Processing Uncertainties in Chemistry (SL IB Chemistry)

What is uncertainty?

• Uncertainty is quantitative indication of the quality of the result 
  • It is the difference between the actual reading taken (caused by the equipment or techniques used) and the true value
  • It is a range of values around a measurement within which the true value is expected to lie and is an estimate
• Uncertainties are not the same as errors
  • Errors arise from equipment or practical techniques that cause a reading to be different from the true value
• Uncertainties in measurements are recorded as a range (±) to an appropriate level of precision

Table showing different uncertainties

	Uncertainty
in a reading	± half the smallest division
in a measurement	at least ±1 smallest division
in repeated data	half the range i.e. ± ½ (largest - smallest value)
in digital readings	± the last significant digit (unless otherwise quoted)

Types of uncertainty

• Uncertainty is grouped into three main types:

  • Absolute uncertainty

    • The actual amount by which the quantity is uncertain
    • e.g.if v = 5.0 ± 0.1 cm, the absolute uncertainty in v is 0.1 cm

  • Fractional uncertainty

    • The absolute uncertainty divided by the quantity itself
    • e.g.if v = 5.0 ± 0.1 cm, the fractional uncertainty in v is =

  • Percentage uncertainty

    • The ratio of the expanded uncertainty to the measured quantity on a scale relative to 100%
    • This is calculated using the following formula:

Percentage uncertainty = 

How to calculate absolute, fractional and percentage uncertainty

 

The key pieces of information from this burette reading are the smallest division and the reading

• The uncertainties in this reading are:
  • Absolute
    • Uncertainty = = 0.05 cm³ 
    • Reading = 19.6 ± 0.05 cm³ 
  • Fractional
    • Uncertainty =  =  =  cm³ 
  • Percentage
    • Uncertainty =  =  = 0.5%
    • Reading = 19.6 ± 0.5% cm³ 

Propagating uncertainties in processed data

• Uncertainty propagates in different ways depending on the type of calculation involved

 

Exponential measurements (HL only)

• When experimental measurements are raised to a power, you multiply the fractional or percentage uncertainty by the power

The coefficient of determination, R²