Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

7.3.3Additional lessons

Processing Uncertainties in Chemistry — IB Chemistry HL Revision Notes & Topical Questions

5 min read 6 parts Lesson 165 of 172

📚 IB Chemistry HL Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
0%read

Section 1 of 6Types of Uncertainty

Every measurement is only an estimate, and uncertainty states how good that estimate is.

Random uncertainty
  • Random uncertainty These errors vary unpredictably between readings, so repeating the measurement and averaging reduces their effect.
Systematic error
  • Systematic error The same error affects every reading in one direction,
    • such as a thermometer that reads 1 °C too high,
    • and repetition does not remove it.
Absolute uncertainty
  • Absolute uncertainty The size of the possible error in the units of the measurement, written as ± a number.
Percentage uncertainty
  • Percentage uncertainty Absolute uncertainty divided by the measured value, multiplied by 100, which allows fair comparison between measurements.

Section 2 of 6Propagating Uncertainty

Propagating Uncertainty
Adding or subtracting
  • Adding or subtracting Add the absolute uncertainties, as in a titre found from two burette readings.
Multiplying or dividing
  • Multiplying or dividing Add the percentage uncertainties of the values being multiplied or divided.
Powers
  • Powers Multiply the percentage uncertainty by the power to which the value is raised.
Final answer
  • Final answer Round the uncertainty to one significant figure and quote the result to the same decimal place.

Section 3 of 6Working Through an Uncertainty Calculation

1
List each measured value with its absolute uncertainty and convert each to a percentage uncertainty.
2
Decide whether each step in the calculation is an addition, a multiplication or a power.
3
Combine the uncertainties by the rule that matches each step.
4
Convert the total percentage uncertainty back to an absolute value by multiplying by the final result.
5
Compare the total uncertainty with the difference from the accepted value to judge whether the error is explained.

Section 4 of 6Using Uncertainty in Evaluation

Dominant source
  • Dominant source The measurement with the largest percentage uncertainty has the biggest effect, and improving it gives the largest gain.
Percentage error
  • Percentage error Calculate the difference from the literature value divided by the literature value, multiplied by 100.
Explained or not
  • Explained or not If the percentage error is smaller than the total uncertainty, random uncertainty may explain the difference;
    • otherwise a systematic error is likely.
Range
  • Range The spread of repeat results gives an estimate of the random uncertainty, which can be shown with error bars.

Section 5 of 6Worked Example

Question

  • In a calorimetry experiment 50.0 g of water (±0.1 g) rises in temperature by 8.0 °C, from two thermometer readings each ±0.5 °C.
  • Calculate q = mcΔT with its uncertainty, taking c = 4.18 J g⁻¹ K⁻¹ as exact.

  1. q = 50.0 × 4.18 × 8.0 = 1672 J = 1.7 kJ.
  2. Percentage uncertainty in mass = 0.1 ÷ 50.0 × 100 = 0.2 %.
  3. ΔT uncertainty = 0.5 + 0.5 = ±1.0 °C, which is 1.0 ÷ 8.0 × 100 = 12.5 %.
    • Total = 0.2 + 12.5 = 12.7 %, and 12.7 % of 1672 J is about 212 J, rounded to 0.2 kJ.

Answer q = 1.7 ± 0.2 kJ

Section 6 of 6Exam Checklist & Tips

7.3.3 – Key Points for the Exam

  • Random error A scatter in readings that varies unpredictably from one measurement to the next.
  • Systematic error A consistent offset in the readings caused by the method or the instrument.
  • Absolute uncertainty The possible error in a value, in the same unit as the value.
  • Percentage uncertainty The absolute uncertainty as a percentage of the measured value.
  • Error propagation Combining the uncertainties of individual measurements to find the uncertainty in a calculated result.

Common Mistakes

  • Adding percentage uncertainties for a subtraction, when absolute uncertainties should be added.
  • Quoting uncertainties to many significant figures, when one figure is normally enough.
  • Treating a systematic error as if averaging more readings would remove it.
  • Ignoring the uncertainty of the temperature change, which is often the largest one in calorimetry.

Last updated:

\n