1. Topic 11: Measurement and Data Processing
Honors Chemistry
Mrs. Peters
Fall 2014

2. 11.1 Uncertainty and Error in Measurement
Measurement is important in chemistry.
Many different measurement apparatus are used, some are more appropriate than others.
Have out each of the different types of measurement devices, have students walk around and record what they notice about the increments and measurements of each item.

3. 11.1 Uncertainty and Error in Measurement
Example: You want to measure 25 cm3 (25 ml) of water, what can you use?
Beaker, volumetric flask, graduated cylinder, pipette, buret, or a balance
All of these can be used, but will have different levels of uncertainty. Which will be the best?
Have out each of the different types of measurement devices, have students walk around and record what they notice about the increments and measurements of each item.

4. A & S 1. Systematic Errors
Systematic Error: occur as a result of poor experimental design or procedure.
Cannot be reduced by repeating experiment
Can be reduced by careful experimental design

5. A & S 1. Systematic Errors
Systematic Error Example: measuring the volume of water using the top of the meniscus rather than the bottom
Measurement will be off every time, repeated trials will not change the error

6. A & S 1. Random Error
Random Error: imprecision of measurements, leads to value being above or below the “true” value.
Causes:
Readability of measuring instrument
Effects of changes in surroundings (temperature, air currents)
Insufficient data
Observer misinterpreting the reading
Can be reduced by repeating measurements

7. A & S 1: Random and Systematic Error
Systematic and Random Error Example
Random: estimating the mass of Magnesium ribbon rather than measuring it several times (then report average and uncertainty)
g, g, g, g, g, g
Avg Mass= g

8. A & S 1: Random and Systematic Error
Systematic and Random Error Example
Systematic: The balance was zeroed incorrectly with each measurement, all previous measurements are off by g
g, g, g, g, g, g
Avg Mass =

9. A & S 8. Distinguish between precision and accuracy in evaluating results
Precision: how close several experimental measurements of the same quantity are to each other
how many sig figs are in the measurement.
Smaller random error = greater precision

10. Accuracy: how close a measured value is to the correct value
A & S 8. Distinguish between precision and accuracy in evaluating results
Accuracy: how close a measured value is to the correct value
Smaller systematic error = greater accuracy
Example: masses of Mg had same precision, 1st set was more accurate.

11. U 5. Reduction of Random Error
Random errors can be reduced by
Use more precise measuring equipment
Repeat trials and measurements (at least 3, usually more)

12. A & S 2. Uncertainty Range (±)
Random uncertainty can be estimated as half of the smallest division on a scale
Always state uncertainty as a ± number

13. A & S 2. Uncertainty Range (±)
Example:
A graduated cylinder has increments of 1 mL
The uncertainty or random error is
1mL / 2 = ± 0.5 mL

14. A & S 2. Uncertainty Range (±)
Uncertainty of Electronic Devises
On an electronic devices the last digit is rounded up or down by the instrument and will have a random error of ± the last digit.
Example:
Our balances measure ± 0.01 g
Digital Thermometers measure ± 0.1 oC

15. State uncertainties as absolute and percentage uncertainties
Absolute uncertainty
The uncertainty of the apparatus
Most instruments will provide the uncertainty
If it is not given, the uncertainty is half of a measurement
Ex: a glass thermometer measures in 1oC increments, uncertainty is ±0.5oC; absolute uncertainty is 0.5oC

16. State uncertainties as absolute and percentage uncertainties
Percentage uncertainty
= (absolute uncertainty/measured value) x 100%

17. Determine the uncertainties in results
Calculate uncertainty
Using a 50cm3 (mL) pipette, measure 25.0cm3. The pipette uncertainty is ± 0.1cm3.
What is the absolute uncertainty?
0.1cm3
What is the percent uncertainty?
0.1/25.0 x 100= 0.4%

18. Determine the uncertainties in results
Calculate uncertainty
Using a 150 mL (cm3) beaker, measure 75.0 ml (cm3). The beaker uncertainty is ± 5 ml (cm3).
What is the absolute uncertainty?
5 ml (cm3)
What is the percent uncertainty?
5/75.0 x 100= 6.66%  7%

19. Determine the uncertainties in results
Percent error = I error l x 100
accepted
When…
Percent error > Uncertainty
Systematic errors are the problem
Uncertainty > Percent error
Random error is causing the inaccurate data

20. Determine the uncertainties in results
Error Propagation: If the measurement is added or subtracted, then absolute uncertainty in multiple measurements is added together.

21. Determine the uncertainties in results
Example:
If you are trying to find the temperature of a reaction, find the uncertainty of the initial temperature and the uncertainty of the final temperature and add the absolute uncertainty values together.

22. Determine the uncertainties in results
Example: Find the change in temperature
Initial Temp: 22.1 ± 0 .1oC
Final Temp: 43.0 ± 0.1oC
Change in temp: = 20.9
Uncertainty: = 0.2
Final Answer: Change in Temp is 20.9 ± 0.2 oC

23. Determine the uncertainties in results
Error Propagation: If the measurement requires multiplying or dividing: percent uncertainty in multiple measurements is added together.

24. Determine the uncertainties in results
Example:
If you are trying to find the density of an object, find the uncertainty of the mass, the uncertainty of the volume, you add the percent uncertainty for each to get the uncertainty of the density.

25. Determine the uncertainties in results
Example: Find the Density given:
Mass: ± 0.01 g and Volume: 10.3 ± 0.05 mL
Density: /10.3 = 2.47 g/mL
% uncertainty Mass: (0.01/25.45) x 100 = 0.04%
% uncertainty Volume: (0.05/10.3) x 100 = .5%
= .54%
Final Answer: Density is 2.47 ± .54%

26. Determine the uncertainty in results
Uncertainty in Results (Error Propagation)
1. Calculate the uncertainty
a. From the smallest division (on a graduated cylinder or glassware)
b. From the last significant figure in a measurement (a balance or digital thermometer)
c. From data provided by the manufacturer (printed on the apparatus)
2. Calculate the percent error
3. Comment on the error
a. Is the uncertainty greater or less than the % error?
b. Is the error random or systematic? Explain.