Measurements and Uncertainties

1
Measurements and Uncertainties

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

2
Resources Available

• Zumdahl Appendix A1.5-A1.6
• Exp. DD Uncertainties in Measurements and Error
  Analysis

3
Measurements

• Measurement refers to the process of obtaining a
  physical value by comparing it to an accepted
  standard.
• Example determining the length of a room with a
  tape measure.

4
Uncertainty

• Every measurement is accurate to a degree of
  uncertainty.
• tolerance sign,
• It doesnt refer to a mistake, but rather a
  recognition that when a measurement is made, it
  isnt 100 perfect.

Room length 147.5 0.2 inches
5
Measurements Without Uncertainty

• Some values are not measured but defined.
• 1 inch 2.54 cm
• 1 atm 760 torr
• 1 min 60 seconds
• Conversion factors of defined values have no
  uncertainty.

• Some relationship values are exact.
• Two hydrogen atoms per oxygen in water.

6
Determining the Uncertainty in a Measurement

• Repetitive measurements
• standard deviation
• Estimation
• smallest gradation
• limiting digit
• Uncertainties add together

0.03 mL
7
Determining the Uncertainty in a Measurement
Direct determination of mass
0.000 g
17.345 g
tare
sample
Each reading has an uncertainty
What is the uncertainty in the mass of the sample?
0.000 g
0.001 g
0.002 g
0.002 g
8
Determining the Uncertainty in a Measurement
Determination of mass by difference
0.000 g
17.345 g
1.000 g
tare
sample tray
weighing tray
Each reading has an uncertainty
What is the uncertainty in the mass of the sample?
0.001 g
0.002 g
0.003 g
0.002 g
9
Determining the Uncertainty in a Measurement
The balance is tared, a reactant is weighed, a
reaction is performed, the balance is tared, the
product is weighed.
0.000 g
17.000 g
17.345 g
0.000 g
tare
product
reactant
tare
Each reading has an uncertainty
What is the uncertainty in the lost mass?
0.002 g
0.003 g
0.004 g
0.004 g
10
Propagation of ErrorError Analysis

• The uncertainties in several measurements lead to
  a cumulative uncertainty in a calculated value.
• Partial differential estimate of uncertainty
• Sum of percentage uncertainty values
• Worst case Maximum-minimum method

11
Maximum-MinimumEstimate of Uncertainty
values which are added or subtracted have
their uncertainty values added together
numbers in the numerator are maximized
numbers in the denominator are minimized
12
FunctionsEstimate of Uncertainty
If the temperature of water is 25.4 0.2
C, what is the vapor pressure and
its uncertainty?
13
If 235 3 mL of gas is trapped by water
displacement at 25.4 0.2 C, and the barometric
pressure is 732.4 0.2 torr, then how many of
moles of gas were trapped and what is the
uncertainty in this value?
n 0.008939 nmax 0.009066
n 0.0089 0.0001 mol
14
(No Transcript)
15
(No Transcript)