SCIENCE · INVESTIGATE AND EXPLAIN

Infer a constant from an actual electrometric titration

Reconstruct apparent pK from historical NBS observations, distinguish derived columns from measurements, and inspect the authors’ endpoint exclusion.

Learning outcome: Use a documented measurement chain to infer an equilibrium quantity while preserving activity conventions and evidence limits.

Starting recap

pK means −log₁₀K. A species mole ratio equals its concentration ratio when both share the same solution volume; an activity correction can still be necessary.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

A published observation gives pH 4.818 and log₁₀(A⁻/HA) = 0.177. Does subtracting those two numbers finish the inference?

Open the experiment

Predict

Predict how omitting the +0.114 activity term changes pK′ and the inferred apparent K. Decide whether a correct calculation makes a near-endpoint observation equally reliable.

Your prediction and reason

Experiment

Repair the proposed apparent pK′ for a central row. Compare another central row and both near-endpoint rows. Capture a retained and an excluded observation, identify measured versus derived inputs, and explain why a selected-row mean cannot replace the authors’ full-table average.

Reconstruct an apparent equilibrium constant from a historical measurement

Historical measured and derived reference evidence · Selected historical reference observations: Bates, Siegel and Acree (1943), Table 5, experiment 4, acetic acid at 25 °C and ionic strength 0.0998. EMF is in historical international volts; pH, corrected species amounts and log ratios are derived source columns. Recalculation uses rounded printed inputs. No new measurement, modern recommended constant, independent uncertainty interval or safety procedure is supplied.

Published observation (acid added): 1.994 mmol acid added row Your proposed apparent pK′: 4.641 dimensionless

Reset keeps your prediction, captures and practice history.

From measured voltage to an apparent constant

Experiment 4: 25 °C; initial acetate 4.984 mmol in 100 mL of 0.05-m sodium chloride; ionic strength 0.0998. These are historical source conditions, not instructions for an experiment.

E°′ = 0.30606 Int. V and k = 0.05914 Int. V. Recomputing from printed EMF gives pH 4.818397; the source prints 4.818. Rounded columns need not reproduce every final digit.

Corrected HA = 1.991 mmol; A⁻ = 2.993 mmol. Their printed log ratio is 0.177. These amounts already incorporate the authors’ dissociation correction; they are not independently measured species counts.

4.818 − (0.177) + 0.114 = 4.755. Your proposal differs by -0.114. Apparent K = 10⁻ᵖᴷ′ = 1.757924e-5; this is not the thermodynamic K.

Selected Table 5 rows, not the complete data or independent repetitions
Acid added (mmol)	pH	log ratio	Published pK′	Authors’ averaging decision
1.994	4.818	0.177	4.755	Retained
2.505	4.638	-0.003	4.755	Retained
3.013	4.458	-0.182	4.754	Retained
4.839	3.322	-1.298	4.734	Excluded (>95% neutralization)
4.940	3.168	-1.431	4.713	Excluded (>95% neutralization)

This observation is at 39.95% neutralization by corrected HA / initial acetate. The authors excluded the last two observations from experiment 4. The falling tail is visible; it does not by itself prove a unique error mechanism.

Apparent versus thermodynamic: what the source actually reports

The complete experiment 4 average is pK′ = 4.753, not the mean of our five selected rows. Table 8 applies a literature-based correction of 0.005 to obtain pK = 4.748. Its mean across experiments 4–6 is pK = 4.754. These are distinct calculations and a selected 1943 determination, not a present-day best value.

The paper estimates pH accuracy around ±0.01. Shared calibrations and derived columns prevent treating every printed value as an independent confidence interval. This widget supplies no statistical confidence claim. Changing an activity convention consistently also changes the calibrated potential; do not vary 0.114 alone as an independent physical perturbation.

Bates, Siegel and Acree (1943), equations 6–7 and Tables 5, 7–8. Public-domain federal research; displayed values visually checked against the primary scan.

