Measurement Errors and Measurement Uncertainties

Quantitative Chemistry

What is a random error?

An error caused by unpredictable variations in conditions or measurements.

What can cause random errors?

Unpredictable changes such as temperature, pressure, draughts or small differences in how a reading is taken.

What is a systematic error?

An error that is constant or predictable and causes recorded values to be consistently too high or too low.

What commonly causes systematic errors?

Incorrectly calibrated or faulty apparatus.

What is the key difference between random and systematic errors?

Random errors cause unpredictable variation between measurements, whereas systematic errors consistently shift measurements in the same direction.

Give an example of a random error when measuring gas volume.

Changes in atmospheric pressure or laboratory temperature can cause the measured gas volume to vary.

Give an example of a random error when using a balance.

Changes in temperature, draughts or water vapour condensation can cause the recorded mass to vary slightly.

Give an example of a random error when using a water bath.

The temperature fluctuates slightly as the heater switches on and off.

How can the effect of random errors be reduced?

Repeat the experiment and calculate a mean.

Why does repeating measurements reduce the effect of random errors?

Random fluctuations become less significant when several measurements are averaged.

Does repeating an experiment remove systematic errors?

No, because the same systematic error affects every measurement in a similar way.

Give an example of a systematic error involving a pipette.

A pipette may be incorrectly calibrated so that it consistently delivers less or more than its stated volume.

A 25.0 cm³ pipette consistently delivers less than 25.0 cm³. What type of error is this?

A systematic error.

Give an example of a systematic error involving a thermometer.

An incorrectly calibrated thermometer may consistently record a temperature higher or lower than the true temperature.

Give an example of a systematic error involving a measuring cylinder.

Incorrectly positioned graduation markings could make every measured volume consistently too high or too low.

What type of error can occur if the meniscus is viewed from slightly different angles each time?

A random error.

What type of error occurs if the meniscus is consistently viewed from above?

A systematic error.

How should a meniscus be viewed to minimise measurement error?

At eye level, horizontally with the liquid level.

What is measurement uncertainty?

The potential error involved when using a piece of apparatus to make a measurement.

What determines the size of measurement uncertainty?

The precision of the measuring apparatus.

Does measurement uncertainty mean that an error definitely occurred?

No. It describes the potential error associated with the measurement.

How does increasing the precision of apparatus affect measurement uncertainty?

More precise apparatus has a smaller measurement uncertainty.

What is the measurement uncertainty of a balance reading to 1 decimal place?

±0.05 g.

What is the measurement uncertainty of a balance reading to 2 decimal places?

±0.005 g.

What is the measurement uncertainty of a balance reading to 3 decimal places?

±0.0005 g.

Why does a balance with more decimal places have a smaller uncertainty?

It has a greater degree of precision.

What is the measurement uncertainty of a 50 cm³ burette for one reading?

±0.05 cm³.

Why is the total measurement uncertainty of a burette titre ±0.10 cm³?

A titre requires two burette readings, an initial and a final reading, each with an uncertainty of ±0.05 cm³.

What is the measurement uncertainty of a 25 cm³ pipette?

±0.06 cm³.

What is the measurement uncertainty of a 250 cm³ volumetric flask?

±0.3 cm³.

What is the formula for percentage uncertainty?

Percentage uncertainty = (absolute uncertainty ÷ measured value) × 100.

How do you calculate the percentage uncertainty of a burette titre?

Percentage uncertainty = (0.10 ÷ titre) × 100.

How can percentage uncertainty in a burette titre be reduced?

Use a larger titre so the fixed absolute uncertainty is a smaller percentage of the measured value.

Why is a pipette generally better than a measuring cylinder for accurately measuring a fixed volume?

A pipette has a smaller measurement uncertainty and therefore greater precision.

Why should a beaker not normally be used for accurate volume measurements?

Its graduations are only approximate and are intended as a guide.

What should be used instead of a beaker when an accurate volume measurement is required?

Appropriate volumetric glassware such as a pipette, burette or volumetric flask.

What are Class A and Class B glassware?

Standards of laboratory glassware based on calibration accuracy.

Which is more accurate, Class A or Class B glassware?

Class A glassware.

Why is Class A glassware generally more expensive?

It is calibrated to tighter tolerances and therefore provides greater accuracy.

Can Class B glassware still be used for accurate measurements?

Yes, it can still provide a high degree of accuracy when used correctly.

At what temperature is volumetric glassware commonly calibrated?

20°C.

Why can temperature affect volumetric glassware measurements?

The glass and solution expand when heated, changing the volume.

What happens to the volume of glassware above its calibration temperature?

The glass expands, so the actual volume it contains changes.

How can measurement uncertainty in volumetric analysis be minimised?

Use precise calibrated apparatus correctly, read the meniscus at eye level and choose apparatus with a small uncertainty relative to the measured quantity.