret reading). Stop the titration when you have reached pH > 11.5. For each pH reading, convert your buret readings to volumes of NaOH added. Examine this data and determine between which volumes the largest change in pH occurs. The NaOH volumes at both ends of the largest pH change bracket the endpoint. Based on the pH of your endpoint, was the indicator you selected the best choice? Why or why not? If not, select the other indicator.
2. Set up your second titration by repeating step 2. For your second titration, refine your procedure based on your first titration by adding 1 drop of NaOH at a time from well below the endpoint to well above the endpoint. Record your buret readings after the addition of each increment. Allow time for the reaction vessel to become equilibrated and for the pH reading to become stabilized and then record the pH value in your notebook alongside the buret reading. Leave an empty column between the buret reading and the pH in which to place the volume of NaOH added. Stop the titration when you have reached pH > 11.5.
3. Repeat the titration procedure as time allows so that you have as many trials as possible to improve the statistics of your standardization of HCl.
4. Use a spreadsheet program such as Excel to enter your titration data and make your titration curves by plotting pH vs. volume of added NaOH solution. Enter the volume of NaOH as a column headed V and the pH as an adjacent column headed pH. Leave four empty columns to the right of each curve for developing the derivative curves in step 5. Head these columns with the labels Vm, D1, Vd, and D2. Use the plot wizard to create a plot from the first two columns. Make sure you use the type of plot that will accept both a randomly spaced x value and a corresponding y value. Such plots are called scatter plots in commonly used spreadsheet programs. Use this plot to estimate the position of the endpoint (that volume of NaOH which is midway between the two nearly linear asymptotic regions at low pH and at high pH). What is your best estimate of the volume of NaOH at the endpoint for each of your titration curves based on this plot?
5. A property of the equivalence point of an acid-base titration curve is that it is the volume at which the rate of change of pH is greatest (the first derivative reaches a maximum). It is also that volume at which there is an inflection point in the curve (the second derivative will change sign). These first and second derivative plots, which we will approximate by calculating and plotting forward divided difference curves, can help you identify this volume, perhaps more precisely than you can from the direct plot of pH vs. NaOH volume. Following the directions below, use your spreadsheet program to calculate the forward divided difference approximation to the first derivative (rate of change) of the titration curve and the second forward divided difference approximation to the second derivative (rate of change of the rate of change) of the titration curve.
The first forward divided difference best represents the derivative or rate of change of the titration curve at the volume midway between volumes V(i) and V(i+1). Here i is one of the data points and i+1 is the next data point in the sequence. In the column immediately to the right of the pH values, enter the formula that will calculate the volume midway between V(i) and V(i+1),
Vm(i) = (V(i) + V(i+1))/2
The forward divided difference approximation for a series of data points of the type pH(i), V(i) is given by:
D1(i) = [pH(i+1) - pH(i)]/[V(i+1) - V(i)]
In the column to the right of Vm, enter the formula for D1. It is easy to set up a formula by referencing the data in the cells for pH(2), pH(1), V(2), and V(1) to calculate this forward difference for the first data point in the sequence in a column adjacent to the pH of the first point. This formula may then be copied down the column and the spreadsheet will update the references to the correct cells for the pH and Volume for each row automatically. The column then is the forward divided difference approximation to the derivative. Notice that you will not be able to calculate a forward difference for the last row of the data since there are no data values beyond the last row to use for pH(N+1) or V(N+1).
Likewise in the next column enter the formula for the volume midway between Vm(i) and Vm(i+1) given by,
Vd(i) = (Vm(i) + Vm(i+1))/2
Then in the next and final column to the right, enter the formula for the second forward divided difference approximation to the second derivative (rate of change of the rate of change)
D2(i) = [D1(i+1)-D1(i)]/[Vm(i+1) - Vm(i)]
Invoke the plot wizard to plot the first forward divided difference (D1) vs. Vm, and then again to plot the second forward divided difference (D2) vs. Vd. These approximations to the first and second derivative illustrate the properties, mentioned above, of the titration curve.
The forward divided difference expressions do tend to amplify experimental error (commonly called noise), but your data should be good enough that these plots of the forward divided differences can help you to identify the equivalence point. You will find some plots at the end of this section of the laboratory manual that work up the first and second forward divided difference plots for some old titration data. You can see what the expressions do to the data. Your plots should look similar. Print copies of all your graphs by saving them as pdfs and upload them as Appendixes with your laboratory report. Clearly, title and label the vertical and horizontal axes.
