Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 107	Fundamentals of Chemistry	Fall 2008
Lecture Notes: 4 September	© R. Paselk 2005
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Measurements, cont.

Significant Figures, cont.

For measurements we want to be sure we convey the precision (repeatability) of our measurements using significant figures. [examples] See lab book exercises.

• Look at example of making measurements with a ruler, and adding or subtracting them.
  • Which digits should we keep? Which did we measure?
  • For addition and subtraction, it turns out we look at the decimal place to determine if a figure is significant (if we should keep it).
    • Note that with addition and subtraction we can end up with more or fewer significant digits in an answer.

Significant Figures and Calculations: Two basic sets of rules:

1. Addition/Subtraction rule: Significant figures are determined by looking at the decimal place of the numbers being added or subtracted. The number with the "least decimal places" determines the decimal place of the answer, e.g. if we add 1,216,956 to 214.879, the first number has the fewest decimal places, so the answer is rounded off to the 1's place: 1217170.879 goes to 1217171.
• Note that this is based on the idea that the error in the "least decimal place" measured figure is larger than the subsequent decimal figures, so they are dropped after rounding.
• examples.
2. Multiplication/Division rule: In this case we count the digits. The number with the fewest significant digits determines the number of significant digits in the answer.
   • Note that in this case we are looking at how the error propagates as a fraction of the total (% error), for example
     • for the problem 2.0 x 201 = 402 should be written as 4.0 x 10².
     • This can be understood by doing the problem with upper and lower ranges of the measured number: 1.95<2.0<2.05
       • 1.95 x 201 = 391.95
       • 2.05 x 201 = 412.05
     • Obviously we can't claim agreement with more than 2 significant figures. In fact, 4.0 is stretching it!
   • examples.

SI Units ("metric" system)

The metric system originated in the French Revolution as a rational system of measurements to rescue France from the chaos of pre-revolutionary measurements and thus prevent tax collectors from cheating.

Wanted to base system on "natural" universal standards. Thus for length they chose the size of the Earth: specifically the meter was defined as one ten-millionth (10^-7) of one quarter of the Earth's meridian* passing through Paris (the line along the "surface" of the Earth from the north pole though Paris to the equator). For mass the Kilogram was defined as the mass of a cube of water 0.1 meter on a side. Of course these are not convenient, so other standards were quickly created: the meter became the distance between two lines on a platinum-iridium bar stored in a vault in Paris, while the kilogram became a cylindrical mass of platinum-iridium alloy stored in the same vault.

Today the various units are defined by international agreement to give the SI (Systéme International) units:

• Length: the meter (m) is defined as the distance light travels in a vacuum in 1/299,792,458 sec. (Note that this is truly universal: in principle it can be determined by anyone, anytime, anywhere in the Universe. It also fixes the speed of light, c, as 299,792,458 m/s = 2.99792458 x 10⁸ m sec^-1)
• Mass: the kilogram (kg) however is still based on the International Prototype Kilogram in Paris and the derived standard kilogram standards held by governments around the world.
• Time: the second (s) is defined today as the duration of 9,192,631,770 periods of the radiation of two hyperfine levels of the ground state of the cesium 133 atom.
• Amount of substance: the mole (mol) is defined as the number of atoms in 0.012 kg (defined, so sig figs not restricted) of carbon 12 atoms. One mole = 6.022 x 10²³ particles.
• Temperature: the kelvin (K) is defined as 1/273.15 of the thermodynamic temperature of the triple point of water.

Prefixes:

Note Table 3.2 in your text (p 38). You should know and be able to interconvert the prefixes in the table below:

Prefix Symbol Magnitude kilo- k 103 base   100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- (or mc) 10-6 nano- n 10-9

Other common prefixes which you should be familiar with but do not need to memorize include: tera- (T, 10¹²), giga- (G, 10⁹), mega- (M, 10⁶), pico- (p, 10^-12), and fempto- (f, 10^-15).

Memorize: 1 mL = 1 cm³; 1 inch = 2.54 cm; 1 liter is about 1 quart; density of water = 1 g/mL; 0° C = 32 °F, 100°C = 212 °F, -40 °C = -40 °F

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Last modified 4 September 2008