Overall Measurements Uncertainty

Quantitative Chemistry

What is percentage measurement uncertainty?

The measurement uncertainty expressed as a percentage of the measured value.

What is the formula for percentage uncertainty?

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

What determines the percentage uncertainty of a measurement?

The uncertainty of the apparatus and the size of the value being measured.

How does increasing the measured value affect percentage uncertainty?

It decreases the percentage uncertainty because the fixed uncertainty becomes a smaller proportion of the measurement.

Why does a burette have a total measurement uncertainty of ±0.10 cm³ in a titration?

Two readings are taken, each with an uncertainty of ±0.05 cm³, so the uncertainties are added.

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

(0.10 ÷ titre) × 100.

What is the percentage uncertainty of a 22.50 cm³ burette titre with ±0.10 cm³ uncertainty?

±0.44%.

What is the uncertainty of a 25 cm³ pipette?

±0.06 cm³.

What is the percentage uncertainty of a 25 cm³ pipette with ±0.06 cm³ uncertainty?

±0.24%.

Why is the pipette uncertainty only counted once?

Only one volume reading is taken.

What is the uncertainty of a 250 cm³ volumetric flask?

±0.3 cm³.

What is the percentage uncertainty of a 250 cm³ volumetric flask with ±0.3 cm³ uncertainty?

±0.12%.

What factors affect percentage uncertainty when using a balance?

The precision of the balance and the mass being weighed.

Why does weighing a larger mass reduce percentage uncertainty?

The fixed balance uncertainty becomes a smaller proportion of the measured mass.

When must balance uncertainty be counted twice?

When two balance readings are required to determine the mass, such as weighing by difference.

Why is balance uncertainty counted twice when weighing by difference?

The final mass is calculated from two separate balance readings, each with its own uncertainty.

How do you calculate percentage uncertainty when a balance reading is taken twice?

Percentage uncertainty = (2 × balance uncertainty ÷ mass measured) × 100.

A two-decimal-place balance has what measurement uncertainty?

±0.005 g per reading.

A marble chip has a mass of 3.57 g measured using a two-decimal-place balance. What is the percentage uncertainty if two readings are required?

(2 × 0.005 ÷ 3.57) × 100 = ±0.28%.

Why can a more precise balance still give a relatively large percentage uncertainty?

If the mass being measured is very small, the uncertainty is still a relatively large proportion of the measurement.

How can percentage uncertainty when using a balance be reduced?

Measure a larger mass where possible.

How can percentage uncertainty in a titration be reduced?

Use a larger titre where possible.

Why is a titre of 30 cm³ preferable to a titre of 10 cm³ for uncertainty?

The same absolute burette uncertainty represents a smaller percentage of 30 cm³.

How is overall percentage uncertainty estimated when several pieces of apparatus are used?

Add together the individual percentage uncertainties.

If the uncertainties are ±0.09%, ±0.12%, ±0.24% and ±0.47%, what is the overall percentage uncertainty?

±0.92%.

How do you convert an overall percentage uncertainty into an absolute uncertainty?

Absolute uncertainty = (percentage uncertainty ÷ 100) × calculated value.

If a concentration is 0.118 mol dm⁻³ with an overall uncertainty of 0.92%, what is the approximate absolute uncertainty?

About ±0.001 mol dm⁻³.

How would a concentration of 0.118 mol dm⁻³ with an uncertainty of ±0.001 mol dm⁻³ be written?

0.118 ± 0.001 mol dm⁻³.

What does 0.118 ± 0.001 mol dm⁻³ mean?

The true value is expected to lie approximately between 0.117 and 0.119 mol dm⁻³.

How can experimental uncertainty be minimised?

Use suitable precise apparatus and design the experiment so the main sources of uncertainty or error are reduced.

Why is simply using more decimal places not always the best way to improve an experiment?

Other sources of error may have a much greater effect on the final result.

In thermochemistry, what may be more important than using a more precise balance?

Reducing heat transfer to the surroundings.

Why should the largest sources of error be improved first?

Reducing them has the greatest effect on the accuracy and overall uncertainty of the final result.