6. Using the combined representations of the titration curves developed in sections 4 and 5, what is your best estimate of the equivalence point volume of NaOH for each of your titration curves? You should be able to make this estimate to within 0.02 mL i.e. 19.34 mL.
7. The recorded molarity of your NaOH solution provided to you, and the equivalence point volume of NaOH determined from the derivative plots, calculate the molarity of your HCl solution for each trial to four significant figures, i.e. 0.2217 M HCl.
8. Calculate the average molarity of your HCl solution.
Assignment: Think about the standardization of NaOH, the titration curves, the forward divided difference approximation (derivative) treatment of the data, and the standardization of your HCl solution. Compose a summary paragraph that describes today's experiment and your understanding of acid-base neutralization reactions.
Data analysis
1. How many trials did you perform to determine the titration curve for the neutralization of HC2H3O2 by NaOH?
2. Using a spreadsheet program such as Excel, enter the volume of NaOH added and corresponding pH levels and plot the pH level on the ordinate (y-axis) and the volume of NaOH added on the abscissa (x-axis) to obtain a titration curve for each set of trial data. Use these plots to estimate the position of the equivalence point (that volume of NaOH which is midway between the two nearly linear asymptotic regions at low pH and at high pH). What is your best estimate of the volume of NaOH required to reach the equivalence point for each of your titration curves?
3. Compare and contrast the shape and trends of this titration curve to the strong acid-strong base titration curve. At what pH, does the equivalence point occur for each of the graphs? How do the slopes of the titration curves compare?
4. As instructed in sections 4 & 5 of the "Strong Acid-Strong Base Titration" experiment, calculate the volumes and the forward difference approximations for the first and second derivatives using each set of trial data. Graph the approximations to the first and second derivatives vs. NaOH volumes as you did in the previous laboratory report. Clearly, title and label the vertical and horizontal axes.
5. Using the combined representations of the derivative graphs developed in questions 3 and 4, estimate the volume of NaOH required to reach the equivalence point for each of your trials. You should be able to make this estimate to within 0.02 mL i.e. 9.45 mL.
6. Using the initial volume of acetic acid, the volume of NaOH at the equivalence point and the molarity of your NaOH, calculate the molarity of acetic acid you obtained in each of your trials. Then calculate the average value of the molarity of your acetic acid solution and use this value in all subsequent calculations where the molarity of the acetic acid solution is required.
7. Average the value of the initial pH of your acetic acid solutions before any NaOH was added, and calculate the Ka of acetic acid based on your calculated average molarity and the average pH of the acetic acid solution before any sodium hydroxide was added.
8. Find the pH of the midpoint for each of the trials using half the volume of NaOH required to reach the equivalence point for that trial. Use the sum of the initial volume and the volume of NaOH to reach the midpoint as the total solution volume at the midpoint. Combine these data with the pH at the midpoint to calculate Ka for each trial.
9. Calculate the average Ka of acetic acid based on the pH at the midpoint from each of your trials.
10. For each trial, calculate the Ka of acetic acid based on your calculated average molarity the initial volume of acetic acid, the volume of NaOH required to reach the equivalence point, and the pH of your acetic acid solution at the equivalence point. Then calculate the average value of Ka from the equivalence point determinations.
11. Compare the rate of change of pH vs. volume of NaOH at the midpoint to the rate of change vs. volume of NaOH at the equivalence point on the weak acid titration curve. The rate of change of pH vs. volume is (pH(i) -pH(i-1))/(V(i) - V(i-1) . Which is larger? Which pH has the greater uncertainty, the equivalence point pH or the midpoint pH?
12. Calculate the concentrations of the acetic acid and the acetate ion at the midpoint.
13. At what volume of NaOH did the indicator change color? Does this agree with the volume of NaOH needed to reach the equivalence point? What does this suggest to you about the selection of an indicator for an acid-base titration?
14. Which solution would have a higher pH, 0.1 M HBr or 0.1 M HC2H3O2? Explain.
Assignment: Summarize the key learnings from today's experiment regarding weak-acid titration reactions. How does the weak-acid titration curve differ from the strong-acid titration curve?