Measurements and Calculations Notes

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Chapter 2

• Measurements and Calculations Notes

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I. SI (System of International) Units of
Measurements
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A. Metric System

• Mass is measured in kilograms (other mass units
  grams, milligrams)
• Volume in liters
• Length in meters
• Time in seconds
• Chemical quantity in moles
• Temperature in Celsius

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B. Prefixes

• Prefix Value Abbreviation
  Example
•  
• Pico l x l0-12 p pm,
  pg
• Nano l x l0-9 n nm
• Micro l x l0-6 ? ?g
• Milli l x l0-3 m mm, mg
• Centi l x l0-2 c cl, cg
• Deci l x l0-1 d dl, dg
• (stem liter, meter, gram)
• Deka l x l01 da dag,
  dal
• Hecto l x l02 h hl,hm
• Kilo l x l03 k kl,
  kg
• Mega l x l06 M Mg, Mm
• Giga 1 X 109 G Gg
• Tera 1 X 1012 T Tg

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C. Derived Units

• C. Derived Units combinations of quantities
  area (m2), Density (g/cm3), Volume (cm3 or mL)
  1cm3 1mL

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D. Temperature- Be able to convert between
degrees Celcius and Kelvin.

• Absolute zero is 0 K, a temperature where all
  molecular motion ceases to exist. Has not yet
  been attained, but scientists are within
  thousandths of a degree of 0 K. No degree sign
  is used for Kelvin temperatures.
• Celcius to Kelvin K C 273
• Convert 98 C to Kelvin 98 C 273 371 K

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II. Density relationship of mass to volume D
M/V Density is a derived unit (from both mass
and volume)

• For solids D grams/cm3
• Liquids D grams/mL
• Gases D grams/liter
• Know these units

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• D M
• V

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Density (cont.)

• Example Problems
• 1. An unknown metal having a mass of 287.8 g was
  added to a graduated cylinder that contained
  31.47 ml of water. After the addition of the
  metal, the water level rose to 58.85 ml.
  Calculate the density of the metal.

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Density (cont.)

• 2. The density of mercury is 13.6 g/mL. How
  many grams would l.00 liter of mercury weigh?
• 3. A solid with a density of 11.3 g/ml has a
  mass of 5.00g. What is its volume?

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IV. Using Scientific Measurements
ACCURATE CORRECT PRECISE CONSISTENT

• A. Precision and Accuracy
• 1. Precision the closeness of a set of
  measurements of the same quantities made in the
  same way (how well repeated measurements of a
  value agree with one another).
• 2. Accuracy is determined by the agreement
  between the measured quantity and the correct
  value.
• Ex Throwing Darts

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B. Counting Significant Figures

• When you report a measured value, it is assumed
  that all the figures are correct except for the
  last one, where there is an uncertainty of 1. If
  your value is expressed in proper exponential
  notation, all of the figures in the
  pre-exponential value are significant, with the
  last digit being the least significant figure
  (LSF).
• 7.143 grams contains 4 significant figures

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B. Counting Significant Figures

• If that value is expressed as 0.007143, it still
  has 4 significant figures. Zeros, in this case,
  are placeholders. If you are ever in doubt about
  the number of significant figures in a value,
  write it in exponential notation.
• Example of nail on page 46 the nail is 6.36cm
  long. The 6.3 are certain values and the final 6
  is uncertain! There are 3 significant figures in
  6.36cm (2 certain and 1 uncertain). The reader
  can see that the 6.3 are certain values because
  they appear on the ruler, but the reader has to
  estimate the final 6.

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Significant Figures

• Indicate precision of a measurement.
• Recording Significant Figures (sig figs)
• Sig figs in a measurement include the known
  digits plus a final estimated digit

2.35 cm
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The rules for counting significant figures are

• 1. Leading zeros do not count.
• Ex 0.0005 cm
• 2. Captive zeros always count.
• Ex 505 cm
• 3. Trailing zeros count only if there is a
  decimal.
• Ex 5,000 vs 5,000.

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Give the number of significant figures in the
following values

• a. 38.4703 mL b. 0.00052 g
• c. 0.05700 s d. 6.19 x 101 years
• Helpful Hint Convert to exponential form if you
  are not certain as to the proper number of
  significant figures.
• A very important idea is that you DO NOT ROUND
  OFF YOUR ANSWER UNTIL THE VERY END OF THE
  PROBLEM.

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Significant Figures Flowchart
Measurement
What is the number?
lt1
gt1
Before the
After the
Yes
No
No- not significant Ex 0.05
Yes, the zero is significant Ex 0.50
All the numbers are significant Ex 5.0
Trailing zeros are not significant Ex 50
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C. Significant Figures in Calculations

• In addition and subtraction, your answer should
  have the same number of decimal places as the
  measurement with the least number of decimal
  places.
• EX find the answer for 12.734
• -3.0

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• Solution 12.734 has 3 figures past the decimal
  point. 3.0 has only 1 figure past the decimal
  point. Therefore, your final result, where only
  addition or subtraction is involved, should round
  off to one figure past the decimal point.
• 12.734
• - 3.0
• 9.734 --------? 9.7

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Add/Subtract additional example
224 g 130 g 354 g
224 g 130 g 354 g
3.75 mL 4.1 mL 7.85 mL
3.75 mL 4.1 mL 7.85 mL
? 350 g
? 7.9 mL
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Multiplication Division with Significant Figures

• 2. In multiplication and division, your answer
  should have the same number of significant
  figures as the least precise measurement.
• 61 x 0.00745 0.45445 0.45 2SF
• a. 32 x 0.00003987
• b.   5 x 1.882
• c.   47. 8823 X 9.322

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Multiplication Division with Significant Figures

• 3. There is no uncertainty in a conversion
  factor therefore they do not affect the degree
  of certainty of your answer. The answer should
  have the same number of SF as the initial value.
• a. Convert 25. meters to millimeters.
• b. Convert 0.12 L to mL.

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E. Scientific Notation

• Converting into Sci. Notation
• Move decimal until theres 1 digit to its left.
  Places moved exponent.
• Large (gt1) ? positive exponentSmall (lt1) ?
  negative exponent
• Only include sig figs.

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E. Scientific Notation

• -used to express very large or very small
  numbers 1 X 10-2
• Convert to scientific notation
• a. 1760 b. 0.00135
• c. 10.2 d. 0.00000673
• e. 301.0 f. 0.000000532

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Practice Problems

• Expand each number (or convert to regular
  notation)
• a. 4.78 x l02 b. 5.50 x l04
• c. 9.3 x l03 d. 8.31 x l0-1
• e. 7.01 x l0-2 f. 8.5 x l0-6

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E. Scientific Notation

• Calculating with Sci. Notation

(5.44 107 ) (8.10 104)
Type on your calculator
5.44
7
8.10
4

671.6049383
672 g/mol
6.72 102 g/mol