Food Analysis Lab · LAB WEEK 1

Volumetric glassware calibration (gravimetric method)

Volumetric Glassware Calibration by Gravimetry

Food Analysis Lab · 4-hour session · 6 interactive mini-games
ISO 4787 gravimetric method · Tanaka density equation · buoyancy correction · intro to data QC

TC (To Contain) vs TD (To Deliver)Class A ±0.02 mLBuoyancy correctionRSD% / 95% CIISO/IEC 17025

Pre-lab video (about 2 min) (Chinese narration)

Watch before class: does your 10 mL pipette really deliver 10 mL?

Contents: gravimetric method → convert water temperature to density → air buoyancy correction → accuracy vs precision, systematic vs random error. (Hand-drawn animation) Open on YouTube →

interactive lab

The truth about a tube of water: Predict → Observe → Explain

Six scenes: predict → TC/TD last drop → read the scale → weigh to get volume → significant ≠ failing → class forest plot; answer correctly to unlock the next scene. Open the lab in a new tab ↗

Think first

Does the 10 mL pipette in your hand
really deliver 10 mL?

Testing labs must calibrate volumetric glassware regularly under ISO/IEC 17025 (the international accreditation standard for the competence of testing and calibration laboratories). The international standard ISO 4787 specifies how to calibrate glass volumetric ware by the “gravimetric method”.
Today you will verify for yourself whether your own pipette and burette are truly “accurate”.

Lab accreditationMeasurement uncertainty (W8) Data QCCorrect record-keeping

Today’s learning goals

Four things you will be able to do after this class

⚖️

Run a gravimetric calibration

Operate the analytical balance and volumetric glassware correctly and complete a 10-replicate gravimetric calibration

🧮

Calculate the true volume

Use the buoyancy-correction formula V=m×F_b/ρ_w to convert apparent mass into actual volume

📊

Judge pass or fail

Judge data quality with the mean, SD, RSD%, and 95% CI, and compare with the Class A tolerance (the maximum error allowed for the highest grade of volumetric glassware)

📝

Understand accuracy vs precision

Tell systematic error from random error, and know that “accurate” and “steady” are not the same thing

Principles 1/2

TC (To Contain) vs TD (To Deliver), Class A tolerance

Instrument	Grade	Tolerance	Standard
10 mL volumetric pipette	Class A	±0.02 mL	ASTM E969
50 mL burette	Class A	±0.05 mL (full length)	ASTM E287
Same-capacity glassware	Class B	Tolerance is about 2× that of Class A	—

Principles 2/2

Reading, delivery, and temperature: the fine points

👁️

Parallax

Read the meniscus at eye level; looking from above misjudges the volume

⏱️

Delivery time and touching the wall

Burettes and volumetric pipettes need a fixed waiting time when delivering; finally touch the tip to the flask wall (tip touch-off). For a regular volumetric pipette (TD, To Deliver), the last small drop left in the tip must “not” be blown out — calibration never counts that drop

🌡️

Temperature changes density

Water density varies with temperature; to convert the measured “mass” back to “volume”, you must know the water temperature at the time

🎈

Air buoyancy correction

The balance weighs in air, and the buoyancy on the weights and on the water differs, so a buoyancy correction is needed; the magnitude is about 0.1%

Mini-game ①TC (To Contain) vs TD (To Deliver)0 / 6

You just learned TC (To Contain) / TD (To Deliver): sort 6 pieces of volumetric glassware/statements into “TC (To Contain)” or “TD (To Deliver)”.

Before we start: instrument calibration

Balance, thermometer, and water all need to be “ready”

⚖️

Daily analytical balance check

Before class, check the balance with standard weights; make sure the level bubble is centered; close the draft shield

🌡️

Thermometer

Used to measure water temperature; keep it in the same environment as the balance and read to 0.1 °C

💧

Equilibrate water to room temperature

Place distilled/deionized water in the lab ahead of time so it matches room temperature, avoiding errors from temperature drift while weighing

📋

Know your glassware

Confirm the model, measuring range, and whether the volumetric pipette/burette is Class A

Core procedure

How to do the gravimetric method

Volumetric pipette: cap the weighing bottle and tare → draw 10.00 mL of water and deliver it into the bottle → cap and weigh immediately (to 0.1 mg) → record water temperature → repeat 10 times
Burette: fill and read the initial level → deliver to 25.00 mL → weigh → repeat 10 times
Apparent mass m_app: the number read directly on the balance in air, before air buoyancy is removed; it is converted to volume in the next step

Today's schedule

How the four hours are divided

🕐 0:00–0:40

Explanation and demo

Balance operation, gravimetric steps, how to record long-format data

🕑 0:40–2:00

Pipette, 10 replicates

Each person uses the 10 mL volumetric pipette to measure water, weigh, and record temperature

🕓 2:00–3:30

Burette, 10 replicates

Operate the 50 mL burette, deliver to 25.00 mL, and weigh

🕟 3:30–4:00

Data entry and checking

Save the data in the shared sheet and flag outliers that look like typos

“Long format” = one row holds only one measurement; the other columns (group, student, item, rep, value, unit, temp_C, note) say who made it, which repeat, the unit, and the water temperature — so the whole class's data can be merged directly.

