Gentle Reader, our story today follows a number of storied histories, most conspicuously in the representation of transformation—making and breaking bonds—in a chemical reaction. Flowcharts, which use arrows to dynamically illustrate a process, also have a storied history, particularly in programming in Computer Science. Titrations have a storied history in chemical analysis and chemical laboratory pedagogy. Many laboratory sessions are leading to confirm a chemical principle, and titration is usually a technique used along the way to confirming a chemical principle (confirmatory laboratory), for example acid-base or redox reactions. However, it is my contention that a more fundamental reason to learn titration is that it teaches the student to be careful—develop technique—in a reasonably cheap and reliable fashion. It is uncanny how titration rewards the student using good and careful technique with good data, and punishes those with poor and careless technique with poor data. 

Titration is an excellent technique to use to illustrate the difference between precision and accuracy. It is best taught one-on-one, but few of us have this luxury. In a previous blog post, “Using a Nautical Analogy for Successful Laboratory Tasks”² (a.k.a. Naval Analogy) the method goes a long way to helping a whole class at a time to visualize the behavior of any analyses that require the most attention once one is close to answer—titration, maximizing signal on a peak, etc.... The three parts of the Naval Analogy can be summed up by 1) At Sea (far from completion), 2) In Port (nearing completion) and 3) At the Dock (bringing it home). The respective parts correspond to actions characterized by 1) free movement, 2) slowed movement, and 3) extremely careful movement. 

Why a Flowchart?

You will find that making your students into a flowchart can better teach them the titration process while you and your class will have more fun than you have ever had in a laboratory introduction session. I warn you; it will take a little set-up (assisted by the PowerPoint slides attached to this post) and buy-in from the students. The flowchart is fun with its twists and turns along with over-the-top repetition. It may initially seem a little crazy and chaotic, but it is held together by your students—the structure of the flowchart. 

Similarity of Acid-base and Potentiometric Titrations

As noted in the previous post, Connecting Acid-Base and Redox Connections,³ pH titration of an acid-base reaction is an electrochemical analysis method based on proton activity concentration cells (pH meter). Being electrochemical in nature, pH titration is fundamentally related to redox titrations, with acid-base titrations using a pH meter and redox titrations using a potentiometer. Though the method described below can work equally well for acid-base and redox titrations, the discussion below will follow acid-base titrations. 

Enter the Method of 8

Generally, there are three methods for deciding when one should take the data point in a titration: one reliable and slow, one quicker and unreliable and one quicker and reliable.  1) The Drift-Stop method waits until the potential value stops drifting, and you record the data point. It gives very good data well before and well after the equivalence point, but this method can chew up time when trying to get the most important data—near the equivalence point. This leads us to a favorite of impatient and careless students, 2) the Try Waiting method. This is where one tries to wait until the potential value stops drifting, gives up at a certain point, and records the data. This speeds the collection of data, but its quality is now suspect.  Finally, my favorite, 3) the Consistent Time method where one takes data at a consistent time after each addition of titrant. I have found 8 seconds, thus the name Method of 8, to be a good compromise though others prefer 10 seconds for the countdown affect (10-9-8-7-6-5-4-3-2-1-Blast Off!). It gives equally good data as the drift-stop method while speeding data collection. In the next section, I will go into a detailed description of the Consistent Time/Method of 8, but if you are already familiar, or already get the idea you can skip the next section and go straight to the student flowchart discussion.   

Explaining the Consistent Time method

The Consistent Time method codifies the method experienced titrators already use. They may start with a 1.00 mL titrant addition, watch how the pH changes (ΔpH). As the ΔpH near the equivalence point, they reduce addition volume. Using the Naval Analogy, at the beginning of the titration we are At Sea, so in the Method of 8, one waits 8 seconds, records pH and volume, and repeats. The titrator At Sea can move freely, but needs to monitor consistently. 

The ΔpH will increase as one gets closer to the equivalence point (In Port), and when the ΔpH ≥ 0.08 (another “8” in the Method of 8), the addition volume is halved.(Use 8 mV in a potentiometric titration.) A 0.08 pH unit change is about a 20% change in the reaction quotient, Q—that is [base]/[acid]. 

Keeping the ΔpH this small prevents overshooting the equivalence point, and makes the graphed data points closer together near the equivalence point. The sequence of volume decreases starting with 1.00 mL = 20 drops of aqueous solution, becomes in drops (mL) is: 20 (1.00) to 10 (0.50) to 5 (0.25).