Calculated values on the same fixed scale
Row	Quantity	Value (pK)
1	Without activity term	4.641
2	Reconstructed apparent pK′	4.755
3	Your proposed pK′	4.641

Repair the sign and activity term in pK′ = pH − log₁₀(A⁻/HA) + 0.114.

Reconstructed pK′ 4.755; published 4.755. This observation belongs to the range retained in the authors’ average. Matching arithmetic does not establish thermodynamic pK or an independent replication.

Observation to attach to a capture

Captures retain a selected historical observation and your apparent pK proposal. Replay reconstructs rounded published arithmetic; it is not a new titration, independent replication or thermodynamic constant measurement.

Understand

A constant needs a measurement chain

A 1943 National Bureau of Standards study reports an electrometric titration of acetate. At one observation, the corrected cell voltage is 0.59102 international volts. The authors derive pH 4.818 and a logarithmic acetate-to-acetic-acid ratio of 0.177. Your first task is to reconstruct the apparent equilibrium constant, not to treat pH itself as the constant.

Use the lab to repair the proposed pK′. Then compare a central observation with the two observations nearest complete neutralization. State which quantities were measured, which were derived, and which correction belongs to the source’s convention.

Read the symbols before calculating

For the dissociation HA ⇌ H⁺ + A⁻, HA denotes undissociated acetic acid and A⁻ denotes acetate. A lower pK corresponds to a larger K because pK = −log₁₀K. A prime marks the paper’s apparent pK′ at a stated ionic strength; it must not disappear from the conclusion.

The source reconstruction is pK′ = pH − log₁₀(M_A/M_HA) − log₁₀(fᵢ). Here M_A and M_HA are corrected species mole amounts in the same volume. Their ratio is dimensionless. The paper supplies −log₁₀(fᵢ) = 0.114 for this experiment. Thus 4.818 − 0.177 + 0.114 = 4.755. Omitting the term gives 4.641 and overestimates apparent K by the factor 10^0.114, about 1.30.

The calibrated potential E°′ and voltage slope k connect EMF to pH. Both use the paper’s historical international-volt convention; this lesson does not silently convert those readings to modern SI volts. Recomputing rounded source columns can differ in the last displayed digit.

Inspect the observations before summarizing

The last two experiment 4 observations exceed 95% neutralization and were excluded from the authors’ average. Their reconstructed pK′ values are lower than the central values. Correct arithmetic does not repair an unsuitable observation, establish its error mechanism, or make repeated readings independent.

Our five rows are an intentionally selected teaching excerpt. Do not average them and label the result the paper’s full experiment. The complete-table apparent average 4.753 receives a separate literature-based 0.005 correction to give thermodynamic pK 4.748 for experiment 4. The paper’s cross-experiment mean 4.754 is yet another quantity. None is claimed as a current recommended constant.

Transfer the method, not a memorized correction

Experiment 6 uses a different ionic strength and activity term 0.104. The nearby practice asks you to reconstruct its apparent pK′. Explain why using experiment 4’s correction would be a context error even if the subtraction is flawless.

Record a central and an excluded observation in your notebook. Explain what further calibration, activity-model and uncertainty information would be needed for an independent modern determination. These are public historical data, not an unseen assessment or a laboratory procedure.

Sources and continuation

Bates, Siegel and Acree, Journal of Research of the National Bureau of Standards 30 (1943), 347–359, equations 6–7, Tables 5, 7 and 8. The selected original federal research is public domain. Original learner questions and reconstructions are separate from the source measurements.

Return to equilibrium particle construction to compare a fully stipulated model with this measured-and-inferred evidence chain, or use the Unit 7 mixed evidence review.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain why the apparent pK′ differs from thermodynamic pK. Which evidence supports the endpoint exclusion? What information would you still need to assign a confidence interval or claim a current best constant?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Construct and challenge an equilibrium quotient Next: Build an equilibrium particle diagram with an honest scale

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.