Safety and waste

Three rules you must follow

🚫

Never pipette by mouth

Always use a pipette bulb or pipette pump; mouth pipetting is strictly forbidden

🧹

Broken glass disposal

Put broken glassware in the dedicated broken glass box, never in the regular trash

🧽

Clean the balance as you go

After weighing, wipe the balance pan and surroundings so water stains don't affect the next student's readings

Mini-game ②Ordering the gravimetric calibration steps— / 6

Use ▲▼ to put the 6 steps of gravimetric calibration in the correct order.

Data processing

From apparent mass to true volume

V = m_app × F_b / ρ_w

F_b = 1 + ρ_air(1/ρ_w − 1/ρ_weights)

ρ_air=0.0012 g/mL ρ_weights=8.0 g/mL ρ_w is obtained from the Tanaka (2001) equation — the internationally accepted “density–temperature” formula for pure water, from which the table below was calculated.

Example: water delivered from a volumetric pipette has an apparent mass of 9.9700 g at a water temperature of 25.0 °C. ρ_w(25.0°C) = 0.997047 g/mL, F_b ≈ 1.00105 → V ≈ 10.010 mL.

Water temp. (°C)	20	22	24	25	26	28
ρ_w (g/mL)	0.998207	0.997773	0.997299	0.997047	0.996786	0.996235

Mini-game ③Calculation challenge: actual burette volumeUnanswered

The apparent mass of water delivered from the burette is m_app = 24.9215 g at 23.0 °C (ρ_w = 0.997541 g/mL, F_b ≈ 1.00105). Find the actual volume V (mL) to 3 decimal places. Formula: V = m_app × F_b / ρ_w.

Data QC

Mean, SD, RSD%, 95% CI, and bias

Mean, SD: central tendency and spread of the 10 replicates
RSD% = SD/mean × 100: relative spread; the smaller, the more “precise”
95% CI = mean ± t×SD/√n (n=10, t=2.262)
bias = mean − nominal value (10.00 or 25.00 mL): the closer to 0, the more “accurate”
Significant figures: report the CI to 1–2 significant figures and the mean to the same decimal place

Mean bias and 95% CI range (floating bars) for 5 illustrative students; dashed lines are the ±0.02 mL tolerance — illustrative data, not real measurements.

How to read a 95% CI

Significant ≠ failing

📐

SD and t

SD (standard deviation) describes how spread out the data are; t=2.262 is the multiplier from the t table for n=10 (9 degrees of freedom); the smaller n is, the larger t is

🔍

Is the bias significant?

The 95% CI covers the nominal value (the CI of the bias contains 0) → statistically not significant, possibly just random fluctuation; if it does not cover it → significant bias

✅

Does it pass?

Also compare with the Class A tolerance: |bias| ≤ 0.02 mL (pipette). In the figure, student E: the CI contains 0 but the bias exceeds the limit → still needs attention

Statistics site Ch02 Confidence interval ↗

The two main types of error

Systematic error vs random error

	Systematic error (determinate error)	Random error (indeterminate error)
Direction	Always off to the same side (always high or always low)	Sometimes positive, sometimes negative, no fixed direction
Cause	A specific cause can be found: instrument, method, operating habit	Many tiny variations add up; no single cause can be named
Which metric it affects	Mean departs from the true value → bias (accuracy)	Data scatter → SD, RSD% (precision)
Does repeating cancel it?	No; even the average of 100 runs is still off	The mean becomes steadier and the CI narrower, but each run still fluctuates
What to do	Find it → calibrate or correct (e.g., buoyancy correction F_b)	Increase replicates and describe with SD and 95% CI

The same action can cause either: the waiting time after delivery — if you never wait long enough, the delivered volume is always low → systematic error; if the waiting time varies each time, the delivered volume fluctuates → random error. The key to deciding is “is the direction fixed?”.

A third type of error

Gross error: caught by checking

Gross error = misreading, miscopying, mistyping: 10.00 read as 1.000, a misplaced decimal point, a wrong unit, weighing without the cap
It is neither systematic nor random error, and statistics cannot “average it out”
How to catch it: after entry, compare with your other 9 replicates and with classmates in your group; if it differs a lot, it is suspicious
What to do: flag the reason in the note column, keep the original value, and redo it if possible — never delete it silently
W8 will teach a formal outlier test (Grubbs)

Practice 1/3

Work through it with today's class data

Predict first (2 min): write down whether you think your RSD will be below 1%. Will your mean be high or low?
Calculate by hand once (10 min): use only a calculator to get the mean, SD, and RSD of your own 10 values. The goal is to understand where SD comes from, not to practice button pressing
Check in Excel: use the functions in the table at right; the range must cover all 10 values
Compute the 95% CI: mean ± t × SD/√n; for n=10, t=2.262
Place it in the class plot: see where you land on the forest plot (next page)

