Measurements

1
Measurements
2
Measurement and Data Processing 1

• SIGNIFICANT DIGITS
• PRECISION ACCURACY
• http//web.me.com/dbyrum/Ris/Resources/page29/file
  s/ErrorAnalysis.pdf
• http//www.wellesley.edu/Chemistry/Chem105manual/A
  ppendices/uncertainty_analysis.html
• Imp
• http//chemwiki.ucdavis.edu/Analytical_Chemistry/Q
  uantifying_Nature/Uncertainties_in_Measurements

3
Types of Observations and Measurements

• We make QUALITATIVE observations of reactions
  changes in color and physical state.
• We also make QUANTITATIVE MEASUREMENTS, which
  involve numbers.

4
Significant Digits

• http//chemsite.lsrhs.net/measurement/sig_fig.html
  

5
Rules

• Rules for deciding the number of significant
  figures in a measured quantity
• (1) All nonzero digits are significant1.234 g
  has 4 significant figures
• (2) Zeroes between nonzero digits are
  significant
• 1002 kg has 4 significant figures
• (3) Leading zeros to the left of the first
  nonzero digits are not significant such zeroes
  merely indicate the position of the decimal
  point (placeholders are not significant)
• 0.012 g has 2 significant figures.

6

• (4) Trailing zeroes that are also to the right of
  a decimal point in a number are significant
• 0.0230 mL has 3 significant figures,0.20 g has 2
  significant figures
• (5) When a number ends in zeroes that are not to
  the right of a decimal point, the zeroes are not
  necessarily significant
• 190 miles may be 2 or 3 significant figures,
• 50,600 calories may be 3, 4, or 5 significant
  figures.

7

• Trayling zeros
• 190000 2 s.d ( could be up to 6)
• In the last example, where the number 19000 has
  an ambiguous number of significant digits,
  scientific notation will clear up this problem.
• 1.90 x 104 19000 and has 3 significant digits.
• 1.9 x 104 19000 and has 2 significant digits.
• 1.9000 x 104 19000 and has 5 significant digits.

8
Problems

• 1)  7000
• 2)  450.0
• 3)  350
• 4)  0.006200
• 7)  565.05
• 8)  5500
• 9)  74.00
• 10)  7040.0

9
IB Problem
10
Rules for mathematical operations

• In carrying out calculations, the general rule is
  that the accuracy of a calculated result is
  limited by the least accurate measurement
  involved in the calculation.
• In addition and subtraction, the result is
  rounded off so that it has the same number of
  decimal places as the measurement having the
  fewest decimal places.
• For example,
• 100 (3 s.f) 23.643 (5 s.f)  123.643, which
  should be rounded to 124 (3 s.f).

11

• II. In multiplication and division, the result
  should be rounded off so as to have the same
  number of significant figures as in the component
  with the least number of significant figures.
• When there are series of calculations, do not
  round off until the end.
• For example,
• 3.0 (2 s.f ) 12.60 (4 s.f)  37.8000 which
  should be rounded off to 38 (2 s.f).

12
(No Transcript)
13
Problems

• http//www.fordhamprep.org/gcurran/sho/sho/lessons
  /lesson23.htm

14
Precision and Accuracy in Measurements

• Accuracy
• How close are the measurements to the true
  value.

• Precision
• How reproducible are measurements?

15
PrecisionAccuracy

• Accuracy
• Accuracy, measures the agreement between a
  measurement and the accepted standard value.
• Refers to how close a measurement is to the real
  value.
• If a balance consistently gives a value of 3.64
  g on repeated measurements, its precision is
  good. However, if the actual mass is 3.75 g, its
  accuracy is poor!

• Precision
• Precision measures the agreement between results
  of repeated measurements.
• Refers to reproducibility or how close the
  measurements are to each other.
• A balance that can read mass to 0.0001 grams
  should be more precise than one that reads mass
  to 0.1 grams.

16
(No Transcript)
17
Precision of a Measurement

• The last digit is an estimate.
• The precision is limited by the instrument.

Measurement 26.13 cm
18
IB Problem
19

• The goal in the Chemistry laboratory is to obtain
  reliable results while realizing that there are
• errors inherent in any laboratory technique.
• http//www.savitapall.com/scientific_measurement/n
  otes/measurement20and20data20processing.pdf

20

• http//teachers.rickards.leon.k12.fl.us/Teachers/m
  cdonald/Senior20IBAP20Webpages/Notes/11.20Measu
  rement20and20Data20Processing/Measurement20and
  20IA.20DP,20CE.htm

21
http//www.dartmouth.edu/chemlab/info/resources/u
ncertain.html

• http//www.wellesley.edu/Chemistry/Chem105manual/A
  ppendices/uncertainty_analysis.html