1. Chapter 11 Notes
Chapter 11.1
All measurement has a limit of precision and accuracy, and this must be taken into account when evaluating experimental results.

2. Terms for this section Uncertainty Significant figures
Addition/subtraction
Multiplication/division
Analogue vs digital instruments
Errors
Random errors
Systematic errors
Accuracy vs precision
Percentage
Uncertainty
Error
Propagation of uncertainty
Addition/subtraction
Mulitplication/division

3. Uncertainty in measurement
Uncertainty of the measurement is dependent on the instrument used
Analogue instruments
Many state the degree of uncertainty
If not stated, the uncertainty is +/- half the smallest division
Ex: if the graduated cylinder shows 40.0 ml, then the reported data with uncertainty should be /- 0.5 ml
Digital instruments
+/- the smallest scale division
Ex: if scale shows g, then the reported uncertainty should be / g

4. Experimental Errors: Random
Random error occurs when:
If there is an equal probability of an error being too high or too low. Exs:
Readability of instrument
Insufficient data
Effects of changes in surroundings (such as air currents or temp)
Observer misinterpreting reading
Can be reduced by repeated measurements
Should be repeatable and reproducible

5. Experimental Errors: Systematic
Systematic occurs when:
There is a poor experimental design or procedure
A specific directional result of data occurs. Exs:
Measuring volume from top of meniscus rather than bottom = vol levels that are too high
Overshooting volume of a liquid delivered in a titration = vol too high
Using indicator whose end-point does not correspond to equivalence point
Heat loss in exothermic rxn = smaller temp changes
Cannot be reduced by repeated measurements

6. Accuracy Vs Precision
Accuracy: Smaller systematic error, greater accuracy
Closer to accepted value
Precision: Smaller random uncertainties, greater precision
Closer to each others’ values (reproducible)
These should be discussed along with types of error (systematic and random) in all lab report conclusions!!!
Also, compare results in labs to literature values whenever possible in labs!!!

8. Percentage Uncertainties vs Percentage Error
Uncertainties can be expressed as a value or as a percentage
Fractional uncert = absolute uncertainty
meas. value
Ex: 0.5/25.7 = +/-0.02
Percentage uncert = absolute uncertainty
meas. value *100
Ex: 0.5/25.7 = +/- 2%
Percentage error is how close your value is to the accepted value (or literature value)
Percentage error = accepted value - experimental value accepted value *100

9. Propagation of Uncertainties: Addition and Subtraction
Note: Uncertainties need to match the end decimal of the measurement. Ex: /- 0.5 g
When adding or subtracting measurements, the uncertainties, find the max and min of the ranges and the average of the possible values.
And, Add the uncertainties
Ex: measurements – /- 0.1 g, /- 0.1 g
23.5: 23.6 or : 28.3 or 28.1
Max mass difference = = 4.9
Min mass difference = = 4.5
Mass difference is then = 4.7 +/- 0.2 g

10. Propagation of Uncertainties: Multiplication and Division

11. Significant Figures: Addition and Subtraction
The number of decimal places determines the sig figs (precision of calculated value)
Solve: (Assume digital measurements)
= _____ +/- _____
= _____ +/- _____
= _____ +/- _____
= _____ +/- _____

13. Read page 538 for lab conclusions/evaluations
If you calculated the possible max and min, how does this compare to the absolute uncertainty?
40.5*19.5 = (remember, 3 sig figs)
39.5*20.5 =
Are they within range?
800 +/- 30 mm2
Read page 538 for lab conclusions/evaluations