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| Chem 109 |
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Summer 2002 |
| Lecture Notes:: 4 June |
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| PREVIOUS |
Last time we were looking at the Scientific Method summarized in the steps below:
The remaining steps are noted below:
Significant figures: For measurements we want to be sure we convey the precision (repeatability) of our measurements using significant figures. [covered in lab & problem set] You should note a couple of aspects of significant figures:
Exponential or scientific notation: It is often convenient to express numbers in exponential or scientific notation to indicate significant figures, and to just avoid writing the huge numbers of zeros we often run into in the natural world. [covered in problem session]
SI Units: The metric system originated around the French Revolution as a rational system of measurements to rescue France from the chaos of pre-revolutionaary 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 the Earth's meridian (line from the S to the N pole) through Paris. 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 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 stored in the same vault.
Today the various units are defined by international agreement to give the SI (Systéme International) units:
Prefixes: Note Table 1.2 in your text (p 9). You should know (memorize) and be able to interconvert the prefixes in the table below:
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Other common prefixes which you should be familiar with but do not need to memorize include: tera- (T, 1012), giga- (G, 109), pico- (p, 10-12), and fempto- (f, 10-15).
Memorize: 1 mL = 1 cm3; 1 inch = 2.54 cm (defined); 1 liter is about 1 quart; density of water = 1 g/mL; 0° C = 32 °F, 100°C = 212 °F, -40 °C = -40 °F.
A convenient check on your work, or even a way to determine the best approach to a problem, is to use dimensional analysis. This simply means to include all of the units for each factor in an equation, and then to check to see that the units on both sides of the equation are equal.
For example: How many centimeters are there in one foot?
Known: 1 ft = 12 inches (defined, therefore exactly); 2.54 cm = 1 inch (defined).
Set up: (1 ft)(12 inches/ft)(2.54 cm/inch) note that ft cancels ft and inches cancels inches to give cm! Solve: (1 ft)(12 inches/ft)(2.54 cm/inch) = 30.48 cm. How about sig figs? In this problem there are no significant figures the way its set up, because there are no measurements! That is, all of the numbers are part of definitions, so they are exact, and that means the answer is exact as well.
Density is defined as the mass of a given volume of a substance: Density = mass/volume.
Let's try some density problems. First note that the units of density are g/cm3 or g.cm-3.
Known: Density = mass/volume, generally expressed as g/mL = g/cm3
Solve: (35.987 g) / (20.0 mL) = 1.79935 g/mL note that the units are those of density so we are confident we set it up correctly. How about sig figs? Use multiplication/division rules, so count: 3 for 20.0 and 5 for 35.987, therefore should have three sig figs:
1.79935 g/mL = 1.80 g/mL
Known: 1 carat = 200 mg (defined), density is g/mL
Solve: (2.34 carats)(200 mg/carat)(1 g/1,000 mg) / 0.034 mL = 13.764706 g/mL How about sig figs? Both conversion factors are defined, so exact. Two measurements: 2.34 and 0.034 = 3.4 x 10-2. Thus the answer will have only two sig figs since using counting rule - least number of sig figs.
13.764706 g/mL = 14 g/mL
Look in your text for conversions between °C and °F.
Memorize the relationship between Celsius and Kelvin scales:
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© R A Paselk
Last modified 4 June 2002