Even greater care needs to be taken once the titrator goes below 5 drops—At the Dock in the Naval Analogy. Typically, I have students go from 5 to 3 to 2 to 1 drop and then proceed dropwise. It is both impractical and unnecessary for a good equivalence point to further halve the volume added. 

The Method of 8 anticipates the drift in pH caused by lag in electrode response. Record whatever pH value flies by at 8 seconds and make the next addition, adjusting volume until only one drop at a time is added. Repeat as necessary until past the equivalence point. Once the ΔpH is no longer changing by 0.08 pH units within 8 seconds, to continue the Naval Analogy, the titration is heading Out of Port. Between data points, the number of drops increases from 2 then 3 then 5 then 10.   Once back to 1.00 mL additions (At Sea), five 1.00 mL additions are sufficient to finish. 

(Flow) Charting the Naval Analogy

The beauty of the flowchart is that it channels a process in a way where it is all out front of the users all at once.  Thus, it is an excellent way to set the process, in our case titration using the Method of 8 / Consistent Time method, into the minds of all students in a section as the method is learnt while simultaneously teaching about flowcharts.  An additional advantage of using it for the Consistent Time method, is that a flowchart creates the certain necessary rhythm between titrant additions.  The challenge of introducing flowcharts to college students (let alone high school students) is that it has familiar shapes and symbols used in an unfamiliar, stylized manner.  The stylized use of shapes and symbols creates a barrier precisely because they are simple, compact, unexplained expressions.  As with anything stylized, these expressions are familiar to those that are familiar with them.  So having the students internal to the process, a) internalizes the process and idea of process, but b) in the process, it is vital to spend the time in set-up the students do not become befuddled when complexities arise. So, time spent on set-up determines whether the experience is a) chaotic and slowed down by stops and starts or b) flows by quickly in a fun experience for all. To help with the set-up of the students and provide visuals for the flow of the laboratory, a MS PowerPoint Presentation is provided. I would encourage you to download it and follow along in parallel.

Figure 1* shows a laboratory flowchart for a titration from beginning to end. The laboratory illustrated has a typical bench/seating arrangement. Within the laboratory flowchart are shown, a) the loci types for each student position, and b) how each student connects within the flowchart to neighboring student(s). Figure 2 shows a conventional flowchart that reflects the titration process before the equivalence point. Detailed explanation is given below the Figure 2 in bullet-form by shape. Depending upon student number and lab configuration, clearly, adjustments are likely for your particulars. (*You might find the animated slides in the MS PowerPoint Presentation in the Supplemental helpful in following the discussion. In the Supplemental PPT, after PowerPoint Presentation introductory slides, the initial set-up for a 20-student laboratory section is on Slides #4 and 5. Like the text here, Slide #4 has the student assignments by name.)

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Figure 1: A generic chemistry laboratory with 20 students (blue circles arrayed behind blue benches) set within a titration flowchart.  (See text for student assignments.)

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Figure 2: Flowchart using Method of 8 before the titration equivalence point.

• Ovals are Action/Experimenters.
  • Two students are Experimenter—Titrator and Recorder—no arrow.
  • One student is the Volume Determiner—one arrow.
  • One student takes the time at “Mark” and Observes the pH—one arrow. 
• Diamonds are Decision.
  • Four students
  • Two arrows each: Yes and No. 
• Rectangles are Multipliers.
  • Three students
  • They take the information from the decision and relate what action or change in action needs to be done by the titrator. 
  • One arrow each
• The count-off returns the flowchart to the titration. 
  • Nine students
  • One arrow each
  • They could get an arrow each or you could have them form a wave. 
• Upon recording, the process cycles back into the flow.
• Hand out a total of 22 arrows (printouts at the end of the PowerPoint Presentation)
  • Four “Yes” (B4, B, β, C)
  • Four “No” (B4, B, β, C)
  • Four “Computation” (D, E, ε, F)
  • Ten “Sequence” (A, 1-8, Mark: Numbers for the Sequence are optional)

Figure 1 has the whole flowchart, and though the instructor will be familiar with the whole, the whole is more than many students can swallow at once (avoid my painful experience). To avoid overwhelming them, a) show the flowchart, b) explain the symbols, c) take questions, and d) explain them again. Before the students fully take over, e) a demonstration titration can help the students find their place and a bit of the big picture. This demonstration is where the Naval Analogy can be brought in and followed one part of at a time. 