What to calculate	Excel function	In plain words
Mean	`=AVERAGE(range)`	Add the 10 values and divide by 10
SD	`=STDEV(range)`	The “typical” distance of each value from the mean
RSD%	`=SD/mean*100`	SD as a percentage of the mean
t value	`=TINV(0.05,9)`	Look up n=10 to get 2.262
CI half-width	`=t*SD/SQRT(10)`	Mean ± this number = 95% CI

📥 Class measurement data (0.2 mL pipette, student IDs anonymized) + correct formulas ⬇ (Chinese) Every column is a formula; click a cell to see how it was calculated.
🕵️ Want to play it as a challenge? Data Detective ↗
🔐 Want an escape-room challenge? Calibration Room Escape ↗

Practice 2/3

Class forest plot: see at a glance who is accurate and who is steady

Dots = mean, horizontal lines = 95% CI, red dashed line = nominal value 200 µL
Shorter line = more precise (small SD); closer to the red line = more accurate (small bias)
Orange = CI touches the red line (S08, S11), but that is because the line is so long, not because they are accurate
The other 13 students all fall to the left of the red line (mean about 191 µL, about 4% low) — a consistent direction is a sign of systematic error; look for the cause together

Pipette 0.2 mL, water at 32 °C, V = m×F_b/ρ_w (ρ_w=0.99503, F_b=1.0011), n=10, measured 2026-09-29.

Practice 3/3

Spot the error: what is wrong with this spreadsheet?

📏

Error 1: only 8 values used

The range for mean/SD is written as P2:W2 (8 cells), missing X and Y.
Example: S14's 10th value 0.1970 is left out → RSD shows 0.26% (looks “excellent”); the correct 10-value RSD is 1.38%

🏷️

Error 2: mislabeled column

The “95% CI” column formula is =mean/0.9956, which is just the volume conversion of mass divided by density, unrelated to the confidence interval (and it omits F_b too).
Correct: mean ± 2.262×SD/√10

🎯

Error 3: two errors cancel each other

S11's 7th and 8th values are 0.2487 and 0.1353 (normal is about 0.19). The cumulative column looks smooth, but the individual values swing one high, one low → RSD 14%. This is a gross error: go back to the raw record, flag it, and don't silently delete it

How to prevent it: ① after selecting the range, check the status bar for “Count=10”; ② column titles must match the formulas; ③ a normal cumulative column ≠ normal individual values, so check both columns. Think about it: S11's two extreme values both inflate the SD, so a test based on “how many SDs from the mean” cannot see them — W8 covers the Grubbs test; come back to this example then.

Mini-game ④Spot-the-error in practice: class data0 / 4

Mini-game ⑤Systematic vs random error0 / 8

Use the principles you just learned (is the direction fixed? can a cause be found?) to sort 8 scenarios into “systematic error” or “random error”.

Mini-game ⑥Decision challenge: judging accuracy and precision0 / 5

Mini-game ⑦Instant quiz on common mistakes0 / 5

Homework

Open Colab and swap in the class data

Open NB01_volumetric_calibration.ipynb ↗
Not coding yet? Start with the Excel practice workbook EX01 ⬇ and do the same calculations; the answers should match Colab. To see distributions and outliers, open Orange workflow OR01 ↗
Swap the sample data for the measured data in the class's shared Google Sheet; first use the version with correct formulas ⬇ to find the errors in your own sheet
Complete the 5 exercises in the notebook (buoyancy correction, mean/SD/CI, comparison with tolerance…)

📄

Report requirements

Each student: one “mean ± CI” table (one row each for pipette and burette); mark whether the bias exceeds the tolerance; one paragraph discussing possible error sources (systematic/random)

Further reading: Food Analysis Statistics site ↗ (confidence interval chapter)

Self-check

By the end of today you should be able to…

✓Distinguish TC (To Contain) from TD (To Deliver) glassware and state the Class A tolerances (10 mL pipette ±0.02 mL, 50 mL burette ±0.05 mL)
✓Read the meniscus correctly and know how parallax arises
✓Carry out the full gravimetric method: tare weighing bottle → measure water → weigh → record temperature → repeat 10 times
✓Explain why the air buoyancy correction is needed and roughly how large it is (~0.1%)
✓Use V = m_app × F_b / ρ_w to calculate the actual volume
✓Calculate mean, SD, RSD%, 95% CI (and check that the spreadsheet range covers all 10 values), and read the class forest plot to judge whether bias exceeds the tolerance
✓Tell systematic error from random error and understand that “precise” does not mean “accurate”
✓Enter data correctly into the long-format shared sheet and flag suspicious data

Tap to tick — make sure you really can do it.

Next step · NEXT

Turn calibration data
into a report

📌 After class: finish the 5 Colab NB01 exercises and upload the report
🔜 Bridge: every measurement in later lab weeks rests on “trusting your own glassware”
🧪 Think: if the bias exceeds the tolerance, is it systematic or random error? What should you do about it?

Gravimetric methodBuoyancy correction95% CITC/TD (To Contain / To Deliver)QC