Figures 1 and 2 are functional for assigning loci and recapitulation at the end, but they are awfully busy. Thus, in paired slides for each part of the titration, you will find a conventional flowchart and the same flowchart laid over the laboratory configuration. The process is broken into a) Beginning to significant changes in pH (At Sea, Figures 3 and 4), b) the approaching equivalence point (In Port, Figures 5 and 6), c) very close to or at the equivalence point (At Dock, Figures 7 and 8) and d) past the equivalence point (Out of Port and Back to Sea, Figures 9 and 10). 

At Sea

Student assignments having been made, you will need to tell each what is expected of each for the beginning, At Sea as illustrated in Figures 3 and 4. 

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Figure 3: Flowchart using Method of 8 at the beginning of the titration—At Sea.

 

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Figure 4: A titration flowchart within laboratory: Method of 8 at the beginning of the titration—At Sea.

 

• One student is the Titrator (even though eventually all the students will be, in this experiment or another).
  • The instructor can demonstrate the proper mechanics of buret filling, draining, and reading of the volume level. 
  • The additions At Sea will start with 1.0 mL added and remain at that volume until the titration get to At Port.
• One student is the Recorder at the Action Oval labeled A “Record V_n, pH_n”. 
  
  • You explain that the value “n” is the data point counter and a good way to organize this is to make a table with n, V and ℰ values (either at a chalkboard or on a spreadsheet). 
  • This “Action Oval” records and reports to the class out loud. 
  • Their arrow always points to the next Decision Diamond.
• The first Decision Diamond is labeled B4 short for “before the equivalence point.”
  • From the start, all the way through At Sea, the answer is “Yes.”
  • The arrow points to B.
• The next student is the Decision Diamond labeled B is “ΔpH ≥ 0.08 pH units?”
  
  • Having done the quick subtraction between the previous posted pH and the current on, they decide and verbally report the “No” or “Yes.” 
  • They must decide which of two arrows to use and then where to point.
  • If the Decision is “No,” the titration addition volume is kept the same, the “No” arrow is pointed to D, “Multiplier =1”. 
    • D never says anything but “Multiplier = 1”. 
    • Suggestion: I would put class clowns in report boxes and let the kids ham it up. 
• The Multiplier, D, will always lead to F: “Add V_n = (m) mL”.
  
  • (m) is the result of the previous volume multiplied by the value from D.
    • At Sea, this Multiply and Report Oval student will repeatedly report “Add 1 mL”.
  • The countdown commences: 8, 7, 6, 5, 4, 3, 2, 1.   
  • The countdown ends with Mark.
• The process returns to B4.
  • “Yes,” B4 (before) the equivalence point.
• A records and reports the Volume and pH.
  • Recorder A needs to ALWAYS record the actual volume in mL, even if the titrator slips and adds too much or too little.
• Spreadsheet inputs the data.
• Decision B notes the new pH and makes a quick mental calculation to determine whether ΔpH ≥ 0.08.
• The titrator adds the volume reported above by F.
• The repetitiveness of the process at this point allows the students to get use to the flow of the chart.
  • Each student has a role. 
  • They should visualize both their place in the chart and how the whole chart reflects the physical and analytical process of titration.

At Port

Coming into Port, as Instructor, you should telegraph the changes as the potential/pH nears the values of 0.08 pH units, so the Decision Diamond will be ready to change from “No” to “Yes”.  This part is illustrated in Figures 5 and 6.

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Figure 5: Flowchart continuing Method of 8 as it nears the equivalence point—In Port.

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Figure 6: A titration flowchart within laboratory: Method of 8 as it nears the equivalence point—In Port.

 

• The following will become very busy as the equivalence point nears. 
• At Port begins with the first Decision Diamond turning to “Yes,” and leads to Decision Diamond C.
• C answers the question “Already at V = 1 drop?” arrows to one of two report boxes. 
  
  • The At Port  is defined as starting at the first time through.  Having started V = 1 mL, the decision “No” and go to the “Multiplier = ½” by Computation locus E. 
  • The student at Add Oval F needs to stay on all ten toes, react to the information and report the new volume.
    • The volumes reduce from 1 à 0.5 à 0.25 (5 drops) à 3 drops à 2 drops à 1 drop
    • Add Oval F can report in drops.
• The Add Oval F, again, flows into the Countdown, and the process returns to B4 and A as above.

At Dock

This is where all the repetitiveness of the Countdown comes to play. The “Consistent Time Method” works when there is a consistent time between drops of titrant near the equivalence point, in this context, from “Record” to “Mark.” If you have good teamwork, you have a good process and you will get good data. The less the student worries about getting “the right answer,” and the more they worry about keeping to the process, the better the data will be. This is illustrated in Figures 7 and 8.

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Figure 7: Flowchart continuing Method of 8 very near, at and closely after the equivalence point—At Dock.

 

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Figure 8: A titration flowchart within laboratory: Method of 8 very near, at and closely after the equivalence point—At Dock. 

 

• At Dock begins when the Decision Diamonds, B and C have:
  
  • B “ΔpH ≥ 0.08 pH units” is at “Yes”
  • C, “Already at V = 1 drop?” is at “Yes”.
    • This flows back to D, “Multiplier =1”. 
    • D lead to F: “Add V_n = one drop”.
• The Add Oval F, again, flows into the Countdown, and the process returns to B4 and A as above.
• The pH may continue to drift.
  • Pay attention to the process, and ignore any drift.
  • Recorder A does not second guess the pH value.  The “right time” to read and record is when the countdown hits “Mark.”
• The equivalence point has the largest ΔpH, but you will not know precisely which volume this is until after the titration.
  • Following the flowchart, you will be adding a consistent 1 drop at a time near (before, at and after) the equivalence point.
  • Thus (ΔpH/Volume) will be at its steepest at the equivalence point.

Back to Sea

Going Back to Sea should be leisurely in comparison to getting “To the Dock.” Getting Back to Sea includes a portion of In Port and finishes At Sea. This is illustrated in Figures 9 and 10.

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Figure 9: A titration flowchart within laboratory: Method of 8 after the equivalence point—Back to Sea.

 

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Figure 10: Flowchart continuing Method of 8 after the equivalence point—Back to Sea.

 

• Necessarily, after the equivalence point the ΔpH will get smaller and smaller.
  • The flowchart now branches with at the Decision Diamond B4 with a “No”.
  • To distinguish the “After” branch, B and E are changed to β and ε.
• The switchover Back to Sea is confirmed once one drop no longer causes a ΔpH ≤ 0.08 units, thus β returns a “Yes” and points to ε.
  • The Multiplier ε. volume now doubles, appropriately, from 1 drop → 2 drops → drops → 5 drops → 10 drops → 1 mL.
  • Once to 1 mL added, the titration is again fully At Sea, moving freely.
  • Once At Sea, five 1 mL additions are sufficient to finish the data set.

If the data was entered into a spreadsheet, the graph of potential vs. volume added displays for the class how the graph slope increases then decreases, just as was demonstrated in the student flowchart at loci E and ε. Adding a spreadsheet column with ΔpH/(volume added) can give a set of good two-point determinations of the slope, and from there it is easy to home in on the maximum. Analytical chemist may add a layer of precision, but with dropwise addition at the equivalence point, the maximum found is, for our purposes, a good equivalence point.     

Reaching the Pinnacle

Confirmatory Laboratories see the pinnacle of general chemistry laboratory class as connecting experiment to one or more Very Important Chemical Concepts (VICC’s). This often puts the instructor in the role of “Sherpa” who leads to the student “Climber” to the pinnacle of VICC’s. Students, impatient of the process, often have the attitude of “just give me the right answer.” However, this laboratory experiment is not specifically about VICC’s. 

This exercise is about learning something new and adding fun into creating technique. Before they realize it, they have lived and learned what a flowchart is and how a flowchart describes titration as a process. Before they realize it, they have worked as a team to perform chemical analysis with good data. In this day and age of science and engineering as a team sport, the students have stumbled into a laboratory class that is uniquely suited to creating teamwork through process. Before they realize it, they have reached what I consider the true pinnacle of general chemistry laboratory class, making the connection between technique, teamwork, and good data. With good data in hand, curiously enough, students can go down the mountain with the instructor, and they have the possibility—impossible without good data—of connecting the laboratory to VICC’s.

ACKNOWLEDGEMENTS: Thanks to the patience of students who have always been the locus of my teaching and were the loci in the flowcharts. Suzanne Q. Lomax ​for encouragement and assistance in manuscript preparation.

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1. flow·​chart ˈflō-ˌchärt. : a diagram that shows step-by-step progression through a procedure or system especially using connecting lines and a set of conventional symbols.  https://www.merriam-webster.com/dictionary/flowchart

2. Joseph F. Lomax, Using a Nautical Analogy for Successful Laboratory Tasks

3. Joseph F. Lomax, “Connecting Acid-Base and Redox Connections”